xref: /petsc/src/ts/tutorials/hamiltonian/ex2.c (revision 42e5ec60e3f6d3f21d92afbe12a337913bc9ad72)
1 static char help[] = "Landau Damping/Two Stream instability test using Vlasov-Poisson equations\n";
2 
3 /*
4   To run the code with particles sinusoidally perturbed in x space use the test "pp_poisson_bsi_1d_4" or "pp_poisson_bsi_2d_4"
5   According to Lukas, good damping results come at ~16k particles per cell
6 
7   To visualize the efield use
8 
9     -monitor_efield
10 
11   To monitor moments of the distribution use
12 
13     -ptof_pc_type lu -monitor_moments
14 
15   To visualize the swarm distribution use
16 
17     -ts_monitor_hg_swarm
18 
19   To visualize the particles, we can use
20 
21     -ts_monitor_sp_swarm -ts_monitor_sp_swarm_retain 0 -ts_monitor_sp_swarm_phase 1 -draw_size 500,500
22 
23 For a Landau Damping verification run, we use
24 
25     -dm_plex_dim 2 -fake_1D -dm_plex_simplex 0 -dm_plex_box_faces 10,1 \
26       -dm_plex_box_lower 0.,-0.5 -dm_plex_box_upper 12.5664,0.5 -dm_plex_box_bd periodic,none \
27     -vdm_plex_dim 1 -vdm_plex_simplex 0 -vdm_plex_box_faces 2000 -vdm_plex_box_lower -10 -vdm_plex_box_upper 10 \
28     -dm_swarm_num_species 1 -charges -1.,1. \
29     -cosine_coefficients 0.01,0.5 -perturbed_weights -total_weight 1. \
30     -ts_type basicsymplectic -ts_basicsymplectic_type 1 -ts_dt 0.03 -ts_max_time 500 -ts_max_steps 500 \
31     -em_type primal -petscspace_degree 1 -em_snes_atol 1.e-12 -em_snes_error_if_not_converged -em_ksp_error_if_not_converged -em_pc_type svd \
32     -output_step 100 -check_vel_res -monitor_efield -ts_monitor -log_view
33 
34 */
35 #include <petscts.h>
36 #include <petscdmplex.h>
37 #include <petscdmswarm.h>
38 #include <petscfe.h>
39 #include <petscds.h>
40 #include <petscbag.h>
41 #include <petscdraw.h>
42 #include <petsc/private/dmpleximpl.h>  /* For norm and dot */
43 #include <petsc/private/petscfeimpl.h> /* For interpolation */
44 #include <petsc/private/dmswarmimpl.h> /* For swarm debugging */
45 #include "petscdm.h"
46 #include "petscdmlabel.h"
47 
48 PETSC_EXTERN PetscErrorCode stream(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
49 PETSC_EXTERN PetscErrorCode line(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
50 
51 const char *EMTypes[] = {"primal", "mixed", "coulomb", "none", "EMType", "EM_", NULL};
52 typedef enum {
53   EM_PRIMAL,
54   EM_MIXED,
55   EM_COULOMB,
56   EM_NONE
57 } EMType;
58 
59 typedef enum {
60   V0,
61   X0,
62   T0,
63   M0,
64   Q0,
65   PHI0,
66   POISSON,
67   VLASOV,
68   SIGMA,
69   NUM_CONSTANTS
70 } ConstantType;
71 typedef struct {
72   PetscScalar v0; /* Velocity scale, often the thermal velocity */
73   PetscScalar t0; /* Time scale */
74   PetscScalar x0; /* Space scale */
75   PetscScalar m0; /* Mass scale */
76   PetscScalar q0; /* Charge scale */
77   PetscScalar kb;
78   PetscScalar epsi0;
79   PetscScalar phi0;          /* Potential scale */
80   PetscScalar poissonNumber; /* Non-Dimensional Poisson Number */
81   PetscScalar vlasovNumber;  /* Non-Dimensional Vlasov Number */
82   PetscReal   sigma;         /* Nondimensional charge per length in x */
83 } Parameter;
84 
85 typedef struct {
86   PetscBag     bag;            /* Problem parameters */
87   PetscBool    error;          /* Flag for printing the error */
88   PetscBool    efield_monitor; /* Flag to show electric field monitor */
89   PetscBool    moment_monitor; /* Flag to show distribution moment monitor */
90   PetscBool    initial_monitor;
91   PetscBool    fake_1D;           /* Run simulation in 2D but zeroing second dimension */
92   PetscBool    perturbed_weights; /* Uniformly sample x,v space with gaussian weights */
93   PetscBool    poisson_monitor;
94   PetscInt     ostep; /* print the energy at each ostep time steps */
95   PetscInt     numParticles;
96   PetscReal    timeScale;              /* Nondimensionalizing time scale */
97   PetscReal    charges[2];             /* The charges of each species */
98   PetscReal    masses[2];              /* The masses of each species */
99   PetscReal    thermal_energy[2];      /* Thermal Energy (used to get other constants)*/
100   PetscReal    cosine_coefficients[2]; /*(alpha, k)*/
101   PetscReal    totalWeight;
102   PetscReal    stepSize;
103   PetscInt     steps;
104   PetscReal    initVel;
105   EMType       em;     // Type of electrostatic model
106   SNES         snes;   // EM solver
107   Mat          M;      // The finite element mass matrix
108   PetscFEGeom *fegeom; // Geometric information for the DM cells
109   PetscDraw    drawic_x;
110   PetscDraw    drawic_v;
111   PetscDraw    drawic_w;
112   PetscDrawHG  drawhgic_x;
113   PetscDrawHG  drawhgic_v;
114   PetscDrawHG  drawhgic_w;
115   PetscReal    drawlgEmin;        // The minimum lg(E) to plot
116   PetscDrawLG  drawlgE;           // Logarithm of maximum electric field
117   PetscDrawSP  drawspE;           // Electric field at particle positions
118   PetscDrawSP  drawspX;           // Particle positions
119   PetscViewer  viewerRho;         // Charge density viewer
120   PetscViewer  viewerPhi;         // Potential viewer
121   PetscBool    monitor_positions; /* Flag to show particle positins at each time step */
122   DM           swarm;
123   PetscRandom  random;
124   PetscBool    twostream;
125   PetscBool    checkweights;
126   PetscInt     checkVRes; /* Flag to check/output velocity residuals for nightly tests */
127 
128   PetscLogEvent RhsXEvent, RhsVEvent, ESolveEvent, ETabEvent;
129 } AppCtx;
130 
131 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
132 {
133   PetscFunctionBeginUser;
134   PetscInt d                      = 2;
135   PetscInt maxSpecies             = 2;
136   options->error                  = PETSC_FALSE;
137   options->efield_monitor         = PETSC_FALSE;
138   options->moment_monitor         = PETSC_FALSE;
139   options->initial_monitor        = PETSC_FALSE;
140   options->fake_1D                = PETSC_FALSE;
141   options->perturbed_weights      = PETSC_FALSE;
142   options->poisson_monitor        = PETSC_FALSE;
143   options->ostep                  = 100;
144   options->timeScale              = 2.0e-14;
145   options->charges[0]             = -1.0;
146   options->charges[1]             = 1.0;
147   options->masses[0]              = 1.0;
148   options->masses[1]              = 1000.0;
149   options->thermal_energy[0]      = 1.0;
150   options->thermal_energy[1]      = 1.0;
151   options->cosine_coefficients[0] = 0.01;
152   options->cosine_coefficients[1] = 0.5;
153   options->initVel                = 1;
154   options->totalWeight            = 1.0;
155   options->drawic_x               = NULL;
156   options->drawic_v               = NULL;
157   options->drawic_w               = NULL;
158   options->drawhgic_x             = NULL;
159   options->drawhgic_v             = NULL;
160   options->drawhgic_w             = NULL;
161   options->drawlgEmin             = -6;
162   options->drawlgE                = NULL;
163   options->drawspE                = NULL;
164   options->drawspX                = NULL;
165   options->viewerRho              = NULL;
166   options->viewerPhi              = NULL;
167   options->em                     = EM_COULOMB;
168   options->numParticles           = 32768;
169   options->monitor_positions      = PETSC_FALSE;
170   options->twostream              = PETSC_FALSE;
171   options->checkweights           = PETSC_FALSE;
172   options->checkVRes              = 0;
173 
174   PetscOptionsBegin(comm, "", "Landau Damping and Two Stream options", "DMSWARM");
175   PetscCall(PetscOptionsBool("-error", "Flag to print the error", "ex2.c", options->error, &options->error, NULL));
176   PetscCall(PetscOptionsBool("-monitor_efield", "Flag to plot log(max E) over time", "ex2.c", options->efield_monitor, &options->efield_monitor, NULL));
177   PetscCall(PetscOptionsReal("-monitor_efield_min", "Minimum E field to plot", "ex2.c", options->drawlgEmin, &options->drawlgEmin, NULL));
178   PetscCall(PetscOptionsBool("-monitor_moments", "Flag to show moments table", "ex2.c", options->moment_monitor, &options->moment_monitor, NULL));
179   PetscCall(PetscOptionsBool("-monitor_ics", "Flag to show initial condition histograms", "ex2.c", options->initial_monitor, &options->initial_monitor, NULL));
180   PetscCall(PetscOptionsBool("-monitor_positions", "The flag to show particle positions", "ex2.c", options->monitor_positions, &options->monitor_positions, NULL));
181   PetscCall(PetscOptionsBool("-monitor_poisson", "The flag to show charges, Efield and potential solve", "ex2.c", options->poisson_monitor, &options->poisson_monitor, NULL));
182   PetscCall(PetscOptionsBool("-fake_1D", "Flag to run a 1D simulation (but really in 2D)", "ex2.c", options->fake_1D, &options->fake_1D, NULL));
183   PetscCall(PetscOptionsBool("-twostream", "Run two stream instability", "ex2.c", options->twostream, &options->twostream, NULL));
184   PetscCall(PetscOptionsBool("-perturbed_weights", "Flag to run uniform sampling with perturbed weights", "ex2.c", options->perturbed_weights, &options->perturbed_weights, NULL));
185   PetscCall(PetscOptionsBool("-check_weights", "Ensure all particle weights are positive", "ex2.c", options->checkweights, &options->checkweights, NULL));
186   PetscCall(PetscOptionsInt("-check_vel_res", "Check particle velocity residuals for nightly tests", "ex2.c", options->checkVRes, &options->checkVRes, NULL));
187   PetscCall(PetscOptionsInt("-output_step", "Number of time steps between output", "ex2.c", options->ostep, &options->ostep, NULL));
188   PetscCall(PetscOptionsReal("-timeScale", "Nondimensionalizing time scale", "ex2.c", options->timeScale, &options->timeScale, NULL));
189   PetscCall(PetscOptionsReal("-initial_velocity", "Initial velocity of perturbed particle", "ex2.c", options->initVel, &options->initVel, NULL));
190   PetscCall(PetscOptionsReal("-total_weight", "Total weight of all particles", "ex2.c", options->totalWeight, &options->totalWeight, NULL));
191   PetscCall(PetscOptionsRealArray("-cosine_coefficients", "Amplitude and frequency of cosine equation used in initialization", "ex2.c", options->cosine_coefficients, &d, NULL));
192   PetscCall(PetscOptionsRealArray("-charges", "Species charges", "ex2.c", options->charges, &maxSpecies, NULL));
193   PetscCall(PetscOptionsEnum("-em_type", "Type of electrostatic solver", "ex2.c", EMTypes, (PetscEnum)options->em, (PetscEnum *)&options->em, NULL));
194   PetscOptionsEnd();
195 
196   PetscCall(PetscLogEventRegister("RhsX", TS_CLASSID, &options->RhsXEvent));
197   PetscCall(PetscLogEventRegister("RhsV", TS_CLASSID, &options->RhsVEvent));
198   PetscCall(PetscLogEventRegister("ESolve", TS_CLASSID, &options->ESolveEvent));
199   PetscCall(PetscLogEventRegister("ETab", TS_CLASSID, &options->ETabEvent));
200   PetscFunctionReturn(PETSC_SUCCESS);
201 }
202 
203 static PetscErrorCode SetupContext(DM dm, DM sw, AppCtx *user)
204 {
205   PetscFunctionBeginUser;
206   if (user->efield_monitor) {
207     PetscDraw     draw;
208     PetscDrawAxis axis;
209 
210     PetscCall(PetscDrawCreate(PETSC_COMM_WORLD, NULL, "Max Electric Field", 0, 300, 400, 300, &draw));
211     PetscCall(PetscDrawSetSave(draw, "ex9_Efield"));
212     PetscCall(PetscDrawSetFromOptions(draw));
213     PetscCall(PetscDrawLGCreate(draw, 1, &user->drawlgE));
214     PetscCall(PetscDrawDestroy(&draw));
215     PetscCall(PetscDrawLGGetAxis(user->drawlgE, &axis));
216     PetscCall(PetscDrawAxisSetLabels(axis, "Electron Electric Field", "time", "E_max"));
217     PetscCall(PetscDrawLGSetLimits(user->drawlgE, 0., user->steps * user->stepSize, user->drawlgEmin, 0.));
218   }
219   if (user->initial_monitor) {
220     PetscDrawAxis axis1, axis2, axis3;
221     PetscReal     dmboxlower[2], dmboxupper[2];
222     PetscInt      dim, cStart, cEnd;
223     PetscCall(DMGetDimension(sw, &dim));
224     PetscCall(DMGetBoundingBox(dm, dmboxlower, dmboxupper));
225     PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
226 
227     PetscCall(PetscDrawCreate(PETSC_COMM_WORLD, NULL, "monitor_initial_conditions_x", 0, 300, 400, 300, &user->drawic_x));
228     PetscCall(PetscDrawSetSave(user->drawic_x, "ex9_ic_x"));
229     PetscCall(PetscDrawSetFromOptions(user->drawic_x));
230     PetscCall(PetscDrawHGCreate(user->drawic_x, (int)dim, &user->drawhgic_x));
231     PetscCall(PetscDrawHGGetAxis(user->drawhgic_x, &axis1));
232     PetscCall(PetscDrawHGSetNumberBins(user->drawhgic_x, (int)(cEnd - cStart)));
233     PetscCall(PetscDrawAxisSetLabels(axis1, "Initial X Distribution", "X", "counts"));
234     PetscCall(PetscDrawAxisSetLimits(axis1, dmboxlower[0], dmboxupper[0], 0, 1500));
235 
236     PetscCall(PetscDrawCreate(PETSC_COMM_WORLD, NULL, "monitor_initial_conditions_v", 400, 300, 400, 300, &user->drawic_v));
237     PetscCall(PetscDrawSetSave(user->drawic_v, "ex9_ic_v"));
238     PetscCall(PetscDrawSetFromOptions(user->drawic_v));
239     PetscCall(PetscDrawHGCreate(user->drawic_v, (int)dim, &user->drawhgic_v));
240     PetscCall(PetscDrawHGGetAxis(user->drawhgic_v, &axis2));
241     PetscCall(PetscDrawHGSetNumberBins(user->drawhgic_v, 1000));
242     PetscCall(PetscDrawAxisSetLabels(axis2, "Initial V_x Distribution", "V", "counts"));
243     PetscCall(PetscDrawAxisSetLimits(axis2, -1, 1, 0, 1500));
244 
245     PetscCall(PetscDrawCreate(PETSC_COMM_WORLD, NULL, "monitor_initial_conditions_w", 800, 300, 400, 300, &user->drawic_w));
246     PetscCall(PetscDrawSetSave(user->drawic_w, "ex9_ic_w"));
