xref: /petsc/src/ts/tutorials/ex48.c (revision 327415f76d85372a4417cf1aaa14db707d4d6c04) 
1 static char help[] = "Evolution of magnetic islands.\n\
2 The aim of this model is to self-consistently study the interaction between the tearing mode and small scale drift-wave turbulence.\n\n\n";
3 
4 /*F
5 This is a three field model for the density $\tilde n$, vorticity $\tilde\Omega$, and magnetic flux $\tilde\psi$, using auxiliary variables potential $\tilde\phi$ and current $j_z$.
6 \begin{equation}
7   \begin{aligned}
8     \partial_t \tilde n       &= \left\{ \tilde n, \tilde\phi \right\} + \beta \left\{ j_z, \tilde\psi \right\} + \left\{ \ln n_0, \tilde\phi \right\} + \mu \nabla^2_\perp \tilde n \\
9   \partial_t \tilde\Omega   &= \left\{ \tilde\Omega, \tilde\phi \right\} + \beta \left\{ j_z, \tilde\psi \right\} + \mu \nabla^2_\perp \tilde\Omega \\
10   \partial_t \tilde\psi     &= \left\{ \psi_0 + \tilde\psi, \tilde\phi - \tilde n \right\} - \left\{ \ln n_0, \tilde\psi \right\} + \frac{\eta}{\beta} \nabla^2_\perp \tilde\psi \\
11   \nabla^2_\perp\tilde\phi        &= \tilde\Omega \\
12   j_z  &= -\nabla^2_\perp  \left(\tilde\psi + \psi_0  \right)\\
13   \end{aligned}
14 \end{equation}
15 F*/
16 
17 #include <petscdmplex.h>
18 #include <petscts.h>
19 #include <petscds.h>
20 
21 typedef struct {
22   PetscInt       debug;             /* The debugging level */
23   PetscBool      plotRef;           /* Plot the reference fields */
24   PetscReal      lower[3], upper[3];
25   /* Problem definition */
26   PetscErrorCode (**initialFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
27   PetscReal      mu, eta, beta;
28   PetscReal      a,b,Jo,Jop,m,ke,kx,ky,DeltaPrime,eps;
29   /* solver */
30   PetscBool      implicit;
31 } AppCtx;
32 
33 static AppCtx *s_ctx;
34 
35 static PetscScalar poissonBracket(PetscInt dim, const PetscScalar df[], const PetscScalar dg[])
36 {
37   PetscScalar ret = df[0]*dg[1] - df[1]*dg[0];
38   return ret;
39 }
40 
41 enum field_idx {DENSITY,OMEGA,PSI,PHI,JZ};
42 
43 static void f0_n(PetscInt dim, PetscInt Nf, PetscInt NfAux,
44                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
45                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
46                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
47 {
48   const PetscScalar *pnDer   = &u_x[uOff_x[DENSITY]];
49   const PetscScalar *ppsiDer = &u_x[uOff_x[PSI]];
50   const PetscScalar *pphiDer = &u_x[uOff_x[PHI]];
51   const PetscScalar *jzDer   = &u_x[uOff_x[JZ]];
52   const PetscScalar *logRefDenDer = &a_x[aOff_x[DENSITY]];
53   f0[0] += - poissonBracket(dim,pnDer, pphiDer) - s_ctx->beta*poissonBracket(dim,jzDer, ppsiDer) - poissonBracket(dim,logRefDenDer, pphiDer);
54   if (u_t) f0[0] += u_t[DENSITY];
55 }
56 
57 static void f1_n(PetscInt dim, PetscInt Nf, PetscInt NfAux,
58                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
59                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
60                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
61 {
62   const PetscScalar *pnDer = &u_x[uOff_x[DENSITY]];
63   PetscInt           d;
64 
65   for (d = 0; d < dim-1; ++d) f1[d] = -s_ctx->mu*pnDer[d];
66 }
67 
68 static void f0_Omega(PetscInt dim, PetscInt Nf, PetscInt NfAux,
69                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
70                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
71                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