247     PetscCall(PetscDrawSetFromOptions(user->drawic_w));
248     PetscCall(PetscDrawHGCreate(user->drawic_w, (int)dim, &user->drawhgic_w));
249     PetscCall(PetscDrawHGGetAxis(user->drawhgic_w, &axis3));
250     PetscCall(PetscDrawHGSetNumberBins(user->drawhgic_w, 10));
251     PetscCall(PetscDrawAxisSetLabels(axis3, "Initial W Distribution", "weight", "counts"));
252     PetscCall(PetscDrawAxisSetLimits(axis3, 0, 0.01, 0, 5000));
253   }
254   if (user->monitor_positions) {
255     PetscDraw     draw;
256     PetscDrawAxis axis;
257 
258     PetscCall(PetscDrawCreate(PETSC_COMM_WORLD, NULL, "Particle Position", 0, 0, 400, 300, &draw));
259     PetscCall(PetscDrawSetSave(draw, "ex9_pos"));
260     PetscCall(PetscDrawSetFromOptions(draw));
261     PetscCall(PetscDrawSPCreate(draw, 10, &user->drawspX));
262     PetscCall(PetscDrawDestroy(&draw));
263     PetscCall(PetscDrawSPSetDimension(user->drawspX, 1));
264     PetscCall(PetscDrawSPGetAxis(user->drawspX, &axis));
265     PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "x", "v"));
266     PetscCall(PetscDrawSPReset(user->drawspX));
267   }
268   if (user->poisson_monitor) {
269     Vec           rho, phi;
270     PetscDraw     draw;
271     PetscDrawAxis axis;
272 
273     PetscCall(PetscDrawCreate(PETSC_COMM_WORLD, NULL, "Electric_Field", 0, 0, 400, 300, &draw));
274     PetscCall(PetscDrawSetFromOptions(draw));
275     PetscCall(PetscDrawSetSave(draw, "ex9_E_spatial"));
276     PetscCall(PetscDrawSPCreate(draw, 10, &user->drawspE));
277     PetscCall(PetscDrawDestroy(&draw));
278     PetscCall(PetscDrawSPSetDimension(user->drawspE, 1));
279     PetscCall(PetscDrawSPGetAxis(user->drawspE, &axis));
280     PetscCall(PetscDrawAxisSetLabels(axis, "Particles", "x", "E"));
281     PetscCall(PetscDrawSPReset(user->drawspE));
282 
283     PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, NULL, "Charge Density", 0, 0, 400, 300, &user->viewerRho));
284     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)user->viewerRho, "rho_"));
285     PetscCall(PetscViewerDrawGetDraw(user->viewerRho, 0, &draw));
286     PetscCall(PetscDrawSetSave(draw, "ex9_rho_spatial"));
287     PetscCall(PetscViewerSetFromOptions(user->viewerRho));
288     PetscCall(DMGetNamedGlobalVector(dm, "rho", &rho));
289     PetscCall(PetscObjectSetName((PetscObject)rho, "charge_density"));
290     PetscCall(DMRestoreNamedGlobalVector(dm, "rho", &rho));
291 
292     PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD, NULL, "Potential", 400, 0, 400, 300, &user->viewerPhi));
293     PetscCall(PetscObjectSetOptionsPrefix((PetscObject)user->viewerPhi, "phi_"));
294     PetscCall(PetscViewerDrawGetDraw(user->viewerPhi, 0, &draw));
295     PetscCall(PetscDrawSetSave(draw, "ex9_phi_spatial"));
296     PetscCall(PetscViewerSetFromOptions(user->viewerPhi));
297     PetscCall(DMGetNamedGlobalVector(dm, "phi", &phi));
298     PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
299     PetscCall(DMRestoreNamedGlobalVector(dm, "phi", &phi));
300   }
301   PetscFunctionReturn(PETSC_SUCCESS);
302 }
303 
304 static PetscErrorCode DestroyContext(AppCtx *user)
305 {
306   PetscFunctionBeginUser;
307   PetscCall(PetscDrawHGDestroy(&user->drawhgic_x));
308   PetscCall(PetscDrawDestroy(&user->drawic_x));
309   PetscCall(PetscDrawHGDestroy(&user->drawhgic_v));
310   PetscCall(PetscDrawDestroy(&user->drawic_v));
311   PetscCall(PetscDrawHGDestroy(&user->drawhgic_w));
312   PetscCall(PetscDrawDestroy(&user->drawic_w));
313 
314   PetscCall(PetscDrawLGDestroy(&user->drawlgE));
315   PetscCall(PetscDrawSPDestroy(&user->drawspE));
316   PetscCall(PetscDrawSPDestroy(&user->drawspX));
317   PetscCall(PetscViewerDestroy(&user->viewerRho));
318   PetscCall(PetscViewerDestroy(&user->viewerPhi));
319 
320   PetscCall(PetscBagDestroy(&user->bag));
321   PetscFunctionReturn(PETSC_SUCCESS);
322 }
323 
324 static PetscErrorCode CheckNonNegativeWeights(DM sw, AppCtx *user)
325 {
326   const PetscScalar *w;
327   PetscInt           Np;
328 
329   PetscFunctionBeginUser;
330   if (!user->checkweights) PetscFunctionReturn(PETSC_SUCCESS);
331   PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&w));
332   PetscCall(DMSwarmGetLocalSize(sw, &Np));
333   for (PetscInt p = 0; p < Np; ++p) PetscCheck(w[p] >= 0.0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Particle %" PetscInt_FMT " has negative weight %g", p, w[p]);
334   PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&w));
335   PetscFunctionReturn(PETSC_SUCCESS);
336 }
337 
338 static PetscErrorCode computeVelocityFEMMoments(DM sw, PetscReal moments[3], AppCtx *user)
339 {
340   DM          vdm;
341   Vec         u[1];
342   const char *fields[1] = {"w_q"};
343 
344   PetscFunctionBegin;
345   PetscCall(PetscObjectQuery((PetscObject)sw, "__vdm__", (PetscObject *)&vdm));
346   PetscCall(DMGetGlobalVector(vdm, &u[0]));
347   PetscCall(DMSwarmPushCellDM(sw, vdm, 1, fields, "velocity"));
348   PetscCall(DMSwarmProjectFields(sw, vdm, 1, fields, u, SCATTER_FORWARD));
349   PetscCall(DMPlexComputeMoments(vdm, u[0], moments));
350   PetscCall(DMSwarmPopCellDM(sw));
351   PetscCall(DMRestoreGlobalVector(vdm, &u[0]));
352   PetscFunctionReturn(PETSC_SUCCESS);
353 }
354 
355 static PetscErrorCode MonitorEField(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
356 {
357   AppCtx    *user = (AppCtx *)ctx;
358   DM         sw;
359   PetscReal *E, *x, *weight;
360   PetscReal  Enorm = 0., lgEnorm, lgEmax, sum = 0., Emax = 0., chargesum = 0.;
361   PetscReal  pmoments[4]; /* \int f, \int v f, \int v^2 f */
362   PetscInt  *species, dim, Np;
363 
364   PetscFunctionBeginUser;
365   if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
366   PetscCall(TSGetDM(ts, &sw));
367   PetscCall(DMGetDimension(sw, &dim));
368   PetscCall(DMSwarmGetLocalSize(sw, &Np));
369   PetscCall(DMSwarmSortGetAccess(sw));
370   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
371   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
372   PetscCall(DMSwarmGetField(sw, "species", NULL, NULL, (void **)&species));
373   PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&weight));
374 
375   for (PetscInt p = 0; p < Np; ++p) {
376     for (PetscInt d = 0; d < 1; ++d) {
377       PetscReal temp = PetscAbsReal(E[p * dim + d]);
378       if (temp > Emax) Emax = temp;
379     }
380     Enorm += PetscSqrtReal(E[p * dim] * E[p * dim]);
381     sum += E[p * dim];
382     chargesum += user->charges[0] * weight[p];
383   }
384   lgEnorm = Enorm != 0 ? PetscLog10Real(Enorm) : -16.;
385   lgEmax  = Emax != 0 ? PetscLog10Real(Emax) : user->drawlgEmin;
386 
387   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
388   PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&weight));
389   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
390   PetscCall(DMSwarmRestoreField(sw, "species", NULL, NULL, (void **)&species));
391   PetscCall(PetscDrawLGAddPoint(user->drawlgE, &t, &lgEmax));
392   PetscCall(PetscDrawLGDraw(user->drawlgE));
393   PetscDraw draw;
394   PetscCall(PetscDrawLGGetDraw(user->drawlgE, &draw));
395   PetscCall(PetscDrawSave(draw));
396 
397   PetscCall(DMSwarmComputeMoments(sw, "velocity", "w_q", pmoments));
398   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%f\t%+e\t%e\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n", (double)t, (double)sum, (double)Enorm, (double)lgEnorm, (double)Emax, (double)lgEmax, (double)chargesum, (double)pmoments[0], (double)pmoments[1], (double)pmoments[1 + dim]));
399   PetscCall(DMViewFromOptions(sw, NULL, "-sw_efield_view"));
400   PetscFunctionReturn(PETSC_SUCCESS);
401 }
402 
403 static PetscErrorCode MonitorMoments(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
404 {
405   AppCtx   *user = (AppCtx *)ctx;
406   DM        sw;
407   PetscReal pmoments[4], fmoments[4]; /* \int f, \int v f, \int v^2 f */
408 
409   PetscFunctionBeginUser;
410   if (step < 0) PetscFunctionReturn(PETSC_SUCCESS);
411   PetscCall(TSGetDM(ts, &sw));
412 
413   PetscCall(DMSwarmComputeMoments(sw, "velocity", "w_q", pmoments));
414   PetscCall(computeVelocityFEMMoments(sw, fmoments, user));
415 
416   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%f\t%f\t%f\t%f\t%f\t%f\t%f\n", (double)t, (double)pmoments[0], (double)pmoments[1], (double)pmoments[3], (double)fmoments[0], (double)fmoments[1], (double)fmoments[2]));
417   PetscFunctionReturn(PETSC_SUCCESS);
418 }
419 
420 PetscErrorCode MonitorInitialConditions(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
421 {
422   AppCtx            *user = (AppCtx *)ctx;
423   DM                 dm, sw;
424   const PetscScalar *u;
425   PetscReal         *weight, *pos, *vel;
426   PetscInt           dim, p, Np, cStart, cEnd;
427 
428   PetscFunctionBegin;
429   if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* -1 indicates interpolated solution */
430   PetscCall(TSGetDM(ts, &sw));
431   PetscCall(DMSwarmGetCellDM(sw, &dm));
432   PetscCall(DMGetDimension(sw, &dim));
433   PetscCall(DMSwarmGetLocalSize(sw, &Np));
434   PetscCall(DMSwarmSortGetAccess(sw));
435   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
436 
437   if (step == 0) {
438     PetscCall(PetscDrawHGReset(user->drawhgic_x));
439     PetscCall(PetscDrawHGGetDraw(user->drawhgic_x, &user->drawic_x));
440     PetscCall(PetscDrawClear(user->drawic_x));
441     PetscCall(PetscDrawFlush(user->drawic_x));
442 
443     PetscCall(PetscDrawHGReset(user->drawhgic_v));
444     PetscCall(PetscDrawHGGetDraw(user->drawhgic_v, &user->drawic_v));
445     PetscCall(PetscDrawClear(user->drawic_v));
446     PetscCall(PetscDrawFlush(user->drawic_v));
447 
448     PetscCall(PetscDrawHGReset(user->drawhgic_w));
449     PetscCall(PetscDrawHGGetDraw(user->drawhgic_w, &user->drawic_w));
450     PetscCall(PetscDrawClear(user->drawic_w));
451     PetscCall(PetscDrawFlush(user->drawic_w));
452 
453     PetscCall(VecGetArrayRead(U, &u));
454     PetscCall(DMSwarmGetField(sw, "velocity", NULL, NULL, (void **)&vel));
455     PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&weight));
456     PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&pos));
457 
458     PetscCall(VecGetLocalSize(U, &Np));
459     Np /= dim * 2;
460     for (p = 0; p < Np; ++p) {
461       PetscCall(PetscDrawHGAddValue(user->drawhgic_x, pos[p * dim]));
462       PetscCall(PetscDrawHGAddValue(user->drawhgic_v, vel[p * dim]));
463       PetscCall(PetscDrawHGAddValue(user->drawhgic_w, weight[p]));
464     }
465 
466     PetscCall(VecRestoreArrayRead(U, &u));
467     PetscCall(PetscDrawHGDraw(user->drawhgic_x));
468     PetscCall(PetscDrawHGSave(user->drawhgic_x));
469 
470     PetscCall(PetscDrawHGDraw(user->drawhgic_v));
471     PetscCall(PetscDrawHGSave(user->drawhgic_v));
472 
473     PetscCall(PetscDrawHGDraw(user->drawhgic_w));
474     PetscCall(PetscDrawHGSave(user->drawhgic_w));
475 
476     PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&pos));
477     PetscCall(DMSwarmRestoreField(sw, "velocity", NULL, NULL, (void **)&vel));
478     PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&weight));
479   }
480   PetscFunctionReturn(PETSC_SUCCESS);
481 }
482 
483 static PetscErrorCode MonitorPositions_2D(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
484 {
485   AppCtx         *user = (AppCtx *)ctx;
486   DM              dm, sw;
487   PetscScalar    *x, *v, *weight;
488   PetscReal       lower[3], upper[3], speed;
489   const PetscInt *s;
490   PetscInt        dim, cStart, cEnd, c;
491 
492   PetscFunctionBeginUser;
493   if (step > 0 && step % user->ostep == 0) {
494     PetscCall(TSGetDM(ts, &sw));
495     PetscCall(DMSwarmGetCellDM(sw, &dm));
496     PetscCall(DMGetDimension(dm, &dim));
497     PetscCall(DMGetBoundingBox(dm, lower, upper));
498     PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
499     PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
500     PetscCall(DMSwarmGetField(sw, "velocity", NULL, NULL, (void **)&v));
501     PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&weight));
502     PetscCall(DMSwarmGetField(sw, "species", NULL, NULL, (void **)&s));
503     PetscCall(DMSwarmSortGetAccess(sw));
504     PetscCall(PetscDrawSPReset(user->drawspX));
505     PetscCall(PetscDrawSPSetLimits(user->drawspX, lower[0], upper[0], lower[1], upper[1]));
506     PetscCall(PetscDrawSPSetLimits(user->drawspX, lower[0], upper[0], -12, 12));
507     for (c = 0; c < cEnd - cStart; ++c) {
508       PetscInt *pidx, Npc, q;
509       PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Npc, &pidx));
510       for (q = 0; q < Npc; ++q) {
511         const PetscInt p = pidx[q];
512         if (s[p] == 0) {
513           speed = PetscSqrtReal(PetscSqr(v[p * dim]) + PetscSqr(v[p * dim + 1]));
514           if (dim == 1 || user->fake_1D) {
515             PetscCall(PetscDrawSPAddPointColorized(user->drawspX, &x[p * dim], &v[p * dim], &speed));
516           } else {
517             PetscCall(PetscDrawSPAddPointColorized(user->drawspX, &x[p * dim], &x[p * dim + 1], &speed));
518           }
519         } else if (s[p] == 1) {
520           PetscCall(PetscDrawSPAddPoint(user->drawspX, &x[p * dim], &v[p * dim]));
521         }
522       }
523       PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Npc, &pidx));
524     }
525     PetscCall(PetscDrawSPDraw(user->drawspX, PETSC_TRUE));
526     PetscDraw draw;
527     PetscCall(PetscDrawSPGetDraw(user->drawspX, &draw));
528     PetscCall(PetscDrawSave(draw));
529     PetscCall(DMSwarmSortRestoreAccess(sw));
530     PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
531     PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&weight));
532     PetscCall(DMSwarmRestoreField(sw, "velocity", NULL, NULL, (void **)&v));
533     PetscCall(DMSwarmRestoreField(sw, "species", NULL, NULL, (void **)&s));
534   }
535   PetscFunctionReturn(PETSC_SUCCESS);
536 }
537 
538 static PetscErrorCode MonitorPoisson(TS ts, PetscInt step, PetscReal t, Vec U, void *ctx)
539 {
540   AppCtx      *user = (AppCtx *)ctx;
541   DM           dm, sw;
542   PetscScalar *x, *E, *weight;
543   PetscReal    lower[3], upper[3], xval;
544   PetscInt     dim, cStart, cEnd, c;
545 
546   PetscFunctionBeginUser;
547   if (step > 0 && step % user->ostep == 0) {
548     PetscCall(TSGetDM(ts, &sw));
549     PetscCall(DMSwarmGetCellDM(sw, &dm));
550     PetscCall(DMGetDimension(dm, &dim));
551     PetscCall(DMGetBoundingBox(dm, lower, upper));
552     PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
553 
554     PetscCall(PetscDrawSPReset(user->drawspE));
555     PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
556     PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
557     PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&weight));
558 
559     PetscCall(DMSwarmSortGetAccess(sw));
560     for (c = 0; c < cEnd - cStart; ++c) {
561       PetscReal Eavg = 0.0;
562       PetscInt *pidx, Npc, q;
563       PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Npc, &pidx));
564       for (q = 0; q < Npc; ++q) {
565         const PetscInt p = pidx[q];
566         Eavg += E[p * dim];
567       }
568       Eavg /= Npc;
569       xval = (c + 0.5) * ((upper[0] - lower[0]) / (cEnd - cStart));
570       PetscCall(PetscDrawSPAddPoint(user->drawspE, &xval, &Eavg));
571       PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Npc, &pidx));
572     }
573     PetscCall(PetscDrawSPDraw(user->drawspE, PETSC_TRUE));
574     PetscDraw draw;
575     PetscCall(PetscDrawSPGetDraw(user->drawspE, &draw));
576     PetscCall(PetscDrawSave(draw));
577     PetscCall(DMSwarmSortRestoreAccess(sw));
578     PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
579     PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&weight));
580     PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
581 
582     Vec rho, phi;
583 
584     PetscCall(DMGetNamedGlobalVector(dm, "rho", &rho));
585     PetscCall(VecView(rho, user->viewerRho));
586     PetscCall(DMRestoreNamedGlobalVector(dm, "rho", &rho));
587 
588     PetscCall(DMGetNamedGlobalVector(dm, "phi", &phi));
589     PetscCall(VecView(phi, user->viewerPhi));
590     PetscCall(DMRestoreNamedGlobalVector(dm, "phi", &phi));
591   }
592   PetscFunctionReturn(PETSC_SUCCESS);
593 }
594 
595 static PetscErrorCode SetupParameters(MPI_Comm comm, AppCtx *ctx)
596 {
597   PetscBag   bag;
598   Parameter *p;
599 
600   PetscFunctionBeginUser;
601   /* setup PETSc parameter bag */
602   PetscCall(PetscBagGetData(ctx->bag, (void **)&p));
603   PetscCall(PetscBagSetName(ctx->bag, "par", "Vlasov-Poisson Parameters"));
604   bag = ctx->bag;
605   PetscCall(PetscBagRegisterScalar(bag, &p->v0, 1.0, "v0", "Velocity scale, m/s"));
606   PetscCall(PetscBagRegisterScalar(bag, &p->t0, 1.0, "t0", "Time scale, s"));
607   PetscCall(PetscBagRegisterScalar(bag, &p->x0, 1.0, "x0", "Space scale, m"));
608   PetscCall(PetscBagRegisterScalar(bag, &p->v0, 1.0, "phi0", "Potential scale, kg*m^2/A*s^3"));
609   PetscCall(PetscBagRegisterScalar(bag, &p->q0, 1.0, "q0", "Charge Scale, A*s"));
610   PetscCall(PetscBagRegisterScalar(bag, &p->m0, 1.0, "m0", "Mass Scale, kg"));
611   PetscCall(PetscBagRegisterScalar(bag, &p->epsi0, 1.0, "epsi0", "Permittivity of Free Space, kg"));
612   PetscCall(PetscBagRegisterScalar(bag, &p->kb, 1.0, "kb", "Boltzmann Constant, m^2 kg/s^2 K^1"));
613 
614   PetscCall(PetscBagRegisterScalar(bag, &p->sigma, 1.0, "sigma", "Charge per unit area, C/m^3"));
615   PetscCall(PetscBagRegisterScalar(bag, &p->poissonNumber, 1.0, "poissonNumber", "Non-Dimensional Poisson Number"));
616   PetscCall(PetscBagRegisterScalar(bag, &p->vlasovNumber, 1.0, "vlasovNumber", "Non-Dimensional Vlasov Number"));
617   PetscCall(PetscBagSetFromOptions(bag));
618   {
619     PetscViewer       viewer;
620     PetscViewerFormat format;
621     PetscBool         flg;
622 
623     PetscCall(PetscOptionsCreateViewer(comm, NULL, NULL, "-param_view", &viewer, &format, &flg));
624     if (flg) {
625       PetscCall(PetscViewerPushFormat(viewer, format));
626       PetscCall(PetscBagView(bag, viewer));
627       PetscCall(PetscViewerFlush(viewer));
628       PetscCall(PetscViewerPopFormat(viewer));
629       PetscCall(PetscViewerDestroy(&viewer));
630     }
631   }
632   PetscFunctionReturn(PETSC_SUCCESS);
633 }
634 
635 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
636 {
637   PetscFunctionBeginUser;
638   PetscCall(DMCreate(comm, dm));
639   PetscCall(DMSetType(*dm, DMPLEX));
640   PetscCall(DMSetFromOptions(*dm));
641   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
642 
643   // Cache the mesh geometry
644   DMField         coordField;
645   IS              cellIS;
646   PetscQuadrature quad;
647   PetscReal      *wt, *pt;
648   PetscInt        cdim, cStart, cEnd;
649 
650   PetscCall(DMGetCoordinateField(*dm, &coordField));
651   PetscCheck(coordField, comm, PETSC_ERR_USER, "DM must have a coordinate field");
652   PetscCall(DMGetCoordinateDim(*dm, &cdim));
653   PetscCall(DMPlexGetHeightStratum(*dm, 0, &cStart, &cEnd));
654   PetscCall(ISCreateStride(PETSC_COMM_SELF, cEnd - cStart, cStart, 1, &cellIS));
655   PetscCall(PetscQuadratureCreate(PETSC_COMM_SELF, &quad));
656   PetscCall(PetscMalloc1(1, &wt));
657   PetscCall(PetscMalloc1(2, &pt));
658   wt[0] = 1.;
659   pt[0] = -1.;
660   pt[1] = -1.;
661   PetscCall(PetscQuadratureSetData(quad, cdim, 1, 1, pt, wt));
662   PetscCall(DMFieldCreateFEGeom(coordField, cellIS, quad, PETSC_FALSE, &user->fegeom));
663   PetscCall(PetscQuadratureDestroy(&quad));
664   PetscCall(ISDestroy(&cellIS));
665   PetscFunctionReturn(PETSC_SUCCESS);
666 }
667 
668 static void ion_f0(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
669 {
670   f0[0] = -constants[SIGMA];
671 }
672 
673 static void laplacian_f1(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
674 {
675   PetscInt d;
676   for (d = 0; d < dim; ++d) f1[d] = u_x[d];
677 }
678 
679 static void laplacian_g3(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
680 {
681   PetscInt d;
682   for (d = 0; d < dim; ++d) g3[d * dim + d] = 1.0;
683 }
684 
685 static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
686 {
687   *u = 0.0;
688   return PETSC_SUCCESS;
689 }
690 
691 /*
692    /  I   -grad\ / q \ = /0\
693    \-div    0  / \phi/   \f/
694 */
695 static void f0_q(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
696 {
697   for (PetscInt d = 0; d < dim; ++d) f0[d] += u[uOff[0] + d];
698 }
699 
700 static void f1_q(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
701 {
702   for (PetscInt d = 0; d < dim; ++d) f1[d * dim + d] = u[uOff[1]];
703 }
704 
705 static void f0_phi_backgroundCharge(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
706 {
707   f0[0] += constants[SIGMA];
708   for (PetscInt d = 0; d < dim; ++d) f0[0] += u_x[uOff_x[0] + d * dim + d];
709 }
710 
711 /* Boundary residual. Dirichlet boundary for u means u_bdy=p*n */
712 static void g0_qq(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
713 {
714   for (PetscInt d = 0; d < dim; ++d) g0[d * dim + d] = 1.0;
715 }
716 
717 static void g2_qphi(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
718 {
719   for (PetscInt d = 0; d < dim; ++d) g2[d * dim + d] = 1.0;
720 }
721 
722 static void g1_phiq(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
723 {
724   for (PetscInt d = 0; d < dim; ++d) g1[d * dim + d] = 1.0;
725 }
726 
727 static PetscErrorCode CreateFEM(DM dm, AppCtx *user)
728 {
729   PetscFE   fephi, feq;
730   PetscDS   ds;
731   PetscBool simplex;
732   PetscInt  dim;
733 
734   PetscFunctionBeginUser;
735   PetscCall(DMGetDimension(dm, &dim));
736   PetscCall(DMPlexIsSimplex(dm, &simplex));
737   if (user->em == EM_MIXED) {
738     DMLabel        label;
739     const PetscInt id = 1;
740 
741     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, dim, simplex, "field_", PETSC_DETERMINE, &feq));
742     PetscCall(PetscObjectSetName((PetscObject)feq, "field"));
743     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, "potential_", PETSC_DETERMINE, &fephi));
744     PetscCall(PetscObjectSetName((PetscObject)fephi, "potential"));
745     PetscCall(PetscFECopyQuadrature(feq, fephi));
746     PetscCall(DMSetField(dm, 0, NULL, (PetscObject)feq));
747     PetscCall(DMSetField(dm, 1, NULL, (PetscObject)fephi));
748     PetscCall(DMCreateDS(dm));
749     PetscCall(PetscFEDestroy(&fephi));
750     PetscCall(PetscFEDestroy(&feq));
751 
752     PetscCall(DMGetLabel(dm, "marker", &label));
753     PetscCall(DMGetDS(dm, &ds));
754 
755     PetscCall(PetscDSSetResidual(ds, 0, f0_q, f1_q));
756     PetscCall(PetscDSSetResidual(ds, 1, f0_phi_backgroundCharge, NULL));
757     PetscCall(PetscDSSetJacobian(ds, 0, 0, g0_qq, NULL, NULL, NULL));
758     PetscCall(PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_qphi, NULL));
759     PetscCall(PetscDSSetJacobian(ds, 1, 0, NULL, g1_phiq, NULL, NULL));
760 
761     PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void))zero, NULL, NULL, NULL));
762 
763   } else {
764     MatNullSpace nullsp;
765     PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, NULL, PETSC_DETERMINE, &fephi));
766     PetscCall(PetscObjectSetName((PetscObject)fephi, "potential"));
767     PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fephi));
768     PetscCall(DMCreateDS(dm));
769     PetscCall(DMGetDS(dm, &ds));
770     PetscCall(PetscDSSetResidual(ds, 0, ion_f0, laplacian_f1));
771     PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, laplacian_g3));
772     PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_TRUE, 0, NULL, &nullsp));
773     PetscCall(PetscObjectCompose((PetscObject)fephi, "nullspace", (PetscObject)nullsp));
774     PetscCall(MatNullSpaceDestroy(&nullsp));
775     PetscCall(PetscFEDestroy(&fephi));
776   }
777   PetscFunctionReturn(PETSC_SUCCESS);
778 }
779 
780 static PetscErrorCode CreatePoisson(DM dm, AppCtx *user)
781 {
782   SNES         snes;
783   Mat          J;
784   MatNullSpace nullSpace;
785 
786   PetscFunctionBeginUser;
787   PetscCall(CreateFEM(dm, user));
788   PetscCall(SNESCreate(PetscObjectComm((PetscObject)dm), &snes));
789   PetscCall(SNESSetOptionsPrefix(snes, "em_"));
790   PetscCall(SNESSetDM(snes, dm));
791   PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, user));
792   PetscCall(SNESSetFromOptions(snes));
793 
794   PetscCall(DMCreateMatrix(dm, &J));
795   PetscCall(MatNullSpaceCreate(PetscObjectComm((PetscObject)dm), PETSC_TRUE, 0, NULL, &nullSpace));
796   PetscCall(MatSetNullSpace(J, nullSpace));
797   PetscCall(MatNullSpaceDestroy(&nullSpace));
798   PetscCall(SNESSetJacobian(snes, J, J, NULL, NULL));
799   PetscCall(MatDestroy(&J));
800   PetscCall(DMCreateMassMatrix(dm, dm, &user->M));
801   PetscCall(DMPlexCreateClosureIndex(dm, NULL));
802   user->snes = snes;
803   PetscFunctionReturn(PETSC_SUCCESS);
804 }
805 
806 PetscErrorCode PetscPDFPertubedConstant2D(const PetscReal x[], const PetscReal dummy[], PetscReal p[])
807 {
808   p[0] = (1 + 0.01 * PetscCosReal(0.5 * x[0])) / (2 * PETSC_PI);
809   p[1] = (1 + 0.01 * PetscCosReal(0.5 * x[1])) / (2 * PETSC_PI);
810   return PETSC_SUCCESS;
811 }
812 PetscErrorCode PetscPDFPertubedConstant1D(const PetscReal x[], const PetscReal dummy[], PetscReal p[])
813 {
814   p[0] = (1. + 0.01 * PetscCosReal(0.5 * x[0])) / (2 * PETSC_PI);
815   return PETSC_SUCCESS;
816 }
817 
818 PetscErrorCode PetscPDFCosine1D(const PetscReal x[], const PetscReal scale[], PetscReal p[])
819 {
820   const PetscReal alpha = scale ? scale[0] : 0.0;
821   const PetscReal k     = scale ? scale[1] : 1.;
822   p[0]                  = (1 + alpha * PetscCosReal(k * x[0]));
823   return PETSC_SUCCESS;
824 }
825 
826 PetscErrorCode PetscPDFCosine2D(const PetscReal x[], const PetscReal scale[], PetscReal p[])
827 {
828   const PetscReal alpha = scale ? scale[0] : 0.;
829   const PetscReal k     = scale ? scale[0] : 1.;
830   p[0]                  = (1 + alpha * PetscCosReal(k * (x[0] + x[1])));
831   return PETSC_SUCCESS;
832 }
833 
834 static PetscErrorCode CreateVelocityDM(DM sw, DM *vdm)
835 {
836   PetscFE        fe;
837   DMPolytopeType ct;
838   PetscInt       dim, cStart;
839   const char    *prefix = "v";
840 
841   PetscFunctionBegin;
842   PetscCall(DMCreate(PETSC_COMM_SELF, vdm));
843   PetscCall(DMSetType(*vdm, DMPLEX));
844   PetscCall(DMPlexSetOptionsPrefix(*vdm, prefix));
845   PetscCall(DMSetFromOptions(*vdm));
846   PetscCall(DMViewFromOptions(*vdm, NULL, "-dm_view"));
847 
848   PetscCall(DMGetDimension(*vdm, &dim));
849   PetscCall(DMPlexGetHeightStratum(*vdm, 0, &cStart, NULL));
850   PetscCall(DMPlexGetCellType(*vdm, cStart, &ct));
851   PetscCall(PetscFECreateByCell(PETSC_COMM_SELF, dim, 1, ct, prefix, PETSC_DETERMINE, &fe));
852   PetscCall(PetscObjectSetName((PetscObject)fe, "distribution"));
853   PetscCall(DMSetField(*vdm, 0, NULL, (PetscObject)fe));
854   PetscCall(DMCreateDS(*vdm));
855   PetscCall(PetscFEDestroy(&fe));
856   PetscFunctionReturn(PETSC_SUCCESS);
857 }
858 