72 {
73   const PetscScalar *pOmegaDer = &u_x[uOff_x[OMEGA]];
74   const PetscScalar *ppsiDer   = &u_x[uOff_x[PSI]];
75   const PetscScalar *pphiDer   = &u_x[uOff_x[PHI]];
76   const PetscScalar *jzDer     = &u_x[uOff_x[JZ]];
77 
78   f0[0] += - poissonBracket(dim,pOmegaDer, pphiDer) - s_ctx->beta*poissonBracket(dim,jzDer, ppsiDer);
79   if (u_t) f0[0] += u_t[OMEGA];
80 }
81 
82 static void f1_Omega(PetscInt dim, PetscInt Nf, PetscInt NfAux,
83                      const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
84                      const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
85                      PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
86 {
87   const PetscScalar *pOmegaDer = &u_x[uOff_x[OMEGA]];
88   PetscInt           d;
89 
90   for (d = 0; d < dim-1; ++d) f1[d] = -s_ctx->mu*pOmegaDer[d];
91 }
92 
93 static void f0_psi(PetscInt dim, PetscInt Nf, PetscInt NfAux,
94                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
95                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
96                    PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
97 {
98   const PetscScalar *pnDer     = &u_x[uOff_x[DENSITY]];
99   const PetscScalar *ppsiDer   = &u_x[uOff_x[PSI]];
100   const PetscScalar *pphiDer   = &u_x[uOff_x[PHI]];
101   const PetscScalar *refPsiDer = &a_x[aOff_x[PSI]];
102   const PetscScalar *logRefDenDer= &a_x[aOff_x[DENSITY]];
103   PetscScalar       psiDer[3];
104   PetscScalar       phi_n_Der[3];
105   PetscInt          d;
106   if (dim < 2) {MPI_Abort(MPI_COMM_WORLD,1); return;} /* this is needed so that the clang static analyzer does not generate a warning about variables used by not set */
107   for (d = 0; d < dim; ++d) {
108     psiDer[d]    = refPsiDer[d] + ppsiDer[d];
109     phi_n_Der[d] = pphiDer[d]   - pnDer[d];
110   }
111   f0[0] = - poissonBracket(dim,psiDer, phi_n_Der) + poissonBracket(dim,logRefDenDer, ppsiDer);
112   if (u_t) f0[0] += u_t[PSI];
113 }
114 
115 static void f1_psi(PetscInt dim, PetscInt Nf, PetscInt NfAux,
116                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
117                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
118                    PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
119 {
120   const PetscScalar *ppsi = &u_x[uOff_x[PSI]];
121   PetscInt           d;
122 
123   for (d = 0; d < dim-1; ++d) f1[d] = -(s_ctx->eta/s_ctx->beta)*ppsi[d];
124 }
125 
126 static void f0_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux,
127                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
128                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
129                    PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
130 {
131   f0[0] = -u[uOff[OMEGA]];
132 }
133 
134 static void f1_phi(PetscInt dim, PetscInt Nf, PetscInt NfAux,
135                    const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
136                    const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
137                    PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
138 {
139   const PetscScalar *pphi = &u_x[uOff_x[PHI]];
140   PetscInt           d;
141 
142   for (d = 0; d < dim-1; ++d) f1[d] = pphi[d];
143 }
144 
145 static void f0_jz(PetscInt dim, PetscInt Nf, PetscInt NfAux,
146                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
147                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