859 static PetscErrorCode InitializeParticles_Centroid(DM sw, PetscBool force1D)
860 {
861   DM_Swarm  *swarm = (DM_Swarm *)sw->data;
862   DM         xdm, vdm;
863   PetscReal  vmin[3], vmax[3];
864   PetscReal *x, *v;
865   PetscInt  *species, *cellid;
866   PetscInt   dim, xcStart, xcEnd, vcStart, vcEnd, Ns, Np, Npc, debug;
867   PetscBool  flg;
868   MPI_Comm   comm;
869 
870   PetscFunctionBegin;
871   PetscCall(PetscObjectGetComm((PetscObject)sw, &comm));
872 
873   PetscOptionsBegin(comm, "", "DMSwarm Options", "DMSWARM");
874   PetscCall(DMSwarmGetNumSpecies(sw, &Ns));
875   PetscCall(PetscOptionsInt("-dm_swarm_num_species", "The number of species", "DMSwarmSetNumSpecies", Ns, &Ns, &flg));
876   if (flg) PetscCall(DMSwarmSetNumSpecies(sw, Ns));
877   PetscCall(PetscOptionsBoundedInt("-dm_swarm_print_coords", "Debug output level for particle coordinate computations", "InitializeParticles", 0, &swarm->printCoords, NULL, 0));
878   PetscCall(PetscOptionsBoundedInt("-dm_swarm_print_weights", "Debug output level for particle weight computations", "InitializeWeights", 0, &swarm->printWeights, NULL, 0));
879   PetscOptionsEnd();
880   debug = swarm->printCoords;
881 
882   PetscCall(DMGetDimension(sw, &dim));
883   PetscCall(DMSwarmGetCellDM(sw, &xdm));
884   PetscCall(DMPlexGetHeightStratum(xdm, 0, &xcStart, &xcEnd));
885 
886   PetscCall(PetscObjectQuery((PetscObject)sw, "__vdm__", (PetscObject *)&vdm));
887   if (!vdm) {
888     PetscCall(CreateVelocityDM(sw, &vdm));
889     PetscCall(PetscObjectCompose((PetscObject)sw, "__vdm__", (PetscObject)vdm));
890     PetscCall(DMDestroy(&vdm));
891     PetscCall(PetscObjectQuery((PetscObject)sw, "__vdm__", (PetscObject *)&vdm));
892   }
893   PetscCall(DMPlexGetHeightStratum(vdm, 0, &vcStart, &vcEnd));
894 
895   // One particle per centroid on the tensor product grid
896   Npc = (vcEnd - vcStart) * Ns;
897   Np  = (xcEnd - xcStart) * Npc;
898   PetscCall(DMSwarmSetLocalSizes(sw, Np, 0));
899   if (debug) {
900     PetscInt gNp;
901     PetscCallMPI(MPIU_Allreduce(&Np, &gNp, 1, MPIU_INT, MPIU_SUM, comm));
902     PetscCall(PetscPrintf(comm, "Global Np = %" PetscInt_FMT "\n", gNp));
903   }
904 
905   // Set species and cellid
906   PetscCall(DMSwarmGetField(sw, "species", NULL, NULL, (void **)&species));
907   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_cellid, NULL, NULL, (void **)&cellid));
908   for (PetscInt c = 0, p = 0; c < xcEnd - xcStart; ++c) {
909     for (PetscInt s = 0; s < Ns; ++s) {
910       for (PetscInt q = 0; q < Npc / Ns; ++q, ++p) {
911         species[p] = s;
912         cellid[p]  = c;
913       }
914     }
915   }
916   PetscCall(DMSwarmRestoreField(sw, "species", NULL, NULL, (void **)&species));
917   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_cellid, NULL, NULL, (void **)&cellid));
918 
919   // Set particle coordinates
920   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
921   PetscCall(DMSwarmGetField(sw, "velocity", NULL, NULL, (void **)&v));
922   PetscCall(DMSwarmSortGetAccess(sw));
923   PetscCall(DMGetBoundingBox(vdm, vmin, vmax));
924   PetscCall(DMGetCoordinatesLocalSetUp(xdm));
925   for (PetscInt c = 0; c < xcEnd - xcStart; ++c) {
926     const PetscInt cell = c + xcStart;
927     PetscInt      *pidx, Npc;
928     PetscReal      centroid[3], volume;
929 
930     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Npc, &pidx));
931     PetscCall(DMPlexComputeCellGeometryFVM(xdm, cell, &volume, centroid, NULL));
932     for (PetscInt s = 0; s < Ns; ++s) {
933       for (PetscInt q = 0; q < Npc / Ns; ++q) {
934         const PetscInt p = pidx[q * Ns + s];
935 
936         for (PetscInt d = 0; d < dim; ++d) {
937           x[p * dim + d] = centroid[d];
938           v[p * dim + d] = vmin[0] + (q + 0.5) * ((vmax[0] - vmin[0]) / (Npc / Ns));
939           if (force1D && d > 0) v[p * dim + d] = 0.;
940         }
941       }
942     }
943     PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Npc, &pidx));
944   }
945   PetscCall(DMSwarmSortRestoreAccess(sw));
946   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&x));
947   PetscCall(DMSwarmRestoreField(sw, "velocity", NULL, NULL, (void **)&v));
948   PetscFunctionReturn(PETSC_SUCCESS);
949 }
950 
951 /*
952   InitializeWeights - Compute weight for each local particle
953 
954   Input Parameters:
955 + sw          - The `DMSwarm`
956 . totalWeight - The sum of all particle weights
957 . force1D     - Flag to treat the problem as 1D
958 . func        - The PDF for the particle spatial distribution
959 - param       - The PDF parameters
960 
961   Notes:
962   The PDF for velocity is assumed to be a Gaussian
963 
964   The particle weights are returned in the `w_q` field of `sw`.
965 */
966 static PetscErrorCode InitializeWeights(DM sw, PetscReal totalWeight, PetscBool force1D, PetscProbFunc func, const PetscReal param[])
967 {
968   DM               xdm, vdm;
969   PetscScalar     *weight;
970   PetscQuadrature  xquad;
971   const PetscReal *xq, *xwq;
972   const PetscInt   order = 5;
973   PetscReal       *xqd   = NULL, xi0[3];
974   PetscReal        xwtot = 0., pwtot = 0.;
975   PetscInt         xNq;
976   PetscInt         dim, Ns, xcStart, xcEnd, vcStart, vcEnd, debug = ((DM_Swarm *)sw->data)->printWeights;
977   MPI_Comm         comm;
978   PetscMPIInt      rank;
979 
980   PetscFunctionBegin;
981   PetscCall(PetscObjectGetComm((PetscObject)sw, &comm));
982   PetscCallMPI(MPI_Comm_rank(comm, &rank));
983   PetscCall(DMGetDimension(sw, &dim));
984   PetscCall(DMSwarmGetCellDM(sw, &xdm));
985   PetscCall(DMSwarmGetNumSpecies(sw, &Ns));
986   PetscCall(DMPlexGetHeightStratum(xdm, 0, &xcStart, &xcEnd));
987   PetscCall(PetscObjectQuery((PetscObject)sw, "__vdm__", (PetscObject *)&vdm));
988   PetscCall(DMPlexGetHeightStratum(vdm, 0, &vcStart, &vcEnd));
989 
990   // Setup Quadrature for spatial and velocity weight calculations
991   if (force1D) PetscCall(PetscDTGaussTensorQuadrature(1, 1, order, -1.0, 1.0, &xquad));
992   else PetscCall(PetscDTGaussTensorQuadrature(dim, 1, order, -1.0, 1.0, &xquad));
993   PetscCall(PetscQuadratureGetData(xquad, NULL, NULL, &xNq, &xq, &xwq));
994   if (force1D) {
995     PetscCall(PetscCalloc1(xNq * dim, &xqd));
996     for (PetscInt q = 0; q < xNq; ++q) xqd[q * dim] = xq[q];
997   }
998   for (PetscInt d = 0; d < dim; ++d) xi0[d] = -1.0;
999 
1000   // Integrate the density function to get the weights of particles in each cell
1001   PetscCall(DMGetCoordinatesLocalSetUp(vdm));
1002   PetscCall(DMSwarmSortGetAccess(sw));
1003   PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&weight));
1004   for (PetscInt c = xcStart; c < xcEnd; ++c) {
1005     PetscReal          xv0[3], xJ[9], xinvJ[9], xdetJ, xqr[3], xden, xw = 0.;
1006     PetscInt          *pidx, Npc;
1007     PetscInt           xNc;
1008     const PetscScalar *xarray;
1009     PetscScalar       *xcoords = NULL;
1010     PetscBool          xisDG;
1011 
1012     PetscCall(DMPlexGetCellCoordinates(xdm, c, &xisDG, &xNc, &xarray, &xcoords));
1013     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Npc, &pidx));
1014     PetscCheck(Npc == (vcEnd - vcStart) * Ns, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Number of particles %" PetscInt_FMT " in cell (rank %d) != %" PetscInt_FMT " number of velocity vertices", Npc, rank, (vcEnd - vcStart) * Ns);
1015     PetscCall(DMPlexComputeCellGeometryFEM(xdm, c, NULL, xv0, xJ, xinvJ, &xdetJ));
1016     for (PetscInt q = 0; q < xNq; ++q) {
1017       // Transform quadrature points from ref space to real space
1018       if (force1D) CoordinatesRefToReal(dim, dim, xi0, xv0, xJ, &xqd[q * dim], xqr);
1019       else CoordinatesRefToReal(dim, dim, xi0, xv0, xJ, &xq[q * dim], xqr);
1020       // Get probability density at quad point
1021       //   No need to scale xqr since PDF will be periodic
1022       PetscCall((*func)(xqr, param, &xden));
1023       if (force1D) xdetJ = xJ[0]; // Only want x contribution
1024       xw += xden * (xwq[q] * xdetJ);
1025     }
1026     xwtot += xw;
1027     if (debug) {
1028       IS              globalOrdering;
1029       const PetscInt *ordering;
1030 
1031       PetscCall(DMPlexGetCellNumbering(xdm, &globalOrdering));
1032       PetscCall(ISGetIndices(globalOrdering, &ordering));
1033       PetscCall(PetscSynchronizedPrintf(comm, "c:%" PetscInt_FMT " [x_a,x_b] = %1.15f,%1.15f -> cell weight = %1.15f\n", ordering[c], (double)PetscRealPart(xcoords[0]), (double)PetscRealPart(xcoords[0 + dim]), (double)xw));
1034       PetscCall(ISRestoreIndices(globalOrdering, &ordering));
1035     }
1036     // Set weights to be Gaussian in velocity cells
1037     for (PetscInt vc = vcStart; vc < vcEnd; ++vc) {
1038       const PetscInt     p  = pidx[vc * Ns + 0];
1039       PetscReal          vw = 0.;
1040       PetscInt           vNc;
1041       const PetscScalar *varray;
1042       PetscScalar       *vcoords = NULL;
1043       PetscBool          visDG;
1044 
1045       PetscCall(DMPlexGetCellCoordinates(vdm, vc, &visDG, &vNc, &varray, &vcoords));
1046       // TODO: Fix 2 stream Ask Joe
1047       //   Two stream function from 1/2pi v^2 e^(-v^2/2)
1048       //   vw = 1. / (PetscSqrtReal(2 * PETSC_PI)) * (((coords_v[0] * PetscExpReal(-PetscSqr(coords_v[0]) / 2.)) - (coords_v[1] * PetscExpReal(-PetscSqr(coords_v[1]) / 2.)))) - 0.5 * PetscErfReal(coords_v[0] / PetscSqrtReal(2.)) + 0.5 * (PetscErfReal(coords_v[1] / PetscSqrtReal(2.)));
1049       vw = 0.5 * (PetscErfReal(vcoords[1] / PetscSqrtReal(2.)) - PetscErfReal(vcoords[0] / PetscSqrtReal(2.)));
1050 
1051       weight[p] = totalWeight * vw * xw;
1052       pwtot += weight[p];
1053       PetscCheck(weight[p] <= 1., PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Particle %" PetscInt_FMT " weight exceeeded 1: %g, %g, %g", p, xw, vw, totalWeight);
1054       PetscCall(DMPlexRestoreCellCoordinates(vdm, vc, &visDG, &vNc, &varray, &vcoords));
1055       if (debug > 1) PetscCall(PetscPrintf(comm, "particle %" PetscInt_FMT ": %g, vw: %g xw: %g\n", p, weight[p], vw, xw));
1056     }
1057     PetscCall(DMPlexRestoreCellCoordinates(xdm, c, &xisDG, &xNc, &xarray, &xcoords));
1058     PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Npc, &pidx));
1059   }
1060   PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&weight));
1061   PetscCall(DMSwarmSortRestoreAccess(sw));
1062   PetscCall(PetscQuadratureDestroy(&xquad));
1063   if (force1D) PetscCall(PetscFree(xqd));
1064 
1065   if (debug) {
1066     PetscReal wtot[2] = {pwtot, xwtot}, gwtot[2];
1067 
1068     PetscCall(PetscSynchronizedFlush(comm, NULL));
1069     PetscCallMPI(MPIU_Allreduce(wtot, gwtot, 2, MPIU_REAL, MPIU_SUM, PETSC_COMM_WORLD));
1070     PetscCall(PetscPrintf(comm, "particle weight sum = %1.10f cell weight sum = %1.10f\n", (double)gwtot[0], (double)gwtot[1]));
1071   }
1072   PetscFunctionReturn(PETSC_SUCCESS);
1073 }
1074 
1075 static PetscErrorCode InitializeParticles_PerturbedWeights(DM sw, AppCtx *user)
1076 {
1077   PetscReal scale[2] = {user->cosine_coefficients[0], user->cosine_coefficients[1]};
1078   PetscInt  dim;
1079 
1080   PetscFunctionBegin;
1081   PetscCall(DMGetDimension(sw, &dim));
1082   PetscCall(InitializeParticles_Centroid(sw, user->fake_1D));
1083   PetscCall(InitializeWeights(sw, user->totalWeight, user->fake_1D, dim == 1 || user->fake_1D ? PetscPDFCosine1D : PetscPDFCosine2D, scale));
1084   PetscFunctionReturn(PETSC_SUCCESS);
1085 }
1086 
1087 static PetscErrorCode InitializeConstants(DM sw, AppCtx *user)
1088 {
1089   DM         dm;
1090   PetscInt  *species;
1091   PetscReal *weight, totalCharge = 0., totalWeight = 0., gmin[3], gmax[3], global_charge, global_weight;
1092   PetscInt   Np, dim;
1093 
1094   PetscFunctionBegin;
1095   PetscCall(DMSwarmGetCellDM(sw, &dm));
1096   PetscCall(DMGetDimension(sw, &dim));
1097   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1098   PetscCall(DMGetBoundingBox(dm, gmin, gmax));
1099   PetscCall(DMSwarmGetField(sw, "w_q", NULL, NULL, (void **)&weight));
1100   PetscCall(DMSwarmGetField(sw, "species", NULL, NULL, (void **)&species));
1101   for (PetscInt p = 0; p < Np; ++p) {
1102     totalWeight += weight[p];
1103     totalCharge += user->charges[species[p]] * weight[p];
1104   }
1105   PetscCall(DMSwarmRestoreField(sw, "w_q", NULL, NULL, (void **)&weight));
1106   PetscCall(DMSwarmRestoreField(sw, "species", NULL, NULL, (void **)&species));
1107   {
1108     Parameter *param;
1109     PetscReal  Area;
1110 
1111     PetscCall(PetscBagGetData(user->bag, (void **)&param));
1112     switch (dim) {
1113     case 1:
1114       Area = (gmax[0] - gmin[0]);
1115       break;
1116     case 2:
1117       if (user->fake_1D) {
1118         Area = (gmax[0] - gmin[0]);
1119       } else {
1120         Area = (gmax[0] - gmin[0]) * (gmax[1] - gmin[1]);
1121       }
1122       break;
1123     case 3:
1124       Area = (gmax[0] - gmin[0]) * (gmax[1] - gmin[1]) * (gmax[2] - gmin[2]);
1125       break;
1126     default:
1127       SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Dimension %" PetscInt_FMT " not supported", dim);
1128     }
1129     PetscCallMPI(MPIU_Allreduce(&totalWeight, &global_weight, 1, MPIU_REAL, MPIU_SUM, PETSC_COMM_WORLD));
1130     PetscCallMPI(MPIU_Allreduce(&totalCharge, &global_charge, 1, MPIU_REAL, MPIU_SUM, PETSC_COMM_WORLD));
1131     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "dim = %" PetscInt_FMT "\ttotalWeight = %f, user->charges[species[0]] = %f\ttotalCharge = %f, Total Area = %f\n", dim, (double)global_weight, (double)user->charges[0], (double)global_charge, (double)Area));