148                   PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
149 {
150   f0[0] = u[uOff[JZ]];
151 }
152 
153 static void f1_jz(PetscInt dim, PetscInt Nf, PetscInt NfAux,
154                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
155                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
156                   PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
157 {
158   const PetscScalar *ppsi = &u_x[uOff_x[PSI]];
159   const PetscScalar *refPsiDer = &a_x[aOff_x[PSI]]; /* aOff_x[PSI] == 2*PSI */
160   PetscInt           d;
161 
162   for (d = 0; d < dim-1; ++d) f1[d] = ppsi[d] + refPsiDer[d];
163 }
164 
165 static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
166 {
167   PetscFunctionBeginUser;
168   options->debug    = 1;
169   options->plotRef  = PETSC_FALSE;
170   options->implicit = PETSC_FALSE;
171   options->mu       = 0;
172   options->eta      = 0;
173   options->beta     = 1;
174   options->a        = 1;
175   options->b        = PETSC_PI;
176   options->Jop      = 0;
177   options->m        = 1;
178   options->eps      = 1.e-6;
179 
180   PetscOptionsBegin(comm, "", "Poisson Problem Options", "DMPLEX");
181   PetscCall(PetscOptionsInt("-debug", "The debugging level", "ex48.c", options->debug, &options->debug, NULL));
182   PetscCall(PetscOptionsBool("-plot_ref", "Plot the reference fields", "ex48.c", options->plotRef, &options->plotRef, NULL));
183   PetscCall(PetscOptionsReal("-mu", "mu", "ex48.c", options->mu, &options->mu, NULL));
184   PetscCall(PetscOptionsReal("-eta", "eta", "ex48.c", options->eta, &options->eta, NULL));
185   PetscCall(PetscOptionsReal("-beta", "beta", "ex48.c", options->beta, &options->beta, NULL));
186   PetscCall(PetscOptionsReal("-Jop", "Jop", "ex48.c", options->Jop, &options->Jop, NULL));
187   PetscCall(PetscOptionsReal("-m", "m", "ex48.c", options->m, &options->m, NULL));
188   PetscCall(PetscOptionsReal("-eps", "eps", "ex48.c", options->eps, &options->eps, NULL));
189   PetscCall(PetscOptionsBool("-implicit", "Use implicit time integrator", "ex48.c", options->implicit, &options->implicit, NULL));
190   PetscOptionsEnd();
191   options->ke = PetscSqrtScalar(options->Jop);
192   if (options->Jop==0.0) {
193     options->Jo = 1.0/PetscPowScalar(options->a,2);
194   } else {
195     options->Jo = options->Jop*PetscCosReal(options->ke*options->a)/(1.0-PetscCosReal(options->ke*options->a));
196   }
197   options->ky = PETSC_PI*options->m/options->b;
198   if (PetscPowReal(options->ky, 2) < options->Jop) {
199     options->kx = PetscSqrtScalar(options->Jop-PetscPowScalar(options->ky,2));
200     options->DeltaPrime = -2.0*options->kx*options->a*PetscCosReal(options->kx*options->a)/PetscSinReal(options->kx*options->a);
201   } else if (PetscPowReal(options->ky, 2) > options->Jop) {
202     options->kx = PetscSqrtScalar(PetscPowScalar(options->ky,2)-options->Jop);
203     options->DeltaPrime = -2.0*options->kx*options->a*PetscCoshReal(options->kx*options->a)/PetscSinhReal(options->kx*options->a);
204   } else { /*they're equal (or there's a NaN), lim(x*cot(x))_x->0=1*/
205     options->kx = 0;
206     options->DeltaPrime = -2.0;
207   }
208   PetscCall(PetscPrintf(comm, "DeltaPrime=%g\n",(double)options->DeltaPrime));
209 
210   PetscFunctionReturn(0);
211 }
212 
213 static void f_n(PetscInt dim, PetscInt Nf, PetscInt NfAux,
214                 const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