1132     param->sigma = PetscAbsReal(global_charge / (Area));
1133 
1134     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "sigma: %g\n", (double)param->sigma));
1135     PetscCall(PetscPrintf(PETSC_COMM_WORLD, "(x0,v0,t0,m0,q0,phi0): (%e, %e, %e, %e, %e, %e) - (P, V) = (%e, %e)\n", (double)param->x0, (double)param->v0, (double)param->t0, (double)param->m0, (double)param->q0, (double)param->phi0, (double)param->poissonNumber,
1136                           (double)param->vlasovNumber));
1137   }
1138   /* Setup Constants */
1139   {
1140     PetscDS    ds;
1141     Parameter *param;
1142     PetscCall(PetscBagGetData(user->bag, (void **)&param));
1143     PetscScalar constants[NUM_CONSTANTS];
1144     constants[SIGMA]   = param->sigma;
1145     constants[V0]      = param->v0;
1146     constants[T0]      = param->t0;
1147     constants[X0]      = param->x0;
1148     constants[M0]      = param->m0;
1149     constants[Q0]      = param->q0;
1150     constants[PHI0]    = param->phi0;
1151     constants[POISSON] = param->poissonNumber;
1152     constants[VLASOV]  = param->vlasovNumber;
1153     PetscCall(DMGetDS(dm, &ds));
1154     PetscCall(PetscDSSetConstants(ds, NUM_CONSTANTS, constants));
1155   }
1156   PetscFunctionReturn(PETSC_SUCCESS);
1157 }
1158 
1159 static PetscErrorCode InitializeVelocities_Fake1D(DM sw, AppCtx *user)
1160 {
1161   DM         dm;
1162   PetscReal *v;
1163   PetscInt  *species, cStart, cEnd;
1164   PetscInt   dim, Np;
1165 
1166   PetscFunctionBegin;
1167   PetscCall(DMGetDimension(sw, &dim));
1168   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1169   PetscCall(DMSwarmGetField(sw, "velocity", NULL, NULL, (void **)&v));
1170   PetscCall(DMSwarmGetField(sw, "species", NULL, NULL, (void **)&species));
1171   PetscCall(DMSwarmGetCellDM(sw, &dm));
1172   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
1173   PetscRandom rnd;
1174   PetscCall(PetscRandomCreate(PetscObjectComm((PetscObject)sw), &rnd));
1175   PetscCall(PetscRandomSetInterval(rnd, 0, 1.));
1176   PetscCall(PetscRandomSetFromOptions(rnd));
1177 
1178   for (PetscInt p = 0; p < Np; ++p) {
1179     PetscReal a[3] = {0., 0., 0.}, vel[3] = {0., 0., 0.};
1180 
1181     PetscCall(PetscRandomGetValueReal(rnd, &a[0]));
1182     if (user->perturbed_weights) {
1183       PetscCall(PetscPDFSampleConstant1D(a, NULL, vel));
1184     } else {
1185       PetscCall(PetscPDFSampleGaussian1D(a, NULL, vel));
1186     }
1187     v[p * dim] = vel[0];
1188   }
1189   PetscCall(PetscRandomDestroy(&rnd));
1190   PetscCall(DMSwarmRestoreField(sw, "velocity", NULL, NULL, (void **)&v));
1191   PetscCall(DMSwarmRestoreField(sw, "species", NULL, NULL, (void **)&species));
1192   PetscFunctionReturn(PETSC_SUCCESS);
1193 }
1194 
1195 static PetscErrorCode CreateSwarm(DM dm, AppCtx *user, DM *sw)
1196 {
1197   PetscReal v0[2] = {1., 0.};
1198   PetscInt  dim;
1199 
1200   PetscFunctionBeginUser;
1201   PetscCall(DMGetDimension(dm, &dim));
1202   PetscCall(DMCreate(PetscObjectComm((PetscObject)dm), sw));
1203   PetscCall(DMSetType(*sw, DMSWARM));
1204   PetscCall(DMSetDimension(*sw, dim));
1205   PetscCall(DMSwarmSetType(*sw, DMSWARM_PIC));
1206   PetscCall(DMSwarmSetCellDM(*sw, dm));
1207   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "w_q", 1, PETSC_SCALAR));
1208   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "velocity", dim, PETSC_REAL));
1209   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "species", 1, PETSC_INT));
1210   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "initCoordinates", dim, PETSC_REAL));
1211   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "initVelocity", dim, PETSC_REAL));
1212   PetscCall(DMSwarmRegisterPetscDatatypeField(*sw, "E_field", dim, PETSC_REAL));
1213   PetscCall(DMSwarmFinalizeFieldRegister(*sw));
1214   PetscCall(DMSetApplicationContext(*sw, user));
1215   PetscCall(DMSetFromOptions(*sw));
1216   user->swarm = *sw;
1217   if (user->perturbed_weights) {
1218     PetscCall(InitializeParticles_PerturbedWeights(*sw, user));
1219   } else {
1220     PetscCall(DMSwarmComputeLocalSizeFromOptions(*sw));
1221     PetscCall(DMSwarmInitializeCoordinates(*sw));
1222     if (user->fake_1D) {
1223       PetscCall(InitializeVelocities_Fake1D(*sw, user));
1224     } else {
1225       PetscCall(DMSwarmInitializeVelocitiesFromOptions(*sw, v0));
1226     }
1227   }
1228   PetscCall(PetscObjectSetName((PetscObject)*sw, "Particles"));
1229   PetscCall(DMViewFromOptions(*sw, NULL, "-sw_view"));
1230   {
1231     Vec gc, gc0, gv, gv0;
1232 
1233     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, DMSwarmPICField_coor, &gc));
1234     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, "initCoordinates", &gc0));
1235     PetscCall(VecCopy(gc, gc0));
1236     PetscCall(VecViewFromOptions(gc, NULL, "-ic_x_view"));
1237     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, DMSwarmPICField_coor, &gc));
1238     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, "initCoordinates", &gc0));
1239     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, "velocity", &gv));
1240     PetscCall(DMSwarmCreateGlobalVectorFromField(*sw, "initVelocity", &gv0));
1241     PetscCall(VecCopy(gv, gv0));
1242     PetscCall(VecViewFromOptions(gv, NULL, "-ic_v_view"));
1243     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, "velocity", &gv));
1244     PetscCall(DMSwarmDestroyGlobalVectorFromField(*sw, "initVelocity", &gv0));
1245   }
1246   {
1247     const char *fieldnames[2] = {DMSwarmPICField_coor, "velocity"};
1248 
1249     PetscCall(DMSwarmVectorDefineFields(*sw, 2, fieldnames));
1250   }
1251   PetscFunctionReturn(PETSC_SUCCESS);
1252 }
1253 
1254 static PetscErrorCode ComputeFieldAtParticles_Coulomb(SNES snes, DM sw, PetscReal E[])
1255 {
1256   AppCtx     *user;
1257   PetscReal  *coords;
1258   PetscInt   *species, dim, Np, Ns;
1259   PetscMPIInt size;
1260 
1261   PetscFunctionBegin;
1262   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)snes), &size));
1263   PetscCheck(size == 1, PetscObjectComm((PetscObject)snes), PETSC_ERR_SUP, "Coulomb code only works in serial");
1264   PetscCall(DMGetDimension(sw, &dim));
1265   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1266   PetscCall(DMSwarmGetNumSpecies(sw, &Ns));
1267   PetscCall(DMGetApplicationContext(sw, (void *)&user));
1268 
1269   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
1270   PetscCall(DMSwarmGetField(sw, "species", NULL, NULL, (void **)&species));
1271   for (PetscInt p = 0; p < Np; ++p) {
1272     PetscReal *pcoord = &coords[p * dim];
1273     PetscReal  pE[3]  = {0., 0., 0.};
1274 
1275     /* Calculate field at particle p due to particle q */
1276     for (PetscInt q = 0; q < Np; ++q) {
1277       PetscReal *qcoord = &coords[q * dim];
1278       PetscReal  rpq[3], r, r3, q_q;
1279 
1280       if (p == q) continue;
1281       q_q = user->charges[species[q]] * 1.;
1282       for (PetscInt d = 0; d < dim; ++d) rpq[d] = pcoord[d] - qcoord[d];
1283       r = DMPlex_NormD_Internal(dim, rpq);
1284       if (r < PETSC_SQRT_MACHINE_EPSILON) continue;
1285       r3 = PetscPowRealInt(r, 3);
1286       for (PetscInt d = 0; d < dim; ++d) pE[d] += q_q * rpq[d] / r3;
1287     }
1288     for (PetscInt d = 0; d < dim; ++d) E[p * dim + d] = pE[d];
1289   }
1290   PetscCall(DMSwarmRestoreField(sw, "species", NULL, NULL, (void **)&species));
1291   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
1292   PetscFunctionReturn(PETSC_SUCCESS);
1293 }
1294 
1295 static PetscErrorCode ComputeFieldAtParticles_Primal(SNES snes, DM sw, PetscReal E[])
1296 {
1297   DM         dm;
1298   AppCtx    *user;
1299   PetscDS    ds;
1300   PetscFE    fe;
1301   Mat        M_p;
1302   Vec        rhoRhs;      // Weak charge density, \int phi_i rho
1303   Vec        rho;         // Charge density, M^{-1} rhoRhs
1304   Vec        phi, locPhi; // Potential
1305   Vec        f;           // Particle weights
1306   PetscReal *coords;
1307   PetscInt   dim, cStart, cEnd, Np;
1308 
1309   PetscFunctionBegin;
1310   PetscCall(DMGetApplicationContext(sw, (void *)&user));
1311   PetscCall(PetscLogEventBegin(user->ESolveEvent, snes, sw, 0, 0));
1312   PetscCall(DMGetDimension(sw, &dim));
1313   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1314 
1315   KSP          ksp;
1316   const char **oldFields;
1317   PetscInt     Nf;
1318   const char **tmp;
1319 
1320   PetscCall(SNESGetDM(snes, &dm));
1321   PetscCall(DMSwarmVectorGetField(sw, &Nf, &tmp));
1322   PetscCall(PetscMalloc1(Nf, &oldFields));
1323   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscStrallocpy(tmp[f], (char **)&oldFields[f]));
1324   PetscCall(DMSwarmVectorDefineField(sw, "w_q"));
1325   PetscCall(DMCreateMassMatrix(sw, dm, &M_p));
1326   PetscCall(DMSwarmVectorDefineFields(sw, Nf, oldFields));
1327   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscFree(oldFields[f]));
1328   PetscCall(PetscFree(oldFields));
1329 
1330   PetscCall(DMGetGlobalVector(dm, &rhoRhs));
1331   PetscCall(PetscObjectSetName((PetscObject)rhoRhs, "Weak charge density"));
1332   PetscCall(DMGetNamedGlobalVector(dm, "rho", &rho));
1333   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
1334   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
1335 
1336   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
1337   PetscCall(MatViewFromOptions(user->M, NULL, "-m_view"));
1338   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
1339 
1340   PetscCall(MatMultTranspose(M_p, f, rhoRhs));
1341   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
1342 
1343   PetscCall(KSPCreate(PetscObjectComm((PetscObject)dm), &ksp));
1344   PetscCall(KSPSetOptionsPrefix(ksp, "em_proj_"));
1345   PetscCall(KSPSetOperators(ksp, user->M, user->M));
1346   PetscCall(KSPSetFromOptions(ksp));
1347   PetscCall(KSPSolve(ksp, rhoRhs, rho));
1348 
1349   PetscCall(VecScale(rhoRhs, -1.0));
1350 
1351   PetscCall(VecViewFromOptions(rhoRhs, NULL, "-rho_view"));
1352   PetscCall(DMRestoreNamedGlobalVector(dm, "rho", &rho));
1353   PetscCall(KSPDestroy(&ksp));
1354   PetscCall(MatDestroy(&M_p));
1355 
1356   PetscCall(DMGetNamedGlobalVector(dm, "phi", &phi));
1357   PetscCall(VecSet(phi, 0.0));
1358   PetscCall(SNESSolve(snes, rhoRhs, phi));
1359   PetscCall(DMRestoreGlobalVector(dm, &rhoRhs));
1360   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));
1361 
1362   PetscCall(DMGetLocalVector(dm, &locPhi));
1363   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
1364   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
1365   PetscCall(DMRestoreNamedGlobalVector(dm, "phi", &phi));
1366   PetscCall(PetscLogEventEnd(user->ESolveEvent, snes, sw, 0, 0));
1367 
1368   PetscCall(DMGetDS(dm, &ds));
1369   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
1370   PetscCall(DMSwarmSortGetAccess(sw));
1371   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
1372   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
1373 
1374   PetscCall(PetscLogEventBegin(user->ETabEvent, snes, sw, 0, 0));
1375   PetscFEGeom *chunkgeom = NULL;
1376   for (PetscInt c = cStart; c < cEnd; ++c) {
1377     PetscTabulation tab;
1378     PetscScalar    *clPhi = NULL;
1379     PetscReal      *pcoord, *refcoord;
1380     PetscInt       *points;
1381     PetscInt        Ncp;
1382 
1383     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
1384     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
1385     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
1386     for (PetscInt cp = 0; cp < Ncp; ++cp)
1387       for (PetscInt d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
1388     {
1389       PetscCall(PetscFEGeomGetChunk(user->fegeom, c - cStart, c - cStart + 1, &chunkgeom));
1390       for (PetscInt i = 0; i < Ncp; ++i) {
1391         const PetscReal x0[3] = {-1., -1., -1.};
1392         CoordinatesRealToRef(dim, dim, x0, chunkgeom->v, chunkgeom->invJ, &pcoord[dim * i], &refcoord[dim * i]);
1393       }
1394     }
1395     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
1396     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
1397     for (PetscInt cp = 0; cp < Ncp; ++cp) {
1398       const PetscReal *basisDer = tab->T[1];
1399       const PetscInt   p        = points[cp];
1400 
1401       for (PetscInt d = 0; d < dim; ++d) E[p * dim + d] = 0.;
1402       PetscCall(PetscFEFreeInterpolateGradient_Static(fe, basisDer, clPhi, dim, chunkgeom->invJ, NULL, cp, &E[p * dim]));
1403       for (PetscInt d = 0; d < dim; ++d) {
1404         E[p * dim + d] *= -1.0;
1405         if (user->fake_1D && d > 0) E[p * dim + d] = 0;
1406       }
1407     }
1408     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
1409     PetscCall(PetscTabulationDestroy(&tab));
1410     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
1411     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
1412     PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Ncp, &points));
1413   }
1414   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
1415   PetscCall(DMSwarmSortRestoreAccess(sw));
1416   PetscCall(DMRestoreLocalVector(dm, &locPhi));
1417   PetscCall(PetscFEGeomRestoreChunk(user->fegeom, 0, 1, &chunkgeom));
1418   PetscCall(PetscLogEventEnd(user->ETabEvent, snes, sw, 0, 0));
1419   PetscFunctionReturn(PETSC_SUCCESS);
1420 }
1421 
1422 static PetscErrorCode ComputeFieldAtParticles_Mixed(SNES snes, DM sw, PetscReal E[])
1423 {
1424   AppCtx         *user;