215                 const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
216                 PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar *f0)
217 {
218   const PetscScalar *pn = &u[uOff[DENSITY]];
219   *f0 = *pn;
220 }
221 
222 static PetscErrorCode PostStep(TS ts)
223 {
224   DM        dm;
225   AppCtx   *ctx;
226   PetscInt  stepi,num;
227   Vec       X;
228 
229   PetscFunctionBegin;
230   PetscCall(TSGetApplicationContext(ts, &ctx));
231   if (ctx->debug<1) PetscFunctionReturn(0);
232   PetscCall(TSGetSolution(ts, &X));
233   PetscCall(VecGetDM(X, &dm));
234   PetscCall(TSGetStepNumber(ts, &stepi));
235   PetscCall(DMGetOutputSequenceNumber(dm, &num, NULL));
236   if (num < 0) PetscCall(DMSetOutputSequenceNumber(dm, 0, 0.0));
237   PetscCall(PetscObjectSetName((PetscObject) X, "u"));
238   PetscCall(VecViewFromOptions(X, NULL, "-vec_view"));
239   /* print integrals */
240   {
241     PetscDS          prob;
242     DM               plex;
243     PetscScalar den, tt[5];
244     PetscCall(DMConvert(dm, DMPLEX, &plex));
245     PetscCall(DMGetDS(plex, &prob));
246     PetscCall(PetscDSSetObjective(prob, 0, &f_n));
247     PetscCall(DMPlexComputeIntegralFEM(plex,X,tt,ctx));
248     den = tt[0];
249     PetscCall(DMDestroy(&plex));
250     PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "%" PetscInt_FMT ") total perturbed mass = %g\n", stepi, (double) PetscRealPart(den)));
251   }
252   PetscFunctionReturn(0);
253 }
254 
255 static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *ctx, DM *dm)
256 {
257   PetscFunctionBeginUser;
258   PetscCall(DMCreate(comm, dm));
259   PetscCall(DMSetType(*dm, DMPLEX));
260   PetscCall(DMSetFromOptions(*dm));
261   PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
262 
263   PetscCall(DMGetBoundingBox(*dm, ctx->lower, ctx->upper));
264   ctx->a = (ctx->upper[0] - ctx->lower[0])/2.0;
265   ctx->b = (ctx->upper[1] - ctx->lower[1])/2.0;
266   PetscFunctionReturn(0);
267 }
268 
269 static PetscErrorCode log_n_0(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
270 {
271   AppCtx *lctx = (AppCtx*)ctx;
272   u[0] = 2.*lctx->a + x[0];
273   return 0;
274 }
275 
276 static PetscErrorCode Omega_0(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
277 {
278   u[0] = 0.0;
279   return 0;
280 }
281 
282 static PetscErrorCode psi_0(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
283 {
284   AppCtx *lctx = (AppCtx*)ctx;
285   /* This sets up a symmetrix By flux aroound the mid point in x, which represents a current density flux along z.  The stability
286      is analytically known and reported in ProcessOptions. */
287   if (lctx->ke!=0.0) {
288     u[0] = (PetscCosReal(lctx->ke*(x[0]-lctx->a))-PetscCosReal(lctx->ke*lctx->a))/(1.0-PetscCosReal(lctx->ke*lctx->a));
289   } else {
290     u[0] = 1.0-PetscPowScalar((x[0]-lctx->a)/lctx->a,2);
291   }
292   return 0;
293 }
294 
295 static PetscErrorCode initialSolution_n(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
296 {
297   u[0] = 0.0;
298   return 0;
299 }
300 
301 static PetscErrorCode initialSolution_Omega(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
302 {
303   u[0] = 0.0;
304   return 0;
305 }
306 
307 static PetscErrorCode initialSolution_psi(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *a_ctx)
308 {
309   AppCtx *ctx = (AppCtx*)a_ctx;
310   PetscScalar r = ctx->eps*(PetscScalar) (rand()) / (PetscScalar) (RAND_MAX);
311   if (x[0] == ctx->lower[0] || x[0] == ctx->upper[0]) r = 0;
312   u[0] = r;
313   /* PetscPrintf(PETSC_COMM_WORLD, "rand psi %lf\n",u[0]); */
314   return 0;
315 }
316 
317 static PetscErrorCode initialSolution_phi(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
318 {
319   u[0] = 0.0;
320   return 0;
321 }
322 
323 static PetscErrorCode initialSolution_jz(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
324 {
325   u[0] = 0.0;
326   return 0;
327 }
328 
329 static PetscErrorCode SetupProblem(DM dm, AppCtx *ctx)
330 {
331   PetscDS        ds;
332   DMLabel        label;
333   const PetscInt id = 1;
334 
335   PetscFunctionBeginUser;
336   PetscCall(DMGetLabel(dm, "marker", &label));
337   PetscCall(DMGetDS(dm, &ds));
338   PetscCall(PetscDSSetResidual(ds, 0, f0_n,     f1_n));
339   PetscCall(PetscDSSetResidual(ds, 1, f0_Omega, f1_Omega));
340   PetscCall(PetscDSSetResidual(ds, 2, f0_psi,   f1_psi));
341   PetscCall(PetscDSSetResidual(ds, 3, f0_phi,   f1_phi));
342   PetscCall(PetscDSSetResidual(ds, 4, f0_jz,    f1_jz));
343   ctx->initialFuncs[0] = initialSolution_n;
344   ctx->initialFuncs[1] = initialSolution_Omega;
345   ctx->initialFuncs[2] = initialSolution_psi;
346   ctx->initialFuncs[3] = initialSolution_phi;
347   ctx->initialFuncs[4] = initialSolution_jz;
348   for (PetscInt f = 0; f < 5; ++f) {
349     PetscCall(PetscDSSetImplicit(ds, f, ctx->implicit));
350     PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, f, 0, NULL, (void (*)(void)) ctx->initialFuncs[f], NULL, ctx, NULL));
351   }
352   PetscCall(PetscDSSetContext(ds, 0, ctx));
353   PetscFunctionReturn(0);
354 }
355 
356 static PetscErrorCode SetupEquilibriumFields(DM dm, DM dmAux, AppCtx *ctx)
357 {
358   PetscErrorCode (*eqFuncs[3])(PetscInt, PetscReal, const PetscReal [], PetscInt, PetscScalar [], void *) = {log_n_0, Omega_0, psi_0};
359   Vec            eq;
360   AppCtx *ctxarr[3];
361 
362   ctxarr[0] = ctxarr[1] = ctxarr[2] = ctx; /* each variable could have a different context */
363   PetscFunctionBegin;
364   PetscCall(DMCreateLocalVector(dmAux, &eq));
365   PetscCall(DMProjectFunctionLocal(dmAux, 0.0, eqFuncs, (void **)ctxarr, INSERT_ALL_VALUES, eq));
366   PetscCall(DMSetAuxiliaryVec(dm, NULL, 0, 0, eq));
367   if (ctx->plotRef) {  /* plot reference functions */
368     PetscViewer       viewer = NULL;
369     PetscBool         isHDF5,isVTK;
370     char              buf[256];
371     Vec               global;
372     PetscInt          dim;
373 
374     PetscCall(DMGetDimension(dm, &dim));
375     PetscCall(DMCreateGlobalVector(dmAux,&global));
376     PetscCall(VecSet(global,.0)); /* BCs! */
377     PetscCall(DMLocalToGlobalBegin(dmAux,eq,INSERT_VALUES,global));
378     PetscCall(DMLocalToGlobalEnd(dmAux,eq,INSERT_VALUES,global));
379     PetscCall(PetscViewerCreate(PetscObjectComm((PetscObject)dmAux),&viewer));
380 #ifdef PETSC_HAVE_HDF5
381     PetscCall(PetscViewerSetType(viewer,PETSCVIEWERHDF5));
382 #else
383     PetscCall(PetscViewerSetType(viewer,PETSCVIEWERVTK));
384 #endif
385     PetscCall(PetscViewerSetFromOptions(viewer));
386     PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERHDF5,&isHDF5));
387     PetscCall(PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERVTK,&isVTK));
388     if (isHDF5) {
389       PetscCall(PetscSNPrintf(buf, 256, "uEquilibrium-%" PetscInt_FMT "D.h5", dim));
390     } else if (isVTK) {
391       PetscCall(PetscSNPrintf(buf, 256, "uEquilibrium-%" PetscInt_FMT "D.vtu", dim));
392       PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_VTK_VTU));
393     }