1425   DM              dm, potential_dm;
1426   KSP             ksp;
1427   IS              potential_IS;
1428   PetscDS         ds;
1429   PetscFE         fe;
1430   Mat             M_p, M;
1431   Vec             phi, locPhi, rho, f, temp_rho, rho0;
1432   PetscQuadrature q;
1433   PetscReal      *coords;
1434   PetscInt        dim, cStart, cEnd, Np, pot_field = 1;
1435   const char    **oldFields;
1436   PetscInt        Nf;
1437   const char    **tmp;
1438 
1439   PetscFunctionBegin;
1440   PetscCall(DMGetApplicationContext(sw, &user));
1441   PetscCall(PetscLogEventBegin(user->ESolveEvent, snes, sw, 0, 0));
1442   PetscCall(DMGetDimension(sw, &dim));
1443   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1444 
1445   /* Create the charges rho */
1446   PetscCall(SNESGetDM(snes, &dm));
1447   PetscCall(DMGetGlobalVector(dm, &rho));
1448   PetscCall(PetscObjectSetName((PetscObject)rho, "rho"));
1449 
1450   PetscCall(DMCreateSubDM(dm, 1, &pot_field, &potential_IS, &potential_dm));
1451 
1452   PetscCall(DMSwarmVectorGetField(sw, &Nf, &tmp));
1453   PetscCall(PetscMalloc1(Nf, &oldFields));
1454   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscStrallocpy(tmp[f], (char **)&oldFields[f]));
1455   PetscCall(DMSwarmVectorDefineField(sw, "w_q"));
1456   PetscCall(DMCreateMassMatrix(sw, potential_dm, &M_p));
1457   PetscCall(DMSwarmVectorDefineFields(sw, Nf, oldFields));
1458   for (PetscInt f = 0; f < Nf; ++f) PetscCall(PetscFree(oldFields[f]));
1459   PetscCall(PetscFree(oldFields));
1460 
1461   PetscCall(DMCreateMassMatrix(potential_dm, potential_dm, &M));
1462   PetscCall(MatViewFromOptions(M_p, NULL, "-mp_view"));
1463   PetscCall(MatViewFromOptions(M, NULL, "-m_view"));
1464   PetscCall(DMGetGlobalVector(potential_dm, &temp_rho));
1465   PetscCall(PetscObjectSetName((PetscObject)temp_rho, "Mf"));
1466   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "w_q", &f));
1467   PetscCall(PetscObjectSetName((PetscObject)f, "particle weight"));
1468   PetscCall(VecViewFromOptions(f, NULL, "-weights_view"));
1469   PetscCall(MatMultTranspose(M_p, f, temp_rho));
1470   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "w_q", &f));
1471   PetscCall(DMGetGlobalVector(potential_dm, &rho0));
1472   PetscCall(PetscObjectSetName((PetscObject)rho0, "Charge density (rho0) from Mixed Compute"));
1473 
1474   PetscCall(KSPCreate(PetscObjectComm((PetscObject)dm), &ksp));
1475   PetscCall(KSPSetOptionsPrefix(ksp, "em_proj"));
1476   PetscCall(KSPSetOperators(ksp, M, M));
1477   PetscCall(KSPSetFromOptions(ksp));
1478   PetscCall(KSPSolve(ksp, temp_rho, rho0));
1479   PetscCall(VecViewFromOptions(rho0, NULL, "-rho0_view"));
1480 
1481   PetscCall(VecISCopy(rho, potential_IS, SCATTER_FORWARD, temp_rho));
1482   PetscCall(VecScale(rho, 0.25));
1483   PetscCall(VecViewFromOptions(rho0, NULL, "-rho0_view"));
1484   PetscCall(VecViewFromOptions(temp_rho, NULL, "-temprho_view"));
1485   PetscCall(VecViewFromOptions(rho, NULL, "-rho_view"));
1486   PetscCall(DMRestoreGlobalVector(potential_dm, &temp_rho));
1487   PetscCall(DMRestoreGlobalVector(potential_dm, &rho0));
1488 
1489   PetscCall(MatDestroy(&M_p));
1490   PetscCall(MatDestroy(&M));
1491   PetscCall(KSPDestroy(&ksp));
1492   PetscCall(DMDestroy(&potential_dm));
1493   PetscCall(ISDestroy(&potential_IS));
1494 
1495   PetscCall(DMGetGlobalVector(dm, &phi));
1496   PetscCall(PetscObjectSetName((PetscObject)phi, "potential"));
1497   PetscCall(VecSet(phi, 0.0));
1498   PetscCall(SNESSolve(snes, rho, phi));
1499   PetscCall(DMRestoreGlobalVector(dm, &rho));
1500 
1501   PetscCall(VecViewFromOptions(phi, NULL, "-phi_view"));
1502 
1503   PetscCall(DMGetLocalVector(dm, &locPhi));
1504   PetscCall(DMGlobalToLocalBegin(dm, phi, INSERT_VALUES, locPhi));
1505   PetscCall(DMGlobalToLocalEnd(dm, phi, INSERT_VALUES, locPhi));
1506   PetscCall(DMRestoreGlobalVector(dm, &phi));
1507   PetscCall(PetscLogEventEnd(user->ESolveEvent, snes, sw, 0, 0));
1508 
1509   PetscCall(PetscLogEventBegin(user->ETabEvent, snes, sw, 0, 0));
1510   PetscCall(DMGetDS(dm, &ds));
1511   PetscCall(PetscDSGetDiscretization(ds, 0, (PetscObject *)&fe));
1512   PetscCall(DMSwarmSortGetAccess(sw));
1513   PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd));
1514   PetscCall(DMSwarmGetField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
1515   PetscCall(PetscFEGetQuadrature(fe, &q));
1516   PetscFEGeom *chunkgeom = NULL;
1517   for (PetscInt c = cStart; c < cEnd; ++c) {
1518     PetscTabulation tab;
1519     PetscScalar    *clPhi = NULL;
1520     PetscReal      *pcoord, *refcoord;
1521     PetscInt       *points;
1522     PetscInt        Ncp;
1523 
1524     PetscCall(DMSwarmSortGetPointsPerCell(sw, c, &Ncp, &points));
1525     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
1526     PetscCall(DMGetWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
1527     for (PetscInt cp = 0; cp < Ncp; ++cp)
1528       for (PetscInt d = 0; d < dim; ++d) pcoord[cp * dim + d] = coords[points[cp] * dim + d];
1529     {
1530       PetscCall(PetscFEGeomGetChunk(user->fegeom, c - cStart, c - cStart + 1, &chunkgeom));
1531       for (PetscInt i = 0; i < Ncp; ++i) {
1532         // Apply the inverse affine transformation for each point
1533         const PetscReal x0[3] = {-1., -1., -1.};
1534         CoordinatesRealToRef(dim, dim, x0, chunkgeom->v, chunkgeom->invJ, &pcoord[dim * i], &refcoord[dim * i]);
1535       }
1536     }
1537     PetscCall(PetscFECreateTabulation(fe, 1, Ncp, refcoord, 1, &tab));
1538     PetscCall(DMPlexVecGetClosure(dm, NULL, locPhi, c, NULL, &clPhi));
1539 
1540     for (PetscInt cp = 0; cp < Ncp; ++cp) {
1541       const PetscInt p = points[cp];
1542 
1543       for (PetscInt d = 0; d < dim; ++d) E[p * dim + d] = 0.;
1544       PetscCall(PetscFEInterpolateAtPoints_Static(fe, tab, clPhi, chunkgeom, cp, &E[p * dim]));
1545       PetscCall(PetscFEPushforward(fe, chunkgeom, 1, &E[p * dim]));
1546       for (PetscInt d = 0; d < dim; ++d) {
1547         E[p * dim + d] *= -2.0;
1548         if (user->fake_1D && d > 0) E[p * dim + d] = 0;
1549       }
1550     }
1551     PetscCall(DMPlexVecRestoreClosure(dm, NULL, locPhi, c, NULL, &clPhi));
1552     PetscCall(PetscTabulationDestroy(&tab));
1553     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &pcoord));
1554     PetscCall(DMRestoreWorkArray(dm, Ncp * dim, MPIU_REAL, &refcoord));
1555     PetscCall(DMSwarmSortRestorePointsPerCell(sw, c, &Ncp, &points));
1556   }
1557   PetscCall(DMSwarmRestoreField(sw, DMSwarmPICField_coor, NULL, NULL, (void **)&coords));
1558   PetscCall(DMSwarmSortRestoreAccess(sw));
1559   PetscCall(DMRestoreLocalVector(dm, &locPhi));
1560   PetscCall(PetscFEGeomRestoreChunk(user->fegeom, 0, 1, &chunkgeom));
1561   PetscCall(PetscLogEventEnd(user->ETabEvent, snes, sw, 0, 0));
1562   PetscFunctionReturn(PETSC_SUCCESS);
1563 }
1564 
1565 static PetscErrorCode ComputeFieldAtParticles(SNES snes, DM sw, PetscReal E[])
1566 {
1567   AppCtx  *ctx;
1568   PetscInt dim, Np;
1569 
1570   PetscFunctionBegin;
1571   PetscValidHeaderSpecific(snes, SNES_CLASSID, 1);
1572   PetscValidHeaderSpecific(sw, DM_CLASSID, 2);
1573   PetscAssertPointer(E, 3);
1574   PetscCall(DMGetDimension(sw, &dim));
1575   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1576   PetscCall(DMGetApplicationContext(sw, &ctx));
1577   PetscCall(PetscArrayzero(E, Np * dim));
1578 
1579   switch (ctx->em) {
1580   case EM_PRIMAL:
1581     PetscCall(ComputeFieldAtParticles_Primal(snes, sw, E));
1582     break;
1583   case EM_COULOMB:
1584     PetscCall(ComputeFieldAtParticles_Coulomb(snes, sw, E));
1585     break;
1586   case EM_MIXED:
1587     PetscCall(ComputeFieldAtParticles_Mixed(snes, sw, E));
1588     break;
1589   case EM_NONE:
1590     break;
1591   default:
1592     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "No solver for electrostatic model %s", EMTypes[ctx->em]);
1593   }
1594   PetscFunctionReturn(PETSC_SUCCESS);
1595 }
1596 
1597 static PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec U, Vec G, void *ctx)
1598 {
1599   DM                 sw;
1600   SNES               snes = ((AppCtx *)ctx)->snes;
1601   const PetscReal   *coords, *vel;
1602   const PetscScalar *u;
1603   PetscScalar       *g;
1604   PetscReal         *E, m_p = 1., q_p = -1.;
1605   PetscInt           dim, d, Np, p;
1606 
1607   PetscFunctionBeginUser;
1608   PetscCall(TSGetDM(ts, &sw));
1609   PetscCall(DMGetDimension(sw, &dim));
1610   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1611   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1612   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
1613   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1614   PetscCall(VecGetArrayRead(U, &u));
1615   PetscCall(VecGetArray(G, &g));
1616 
1617   PetscCall(ComputeFieldAtParticles(snes, sw, E));
1618 
1619   Np /= 2 * dim;
1620   for (p = 0; p < Np; ++p) {
1621     for (d = 0; d < dim; ++d) {
1622       g[(p * 2 + 0) * dim + d] = u[(p * 2 + 1) * dim + d];
1623       g[(p * 2 + 1) * dim + d] = q_p * E[p * dim + d] / m_p;
1624     }
1625   }
1626   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1627   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1628   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
1629   PetscCall(VecRestoreArrayRead(U, &u));
1630   PetscCall(VecRestoreArray(G, &g));
1631   PetscFunctionReturn(PETSC_SUCCESS);
1632 }
1633 
1634 /* J_{ij} = dF_i/dx_j
1635    J_p = (  0   1)
1636          (-w^2  0)
1637    TODO Now there is another term with w^2 from the electric field. I think we will need to invert the operator.
1638         Perhaps we can approximate the Jacobian using only the cellwise P-P gradient from Coulomb
1639 */
1640 static PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec U, Mat J, Mat P, void *ctx)
1641 {
1642   DM               sw;
1643   const PetscReal *coords, *vel;
1644   PetscInt         dim, d, Np, p, rStart;
1645 
1646   PetscFunctionBeginUser;
1647   PetscCall(TSGetDM(ts, &sw));
1648   PetscCall(DMGetDimension(sw, &dim));
1649   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1650   PetscCall(MatGetOwnershipRange(J, &rStart, NULL));
1651   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1652   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1653   Np /= 2 * dim;
1654   for (p = 0; p < Np; ++p) {
1655     const PetscReal x0      = coords[p * dim + 0];
1656     const PetscReal vy0     = vel[p * dim + 1];
1657     const PetscReal omega   = vy0 / x0;
1658     PetscScalar     vals[4] = {0., 1., -PetscSqr(omega), 0.};
1659 
1660     for (d = 0; d < dim; ++d) {
1661       const PetscInt rows[2] = {(p * 2 + 0) * dim + d + rStart, (p * 2 + 1) * dim + d + rStart};
1662       PetscCall(MatSetValues(J, 2, rows, 2, rows, vals, INSERT_VALUES));
1663     }
1664   }
1665   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1666   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1667   PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
1668   PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
1669   PetscFunctionReturn(PETSC_SUCCESS);
1670 }
1671 
1672 static PetscErrorCode RHSFunctionX(TS ts, PetscReal t, Vec V, Vec Xres, void *ctx)
1673 {
1674   AppCtx            *user = (AppCtx *)ctx;
1675   DM                 sw;
1676   const PetscScalar *v;
1677   PetscScalar       *xres;
1678   PetscInt           Np, p, d, dim;
1679 
1680   PetscFunctionBeginUser;
1681   PetscCall(PetscLogEventBegin(user->RhsXEvent, ts, 0, 0, 0));
1682   PetscCall(TSGetDM(ts, &sw));
1683   PetscCall(DMGetDimension(sw, &dim));
1684   PetscCall(VecGetLocalSize(Xres, &Np));
1685   PetscCall(VecGetArrayRead(V, &v));
1686   PetscCall(VecGetArray(Xres, &xres));
1687   Np /= dim;
1688   for (p = 0; p < Np; ++p) {
1689     for (d = 0; d < dim; ++d) {
1690       xres[p * dim + d] = v[p * dim + d];
1691       if (user->fake_1D && d > 0) xres[p * dim + d] = 0;
1692     }
1693   }
1694   PetscCall(VecRestoreArrayRead(V, &v));
1695   PetscCall(VecRestoreArray(Xres, &xres));
1696   PetscCall(PetscLogEventEnd(user->RhsXEvent, ts, 0, 0, 0));
1697   PetscFunctionReturn(PETSC_SUCCESS);
1698 }
1699 
1700 static PetscErrorCode RHSFunctionV(TS ts, PetscReal t, Vec X, Vec Vres, void *ctx)
1701 {
1702   DM                 sw;
1703   AppCtx            *user = (AppCtx *)ctx;
1704   SNES               snes = ((AppCtx *)ctx)->snes;
1705   const PetscScalar *x;
1706   const PetscReal   *coords, *vel;
1707   PetscReal         *E, m_p, q_p;
1708   PetscScalar       *vres;
1709   PetscInt           Np, p, dim, d;
1710   Parameter         *param;
1711 
1712   PetscFunctionBeginUser;
1713   PetscCall(PetscLogEventBegin(user->RhsVEvent, ts, 0, 0, 0));
1714   PetscCall(TSGetDM(ts, &sw));
1715   PetscCall(DMGetDimension(sw, &dim));
1716   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1717   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1718   PetscCall(DMSwarmGetField(sw, "E_field", NULL, NULL, (void **)&E));
1719   PetscCall(PetscBagGetData(user->bag, (void **)&param));
1720   m_p = user->masses[0] * param->m0;
1721   q_p = user->charges[0] * param->q0;
1722   PetscCall(VecGetLocalSize(Vres, &Np));
1723   PetscCall(VecGetArrayRead(X, &x));
1724   PetscCall(VecGetArray(Vres, &vres));
1725   PetscCall(ComputeFieldAtParticles(snes, sw, E));
1726 
1727   Np /= dim;
1728   for (p = 0; p < Np; ++p) {
1729     for (d = 0; d < dim; ++d) {
1730       vres[p * dim + d] = q_p * E[p * dim + d] / m_p;
1731       if (user->fake_1D && d > 0) vres[p * dim + d] = 0.;
1732     }
1733   }
1734   PetscCall(VecRestoreArrayRead(X, &x));
1735   /*
1736     Synchronized, ordered output for parallel/sequential test cases.
1737     In the 1D (on the 2D mesh) case, every y component should be zero.
1738   */
1739   if (user->checkVRes) {
1740     PetscBool pr = user->checkVRes > 1 ? PETSC_TRUE : PETSC_FALSE;
1741     PetscInt  step;
1742 
1743     PetscCall(TSGetStepNumber(ts, &step));
1744     if (pr) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "step: %" PetscInt_FMT "\n", step));
1745     for (PetscInt p = 0; p < Np; ++p) {
1746       if (pr) PetscCall(PetscSynchronizedPrintf(PETSC_COMM_WORLD, "Residual: %.12g %.12g\n", (double)PetscRealPart(vres[p * dim + 0]), (double)PetscRealPart(vres[p * dim + 1])));
1747       PetscCheck(PetscAbsScalar(vres[p * dim + 1]) < PETSC_SMALL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Y velocity should be 0., not %g", (double)PetscRealPart(vres[p * dim + 1]));
1748     }
1749     if (pr) PetscCall(PetscSynchronizedFlush(PETSC_COMM_WORLD, PETSC_STDOUT));
1750   }
1751   PetscCall(VecRestoreArray(Vres, &vres));
1752   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1753   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1754   PetscCall(DMSwarmRestoreField(sw, "E_field", NULL, NULL, (void **)&E));
1755   PetscCall(PetscLogEventEnd(user->RhsVEvent, ts, 0, 0, 0));
1756   PetscFunctionReturn(PETSC_SUCCESS);
1757 }
1758 
1759 static PetscErrorCode CreateSolution(TS ts)
1760 {
1761   DM       sw;
1762   Vec      u;
1763   PetscInt dim, Np;
1764 
1765   PetscFunctionBegin;
1766   PetscCall(TSGetDM(ts, &sw));
1767   PetscCall(DMGetDimension(sw, &dim));
1768   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1769   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
1770   PetscCall(VecSetBlockSize(u, dim));
1771   PetscCall(VecSetSizes(u, 2 * Np * dim, PETSC_DECIDE));
1772   PetscCall(VecSetUp(u));
1773   PetscCall(TSSetSolution(ts, u));
1774   PetscCall(VecDestroy(&u));
1775   PetscFunctionReturn(PETSC_SUCCESS);
1776 }
1777 
1778 static PetscErrorCode SetProblem(TS ts)
1779 {
1780   AppCtx *user;
1781   DM      sw;
1782 
1783   PetscFunctionBegin;
1784   PetscCall(TSGetDM(ts, &sw));
1785   PetscCall(DMGetApplicationContext(sw, (void **)&user));
1786   // Define unified system for (X, V)
1787   {
1788     Mat      J;
1789     PetscInt dim, Np;
1790 
1791     PetscCall(DMGetDimension(sw, &dim));
1792     PetscCall(DMSwarmGetLocalSize(sw, &Np));
1793     PetscCall(MatCreate(PETSC_COMM_WORLD, &J));
1794     PetscCall(MatSetSizes(J, 2 * Np * dim, 2 * Np * dim, PETSC_DECIDE, PETSC_DECIDE));
1795     PetscCall(MatSetBlockSize(J, 2 * dim));
1796     PetscCall(MatSetFromOptions(J));
1797     PetscCall(MatSetUp(J));
1798     PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, user));
1799     PetscCall(TSSetRHSJacobian(ts, J, J, RHSJacobian, user));
1800     PetscCall(MatDestroy(&J));
1801   }
1802   /* Define split system for X and V */
1803   {
1804     Vec             u;
1805     IS              isx, isv, istmp;
1806     const PetscInt *idx;
1807     PetscInt        dim, Np, rstart;
1808 
1809     PetscCall(TSGetSolution(ts, &u));
1810     PetscCall(DMGetDimension(sw, &dim));
1811     PetscCall(DMSwarmGetLocalSize(sw, &Np));
1812     PetscCall(VecGetOwnershipRange(u, &rstart, NULL));
1813     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 0, 2, &istmp));
1814     PetscCall(ISGetIndices(istmp, &idx));
1815     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isx));
1816     PetscCall(ISRestoreIndices(istmp, &idx));
1817     PetscCall(ISDestroy(&istmp));
1818     PetscCall(ISCreateStride(PETSC_COMM_WORLD, Np, (rstart / dim) + 1, 2, &istmp));
1819     PetscCall(ISGetIndices(istmp, &idx));
1820     PetscCall(ISCreateBlock(PETSC_COMM_WORLD, dim, Np, idx, PETSC_COPY_VALUES, &isv));
1821     PetscCall(ISRestoreIndices(istmp, &idx));
1822     PetscCall(ISDestroy(&istmp));
1823     PetscCall(TSRHSSplitSetIS(ts, "position", isx));
1824     PetscCall(TSRHSSplitSetIS(ts, "momentum", isv));
1825     PetscCall(ISDestroy(&isx));
1826     PetscCall(ISDestroy(&isv));
1827     PetscCall(TSRHSSplitSetRHSFunction(ts, "position", NULL, RHSFunctionX, user));
1828     PetscCall(TSRHSSplitSetRHSFunction(ts, "momentum", NULL, RHSFunctionV, user));
1829   }
1830   PetscFunctionReturn(PETSC_SUCCESS);
1831 }
1832 
1833 static PetscErrorCode DMSwarmTSRedistribute(TS ts)
1834 {
1835   DM        sw;
1836   Vec       u;
1837   PetscReal t, maxt, dt;
1838   PetscInt  n, maxn;
1839 
1840   PetscFunctionBegin;
1841   PetscCall(TSGetDM(ts, &sw));
1842   PetscCall(TSGetTime(ts, &t));
1843   PetscCall(TSGetMaxTime(ts, &maxt));
1844   PetscCall(TSGetTimeStep(ts, &dt));
1845   PetscCall(TSGetStepNumber(ts, &n));
1846   PetscCall(TSGetMaxSteps(ts, &maxn));
1847 
1848   PetscCall(TSReset(ts));
1849   PetscCall(TSSetDM(ts, sw));
1850   PetscCall(TSSetFromOptions(ts));
1851   PetscCall(TSSetTime(ts, t));
1852   PetscCall(TSSetMaxTime(ts, maxt));
1853   PetscCall(TSSetTimeStep(ts, dt));
1854   PetscCall(TSSetStepNumber(ts, n));
1855   PetscCall(TSSetMaxSteps(ts, maxn));
1856 
1857   PetscCall(CreateSolution(ts));
1858   PetscCall(SetProblem(ts));
1859   PetscCall(TSGetSolution(ts, &u));
1860   PetscFunctionReturn(PETSC_SUCCESS);
1861 }
1862 
1863 PetscErrorCode line(PetscInt dim, PetscReal time, const PetscReal dummy[], PetscInt p, PetscScalar x[], void *ctx)
1864 {
1865   DM        sw, cdm;
1866   PetscInt  Np;
1867   PetscReal low[2], high[2];
1868   AppCtx   *user = (AppCtx *)ctx;
1869 
1870   sw = user->swarm;
1871   PetscCall(DMSwarmGetCellDM(sw, &cdm));
1872   // Get the bounding box so we can equally space the particles
1873   PetscCall(DMGetLocalBoundingBox(cdm, low, high));
1874   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1875   // shift it by h/2 so nothing is initialized directly on a boundary
1876   x[0] = ((high[0] - low[0]) / Np) * (p + 0.5);
1877   x[1] = 0.;
1878   return PETSC_SUCCESS;
1879 }
1880 
1881 /*
1882   InitializeSolveAndSwarm - Set the solution values to the swarm coordinates and velocities, and also possibly set the initial values.
1883 
1884   Input Parameters:
1885 + ts         - The TS
1886 - useInitial - Flag to also set the initial conditions to the current coordinates and velocities and setup the problem
1887 
1888   Output Parameters:
1889 . u - The initialized solution vector
1890 
1891   Level: advanced
1892 
1893 .seealso: InitializeSolve()
1894 */
1895 static PetscErrorCode InitializeSolveAndSwarm(TS ts, PetscBool useInitial)
1896 {
1897   DM       sw;
1898   Vec      u, gc, gv, gc0, gv0;
1899   IS       isx, isv;
1900   PetscInt dim;
1901   AppCtx  *user;
1902 
1903   PetscFunctionBeginUser;
1904   PetscCall(TSGetDM(ts, &sw));
1905   PetscCall(DMGetApplicationContext(sw, &user));
1906   PetscCall(DMGetDimension(sw, &dim));
1907   if (useInitial) {
1908     PetscReal v0[2] = {1., 0.};
1909     if (user->perturbed_weights) {
1910       PetscCall(InitializeParticles_PerturbedWeights(sw, user));
1911     } else {
1912       PetscCall(DMSwarmComputeLocalSizeFromOptions(sw));
1913       PetscCall(DMSwarmInitializeCoordinates(sw));
1914       if (user->fake_1D) {
1915         PetscCall(InitializeVelocities_Fake1D(sw, user));
1916       } else {
1917         PetscCall(DMSwarmInitializeVelocitiesFromOptions(sw, v0));
1918       }
1919     }
1920     PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
1921     PetscCall(DMSwarmTSRedistribute(ts));
1922   }
1923   PetscCall(TSGetSolution(ts, &u));
1924   PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
1925   PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
1926   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
1927   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initCoordinates", &gc0));
1928   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
1929   PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "initVelocity", &gv0));
1930   if (useInitial) {
1931     PetscCall(VecCopy(gc, gc0));
1932     PetscCall(VecCopy(gv, gv0));
1933   }
1934   PetscCall(VecISCopy(u, isx, SCATTER_FORWARD, gc));
1935   PetscCall(VecISCopy(u, isv, SCATTER_FORWARD, gv));
1936   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
1937   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initCoordinates", &gc0));
1938   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
1939   PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "initVelocity", &gv0));
1940   PetscFunctionReturn(PETSC_SUCCESS);
1941 }
1942 
1943 static PetscErrorCode InitializeSolve(TS ts, Vec u)
1944 {
1945   PetscFunctionBegin;
1946   PetscCall(TSSetSolution(ts, u));
1947   PetscCall(InitializeSolveAndSwarm(ts, PETSC_TRUE));
1948   PetscFunctionReturn(PETSC_SUCCESS);
1949 }
1950 
1951 static PetscErrorCode ComputeError(TS ts, Vec U, Vec E)
1952 {
1953   MPI_Comm           comm;
1954   DM                 sw;
1955   AppCtx            *user;
1956   const PetscScalar *u;
1957   const PetscReal   *coords, *vel;
1958   PetscScalar       *e;
1959   PetscReal          t;
1960   PetscInt           dim, Np, p;
1961 
1962   PetscFunctionBeginUser;
1963   PetscCall(PetscObjectGetComm((PetscObject)ts, &comm));
1964   PetscCall(TSGetDM(ts, &sw));
1965   PetscCall(DMGetApplicationContext(sw, &user));
1966   PetscCall(DMGetDimension(sw, &dim));
1967   PetscCall(TSGetSolveTime(ts, &t));
1968   PetscCall(VecGetArray(E, &e));
1969   PetscCall(VecGetArrayRead(U, &u));
1970   PetscCall(DMSwarmGetLocalSize(sw, &Np));
1971   PetscCall(DMSwarmGetField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1972   PetscCall(DMSwarmGetField(sw, "initVelocity", NULL, NULL, (void **)&vel));
1973   Np /= 2 * dim;
1974   for (p = 0; p < Np; ++p) {
1975     /* TODO generalize initial conditions and project into plane instead of assuming x-y */
1976     const PetscReal    r0    = DMPlex_NormD_Internal(dim, &coords[p * dim]);
1977     const PetscReal    th0   = PetscAtan2Real(coords[p * dim + 1], coords[p * dim + 0]);
1978     const PetscReal    v0    = DMPlex_NormD_Internal(dim, &vel[p * dim]);
1979     const PetscReal    omega = v0 / r0;
1980     const PetscReal    ct    = PetscCosReal(omega * t + th0);
1981     const PetscReal    st    = PetscSinReal(omega * t + th0);
1982     const PetscScalar *x     = &u[(p * 2 + 0) * dim];
1983     const PetscScalar *v     = &u[(p * 2 + 1) * dim];
1984     const PetscReal    xe[3] = {r0 * ct, r0 * st, 0.0};
1985     const PetscReal    ve[3] = {-v0 * st, v0 * ct, 0.0};
1986     PetscInt           d;
1987 
1988     for (d = 0; d < dim; ++d) {
1989       e[(p * 2 + 0) * dim + d] = x[d] - xe[d];
1990       e[(p * 2 + 1) * dim + d] = v[d] - ve[d];
1991     }
1992     if (user->error) {
1993       const PetscReal en   = 0.5 * DMPlex_DotRealD_Internal(dim, v, v);
1994       const PetscReal exen = 0.5 * PetscSqr(v0);
1995       PetscCall(PetscPrintf(comm, "t %.4g: p%" PetscInt_FMT " error [%.2g %.2g] sol [(%.6lf %.6lf) (%.6lf %.6lf)] exact [(%.6lf %.6lf) (%.6lf %.6lf)] energy/exact energy %g / %g (%.10lf%%)\n", (double)t, p, (double)DMPlex_NormD_Internal(dim, &e[(p * 2 + 0) * dim]), (double)DMPlex_NormD_Internal(dim, &e[(p * 2 + 1) * dim]), (double)x[0], (double)x[1], (double)v[0], (double)v[1], (double)xe[0], (double)xe[1], (double)ve[0], (double)ve[1], (double)en, (double)exen, (double)(PetscAbsReal(exen - en) * 100. / exen)));
1996     }
1997   }
1998   PetscCall(DMSwarmRestoreField(sw, "initCoordinates", NULL, NULL, (void **)&coords));
1999   PetscCall(DMSwarmRestoreField(sw, "initVelocity", NULL, NULL, (void **)&vel));
2000   PetscCall(VecRestoreArrayRead(U, &u));
2001   PetscCall(VecRestoreArray(E, &e));
2002   PetscFunctionReturn(PETSC_SUCCESS);
2003 }
2004 
2005 static PetscErrorCode MigrateParticles(TS ts)
2006 {
2007   DM               sw, cdm;
2008   const PetscReal *L;
2009 
2010   PetscFunctionBeginUser;
2011   PetscCall(TSGetDM(ts, &sw));
2012   PetscCall(DMViewFromOptions(sw, NULL, "-migrate_view_pre"));
2013   {
2014     Vec        u, gc, gv, position, momentum;
2015     IS         isx, isv;
2016     PetscReal *pos, *mom;
2017 
2018     PetscCall(TSGetSolution(ts, &u));
2019     PetscCall(TSRHSSplitGetIS(ts, "position", &isx));
2020     PetscCall(TSRHSSplitGetIS(ts, "momentum", &isv));
2021     PetscCall(VecGetSubVector(u, isx, &position));
2022     PetscCall(VecGetSubVector(u, isv, &momentum));
2023     PetscCall(VecGetArray(position, &pos));
2024     PetscCall(VecGetArray(momentum, &mom));
2025     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
2026     PetscCall(DMSwarmCreateGlobalVectorFromField(sw, "velocity", &gv));
2027     PetscCall(VecISCopy(u, isx, SCATTER_REVERSE, gc));
2028     PetscCall(VecISCopy(u, isv, SCATTER_REVERSE, gv));
2029 
2030     PetscCall(DMSwarmGetCellDM(sw, &cdm));
2031     PetscCall(DMGetPeriodicity(cdm, NULL, NULL, &L));
2032     if ((L[0] || L[1]) >= 0.) {
2033       PetscReal *x, *v, upper[3], lower[3];
2034       PetscInt   Np, dim;
2035 
2036       PetscCall(DMSwarmGetLocalSize(sw, &Np));
2037       PetscCall(DMGetDimension(cdm, &dim));
2038       PetscCall(DMGetBoundingBox(cdm, lower, upper));