394     PetscCall(PetscViewerFileSetMode(viewer,FILE_MODE_WRITE));
395     PetscCall(PetscViewerFileSetName(viewer,buf));
396     if (isHDF5) PetscCall(DMView(dmAux,viewer));
397     /* view equilibrium fields, this will overwrite fine grids with coarse grids! */
398     PetscCall(PetscObjectSetName((PetscObject) global, "u0"));
399     PetscCall(VecView(global,viewer));
400     PetscCall(PetscViewerDestroy(&viewer));
401     PetscCall(VecDestroy(&global));
402   }
403   PetscCall(VecDestroy(&eq));
404   PetscFunctionReturn(0);
405 }
406 
407 static PetscErrorCode SetupAuxDM(DM dm, PetscInt NfAux, PetscFE feAux[], AppCtx *user)
408 {
409   DM             dmAux, coordDM;
410   PetscInt       f;
411 
412   PetscFunctionBegin;
413   /* MUST call DMGetCoordinateDM() in order to get p4est setup if present */
414   PetscCall(DMGetCoordinateDM(dm, &coordDM));
415   if (!feAux) PetscFunctionReturn(0);
416   PetscCall(DMClone(dm, &dmAux));
417   PetscCall(DMSetCoordinateDM(dmAux, coordDM));
418   for (f = 0; f < NfAux; ++f) PetscCall(DMSetField(dmAux, f, NULL, (PetscObject) feAux[f]));
419   PetscCall(DMCreateDS(dmAux));
420   PetscCall(SetupEquilibriumFields(dm, dmAux, user));
421   PetscCall(DMDestroy(&dmAux));
422   PetscFunctionReturn(0);
423 }
424 
425 static PetscErrorCode SetupDiscretization(DM dm, AppCtx *ctx)
426 {
427   DM              cdm = dm;
428   PetscFE         fe[5], feAux[3];
429   PetscInt        dim, Nf = 5, NfAux = 3, f;
430   PetscBool       simplex;
431   MPI_Comm        comm;
432 
433   PetscFunctionBeginUser;
434   /* Create finite element */
435   PetscCall(PetscObjectGetComm((PetscObject) dm, &comm));
436   PetscCall(DMGetDimension(dm, &dim));
437   PetscCall(DMPlexIsSimplex(dm, &simplex));
438   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &fe[0]));
439   PetscCall(PetscObjectSetName((PetscObject) fe[0], "density"));
440   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &fe[1]));
441   PetscCall(PetscObjectSetName((PetscObject) fe[1], "vorticity"));
442   PetscCall(PetscFECopyQuadrature(fe[0], fe[1]));
443   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &fe[2]));
444   PetscCall(PetscObjectSetName((PetscObject) fe[2], "flux"));
445   PetscCall(PetscFECopyQuadrature(fe[0], fe[2]));
446   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &fe[3]));
447   PetscCall(PetscObjectSetName((PetscObject) fe[3], "potential"));
448   PetscCall(PetscFECopyQuadrature(fe[0], fe[3]));
449   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &fe[4]));
450   PetscCall(PetscObjectSetName((PetscObject) fe[4], "current"));
451   PetscCall(PetscFECopyQuadrature(fe[0], fe[4]));
452 
453   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &feAux[0]));
454   PetscCall(PetscObjectSetName((PetscObject) feAux[0], "n_0"));
455   PetscCall(PetscFECopyQuadrature(fe[0], feAux[0]));
456   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &feAux[1]));
457   PetscCall(PetscObjectSetName((PetscObject) feAux[1], "vorticity_0"));
458   PetscCall(PetscFECopyQuadrature(fe[0], feAux[1]));
459   PetscCall(PetscFECreateDefault(comm, dim, 1, simplex, NULL, -1, &feAux[2]));
460   PetscCall(PetscObjectSetName((PetscObject) feAux[2], "flux_0"));
461   PetscCall(PetscFECopyQuadrature(fe[0], feAux[2]));
462   /* Set discretization and boundary conditions for each mesh */
463   for (f = 0; f < Nf; ++f) PetscCall(DMSetField(dm, f, NULL, (PetscObject) fe[f]));
464   PetscCall(DMCreateDS(dm));
465   PetscCall(SetupProblem(dm, ctx));
466   while (cdm) {
467     PetscCall(SetupAuxDM(dm, NfAux, feAux, ctx));
468     PetscCall(DMCopyDisc(dm, cdm));
469     PetscCall(DMGetCoarseDM(cdm, &cdm));
470   }
471   for (f = 0; f < Nf; ++f) PetscCall(PetscFEDestroy(&fe[f]));
472   for (f = 0; f < NfAux; ++f) PetscCall(PetscFEDestroy(&feAux[f]));
473   PetscFunctionReturn(0);
474 }
475 
476 int main(int argc, char **argv)
477 {
478   DM             dm;
479   TS             ts;
480   Vec            u, r;
481   AppCtx         ctx;
482   PetscReal      t       = 0.0;
483   PetscReal      L2error = 0.0;
484   AppCtx        *ctxarr[5];
485 
486   ctxarr[0] = ctxarr[1] = ctxarr[2] = ctxarr[3] = ctxarr[4] = &ctx; /* each variable could have a different context */
487   s_ctx = &ctx;
488   PetscFunctionBeginUser;
489   PetscCall(PetscInitialize(&argc, &argv, NULL,help));
490   PetscCall(ProcessOptions(PETSC_COMM_WORLD, &ctx));
491   /* create mesh and problem */
492   PetscCall(CreateMesh(PETSC_COMM_WORLD, &ctx, &dm));
493   PetscCall(DMSetApplicationContext(dm, &ctx));
494   PetscCall(PetscMalloc1(5, &ctx.initialFuncs));
495   PetscCall(SetupDiscretization(dm, &ctx));
496   PetscCall(DMCreateGlobalVector(dm, &u));
497   PetscCall(PetscObjectSetName((PetscObject) u, "u"));
498   PetscCall(VecDuplicate(u, &r));
499   PetscCall(PetscObjectSetName((PetscObject) r, "r"));
500   /* create TS */
501   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
502   PetscCall(TSSetDM(ts, dm));
503   PetscCall(TSSetApplicationContext(ts, &ctx));
504   PetscCall(DMTSSetBoundaryLocal(dm, DMPlexTSComputeBoundary, &ctx));
505   if (ctx.implicit) {
506     PetscCall(DMTSSetIFunctionLocal(dm, DMPlexTSComputeIFunctionFEM, &ctx));
507     PetscCall(DMTSSetIJacobianLocal(dm, DMPlexTSComputeIJacobianFEM, &ctx));
508   } else {
509     PetscCall(DMTSSetRHSFunctionLocal(dm, DMPlexTSComputeRHSFunctionFVM, &ctx));
510   }
511   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
512   PetscCall(TSSetFromOptions(ts));
513   PetscCall(TSSetPostStep(ts, PostStep));
514   /* make solution & solve */
515   PetscCall(DMProjectFunction(dm, t, ctx.initialFuncs, (void **)ctxarr, INSERT_ALL_VALUES, u));
516   PetscCall(TSSetSolution(ts,u));
517   PetscCall(DMViewFromOptions(dm, NULL, "-dm_view"));
518   PetscCall(PostStep(ts)); /* print the initial state */
519   PetscCall(TSSolve(ts, u));
520   PetscCall(TSGetTime(ts, &t));
521   PetscCall(DMComputeL2Diff(dm, t, ctx.initialFuncs, (void **)ctxarr, u, &L2error));
522   if (L2error < 1.0e-11) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: < 1.0e-11\n"));
523   else                   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "L_2 Error: %g\n", (double)L2error));
524   PetscCall(VecDestroy(&u));
525   PetscCall(VecDestroy(&r));
526   PetscCall(TSDestroy(&ts));
527   PetscCall(DMDestroy(&dm));
528   PetscCall(PetscFree(ctx.initialFuncs));
529   PetscCall(PetscFinalize());
530   return 0;
531 }
532 
533 /*TEST
534 
535   test:
536     suffix: 0
537     args: -debug 1 -dm_refine 1 -dm_plex_simplex 0 -dm_plex_box_faces 3,3 -dm_plex_box_bd periodic,none -dm_plex_box_upper 2.0,6.283185307179586 \
538           -ts_max_steps 1 -ts_max_time 10. -ts_dt 1.0
539   test:
540     # Remapping with periodicity is broken
541     suffix: 1
542     args: -debug 1 -dm_plex_shape cylinder -dm_plex_dim 3 -dm_refine 1 -dm_refine_remap 0 -dm_plex_cylinder_bd periodic -dm_plex_boundary_label marker \
543            -ts_max_steps 1 -ts_max_time 10. -ts_dt 1.0
544 
545 TEST*/
546