2039       PetscCall(VecGetArray(gc, &x));
2040       PetscCall(VecGetArray(gv, &v));
2041       for (PetscInt p = 0; p < Np; ++p) {
2042         for (PetscInt d = 0; d < dim; ++d) {
2043           if (pos[p * dim + d] < lower[d]) {
2044             x[p * dim + d] = pos[p * dim + d] + (upper[d] - lower[d]);
2045           } else if (pos[p * dim + d] > upper[d]) {
2046             x[p * dim + d] = pos[p * dim + d] - (upper[d] - lower[d]);
2047           } else {
2048             x[p * dim + d] = pos[p * dim + d];
2049           }
2050           PetscCheck(x[p * dim + d] >= lower[d] && x[p * dim + d] <= upper[d], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "p: %" PetscInt_FMT "x[%" PetscInt_FMT "] %g", p, d, (double)x[p * dim + d]);
2051           v[p * dim + d] = mom[p * dim + d];
2052         }
2053       }
2054       PetscCall(VecRestoreArray(gc, &x));
2055       PetscCall(VecRestoreArray(gv, &v));
2056     }
2057     PetscCall(VecRestoreArray(position, &pos));
2058     PetscCall(VecRestoreArray(momentum, &mom));
2059     PetscCall(VecRestoreSubVector(u, isx, &position));
2060     PetscCall(VecRestoreSubVector(u, isv, &momentum));
2061     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, "velocity", &gv));
2062     PetscCall(DMSwarmDestroyGlobalVectorFromField(sw, DMSwarmPICField_coor, &gc));
2063   }
2064   PetscCall(DMSwarmMigrate(sw, PETSC_TRUE));
2065   PetscCall(DMSwarmTSRedistribute(ts));
2066   PetscCall(InitializeSolveAndSwarm(ts, PETSC_FALSE));
2067   PetscFunctionReturn(PETSC_SUCCESS);
2068 }
2069 
2070 int main(int argc, char **argv)
2071 {
2072   DM        dm, sw;
2073   TS        ts;
2074   Vec       u;
2075   PetscReal dt;
2076   PetscInt  maxn;
2077   AppCtx    user;
2078 
2079   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
2080   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
2081   PetscCall(PetscBagCreate(PETSC_COMM_SELF, sizeof(Parameter), &user.bag));
2082   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
2083   PetscCall(CreatePoisson(dm, &user));
2084   PetscCall(CreateSwarm(dm, &user, &sw));
2085   PetscCall(SetupParameters(PETSC_COMM_WORLD, &user));
2086   PetscCall(InitializeConstants(sw, &user));
2087   PetscCall(DMSetApplicationContext(sw, &user));
2088 
2089   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
2090   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
2091   PetscCall(TSSetDM(ts, sw));
2092   PetscCall(TSSetMaxTime(ts, 0.1));
2093   PetscCall(TSSetTimeStep(ts, 0.00001));
2094   PetscCall(TSSetMaxSteps(ts, 100));
2095   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
2096 
2097   if (user.efield_monitor) PetscCall(TSMonitorSet(ts, MonitorEField, &user, NULL));
2098   if (user.moment_monitor) PetscCall(TSMonitorSet(ts, MonitorMoments, &user, NULL));
2099   if (user.initial_monitor) PetscCall(TSMonitorSet(ts, MonitorInitialConditions, &user, NULL));
2100   if (user.monitor_positions) PetscCall(TSMonitorSet(ts, MonitorPositions_2D, &user, NULL));
2101   if (user.poisson_monitor) PetscCall(TSMonitorSet(ts, MonitorPoisson, &user, NULL));
2102 
2103   PetscCall(TSSetFromOptions(ts));
2104   PetscCall(TSGetTimeStep(ts, &dt));
2105   PetscCall(TSGetMaxSteps(ts, &maxn));
2106   user.steps    = maxn;
2107   user.stepSize = dt;
2108   PetscCall(SetupContext(dm, sw, &user));
2109   PetscCall(TSSetComputeInitialCondition(ts, InitializeSolve));
2110   PetscCall(TSSetComputeExactError(ts, ComputeError));
2111   PetscCall(TSSetPostStep(ts, MigrateParticles));
2112   PetscCall(CreateSolution(ts));
2113   PetscCall(TSGetSolution(ts, &u));
2114   PetscCall(TSComputeInitialCondition(ts, u));
2115   PetscCall(CheckNonNegativeWeights(sw, &user));
2116   PetscCall(TSSolve(ts, NULL));
2117 
2118   PetscCall(SNESDestroy(&user.snes));
2119   PetscCall(MatDestroy(&user.M));
2120   PetscCall(PetscFEGeomDestroy(&user.fegeom));
2121   PetscCall(TSDestroy(&ts));
2122   PetscCall(DMDestroy(&sw));
2123   PetscCall(DMDestroy(&dm));
2124   PetscCall(DestroyContext(&user));
2125   PetscCall(PetscFinalize());
2126   return 0;
2127 }
2128 
2129 /*TEST
2130 
2131    build:
2132     requires: !complex double
2133 
2134   # This tests that we can put particles in a box and compute the Coulomb force
2135   # Recommend -draw_size 500,500
2136    testset:
2137      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
2138      args: -dm_plex_dim 2 -fake_1D -dm_plex_simplex 0 -dm_plex_box_faces 20,1 \
2139              -dm_plex_box_lower 0,-1 -dm_plex_box_upper 12.5664,1 \
2140              -dm_plex_box_bd periodic,none \
2141            -dm_swarm_coordinate_density constant -dm_swarm_num_particles 100 \
2142            -sigma 1.0e-8 -timeScale 2.0e-14 \
2143            -ts_type basicsymplectic -ts_basicsymplectic_type 1 \
2144              -ts_monitor_sp_swarm -ts_monitor_sp_swarm_retain 0 -ts_monitor_sp_swarm_phase 0 \
2145            -output_step 50 -check_vel_res
2146      test:
2147        suffix: none_1d
2148        args: -em_type none -error
2149      test:
2150        suffix: coulomb_1d
2151        args: -em_type coulomb
2152 
2153    # for viewers
2154    #-ts_monitor_sp_swarm_phase -ts_monitor_sp_swarm -em_snes_monitor -ts_monitor_sp_swarm_multi_species 0 -ts_monitor_sp_swarm_retain 0
2155    testset:
2156      nsize: {{1 2}}
2157      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
2158      args: -dm_plex_dim 2 -fake_1D -dm_plex_simplex 0 -dm_plex_box_faces 36,1 \
2159              -dm_plex_box_lower 0.,-0.5 -dm_plex_box_upper 12.5664,0.5 \
2160              -dm_plex_box_bd periodic,none \
2161            -vdm_plex_dim 1 -vdm_plex_simplex 0 -vdm_plex_box_faces 10 \
2162              -vdm_plex_box_lower -3 -vdm_plex_box_upper 3 \
2163            -dm_swarm_num_species 1 -twostream -charges -1.,1. -sigma 1.0e-8 \
2164              -cosine_coefficients 0.01,0.5 -perturbed_weights -total_weight 1. \
2165            -ts_type basicsymplectic -ts_basicsymplectic_type 2 \
2166              -ts_dt 0.01 -ts_max_time 5 -ts_max_steps 10 \
2167            -em_snes_atol 1.e-15 -em_snes_error_if_not_converged -em_ksp_error_if_not_converged \
2168            -output_step 1 -check_vel_res -dm_swarm_print_coords 1 -dm_swarm_print_weights 1
2169      test:
2170        suffix: two_stream_c0
2171        args: -em_type primal -petscfe_default_quadrature_order 2 -petscspace_degree 2 -em_pc_type svd
2172      test:
2173        suffix: two_stream_rt
2174        requires: superlu_dist
2175        args: -em_type mixed \
2176                -potential_petscspace_degree 0 \
2177                -potential_petscdualspace_lagrange_use_moments \
2178                -potential_petscdualspace_lagrange_moment_order 2 \
2179                -field_petscspace_degree 2 -field_petscfe_default_quadrature_order 1 \
2180                -field_petscspace_type sum \
2181                  -field_petscspace_variables 2 \
2182                  -field_petscspace_components 2 \
2183                  -field_petscspace_sum_spaces 2 \
2184                  -field_petscspace_sum_concatenate true \
2185                  -field_sumcomp_0_petscspace_variables 2 \
2186                  -field_sumcomp_0_petscspace_type tensor \
2187                  -field_sumcomp_0_petscspace_tensor_spaces 2 \
2188                  -field_sumcomp_0_petscspace_tensor_uniform false \
2189                  -field_sumcomp_0_tensorcomp_0_petscspace_degree 1 \
2190                  -field_sumcomp_0_tensorcomp_1_petscspace_degree 0 \
2191                  -field_sumcomp_1_petscspace_variables 2 \
2192                  -field_sumcomp_1_petscspace_type tensor \
2193                  -field_sumcomp_1_petscspace_tensor_spaces 2 \
2194                  -field_sumcomp_1_petscspace_tensor_uniform false \
2195                  -field_sumcomp_1_tensorcomp_0_petscspace_degree 0 \
2196                  -field_sumcomp_1_tensorcomp_1_petscspace_degree 1 \
2197                -field_petscdualspace_form_degree -1 \
2198                -field_petscdualspace_order 1 \
2199                -field_petscdualspace_lagrange_trimmed true \
2200              -em_snes_error_if_not_converged \
2201              -em_ksp_type preonly -em_ksp_error_if_not_converged \
2202              -em_pc_type fieldsplit -em_pc_fieldsplit_type schur \
2203                -em_pc_fieldsplit_schur_fact_type full -em_pc_fieldsplit_schur_precondition full \
2204                -em_fieldsplit_field_pc_type lu \
2205                  -em_fieldsplit_field_pc_factor_mat_solver_type superlu_dist \
2206                -em_fieldsplit_potential_pc_type svd
2207 
2208    # For an eyeball check, we use
2209    # -ts_max_steps 1000 -dm_plex_box_faces 10,1 -vdm_plex_box_faces 2000 -monitor_efield
2210    # For verification, we use
2211    # -ts_max_steps 1000 -dm_plex_box_faces 100,1 -vdm_plex_box_faces 8000 -dm_swarm_num_particles 800000 -monitor_efield
2212    # -ts_monitor_sp_swarm_multi_species 0 -ts_monitor_sp_swarm_retain 0 -ts_monitor_sp_swarm_phase 1 -draw_size 500,500
2213    testset:
2214      nsize: {{1 2}}
2215      requires: defined(PETSC_HAVE_EXECUTABLE_EXPORT)
2216      args: -dm_plex_dim 2 -fake_1D -dm_plex_simplex 0 -dm_plex_box_faces 10,1 \
2217              -dm_plex_box_lower 0.,-0.5 -dm_plex_box_upper 12.5664,0.5 \
2218              -dm_plex_box_bd periodic,none \
2219            -vdm_plex_dim 1 -vdm_plex_simplex 0 -vdm_plex_box_faces 10 \
2220              -vdm_plex_box_lower -10 -vdm_plex_box_upper 10 \
2221              -vpetscspace_degree 2 -vdm_plex_hash_location \
2222            -dm_swarm_num_species 1 -charges -1.,1. \
2223              -cosine_coefficients 0.01,0.5 -perturbed_weights -total_weight 1. \
2224            -ts_type basicsymplectic -ts_basicsymplectic_type 1 \
2225              -ts_dt 0.03 -ts_max_time 500 -ts_max_steps 1 \
2226            -em_snes_atol 1.e-12 -em_snes_error_if_not_converged -em_ksp_error_if_not_converged \
2227            -output_step 1 -check_vel_res -dm_swarm_print_coords 1 -dm_swarm_print_weights 1
2228 
2229      test:
2230        suffix: uniform_equilibrium_1d
2231        args: -cosine_coefficients 0.0,0.5 -em_type primal -petscspace_degree 1 -em_pc_type svd
2232      test:
2233        suffix: uniform_equilibrium_1d_real
2234        args: -dm_plex_dim 1 -dm_plex_simplex 1 -fake_1D 0 -dm_plex_box_faces 10 \
2235                -dm_plex_box_lower 0. -dm_plex_box_upper 12.5664 -dm_plex_box_bd periodic \
2236              -cosine_coefficients 0.0 -em_type primal -petscspace_degree 1 -em_pc_type svd
2237      test:
2238        suffix: uniform_primal_1d
2239        args: -em_type primal -petscspace_degree 1 -em_pc_type svd
2240      test:
2241        suffix: uniform_primal_1d_real
2242        args: -dm_plex_dim 1 -dm_plex_simplex 1 -fake_1D 0 -dm_plex_box_faces 10 \
2243                -dm_plex_box_lower 0. -dm_plex_box_upper 12.5664 -dm_plex_box_bd periodic \
2244              -cosine_coefficients 0.01 -em_type primal -petscspace_degree 1 -em_pc_type svd
2245      test:
2246        requires: superlu_dist
2247        suffix: uniform_mixed_1d
2248        args: -em_type mixed \
2249                -potential_petscspace_degree 0 \
2250                -potential_petscdualspace_lagrange_use_moments \
2251                -potential_petscdualspace_lagrange_moment_order 2 \
2252                -field_petscspace_degree 2 -field_petscfe_default_quadrature_order 1 \
2253                -field_petscspace_type sum \
2254                  -field_petscspace_variables 2 \
2255                  -field_petscspace_components 2 \
2256                  -field_petscspace_sum_spaces 2 \
2257                  -field_petscspace_sum_concatenate true \
2258                  -field_sumcomp_0_petscspace_variables 2 \
2259                  -field_sumcomp_0_petscspace_type tensor \
2260                  -field_sumcomp_0_petscspace_tensor_spaces 2 \
2261                  -field_sumcomp_0_petscspace_tensor_uniform false \
2262                  -field_sumcomp_0_tensorcomp_0_petscspace_degree 1 \
2263                  -field_sumcomp_0_tensorcomp_1_petscspace_degree 0 \
2264                  -field_sumcomp_1_petscspace_variables 2 \
2265                  -field_sumcomp_1_petscspace_type tensor \
2266                  -field_sumcomp_1_petscspace_tensor_spaces 2 \
2267                  -field_sumcomp_1_petscspace_tensor_uniform false \
2268                  -field_sumcomp_1_tensorcomp_0_petscspace_degree 0 \
2269                  -field_sumcomp_1_tensorcomp_1_petscspace_degree 1 \
2270                -field_petscdualspace_form_degree -1 \
2271                -field_petscdualspace_order 1 \
2272                -field_petscdualspace_lagrange_trimmed true \
2273              -em_snes_error_if_not_converged \
2274              -em_ksp_type preonly -em_ksp_error_if_not_converged \
2275              -em_pc_type fieldsplit -em_pc_fieldsplit_type schur \
2276                -em_pc_fieldsplit_schur_fact_type full -em_pc_fieldsplit_schur_precondition full \
2277                -em_fieldsplit_field_pc_type lu \
2278                  -em_fieldsplit_field_pc_factor_mat_solver_type superlu_dist \
2279                -em_fieldsplit_potential_pc_type svd
2280 
2281 TEST*/
2282