xref: /petsc/src/ts/tutorials/power_grid/ex6.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
1 static char help[] = "Time-dependent PDE in 2d for calculating joint PDF. \n";
2 /*
3    p_t = -x_t*p_x -y_t*p_y + f(t)*p_yy
4    xmin < x < xmax, ymin < y < ymax;
5    x_t = (y - ws)  y_t = (ws/2H)*(Pm - Pmax*sin(x))
6 
7    Boundary conditions: -bc_type 0 => Zero dirichlet boundary
8                         -bc_type 1 => Steady state boundary condition
9    Steady state boundary condition found by setting p_t = 0
10 */
11 
12 #include <petscdm.h>
13 #include <petscdmda.h>
14 #include <petscts.h>
15 
16 /*
17    User-defined data structures and routines
18 */
19 typedef struct {
20   PetscScalar ws;         /* Synchronous speed */
21   PetscScalar H;          /* Inertia constant */
22   PetscScalar D;          /* Damping constant */
23   PetscScalar Pmax;       /* Maximum power output of generator */
24   PetscScalar PM_min;     /* Mean mechanical power input */
25   PetscScalar lambda;     /* correlation time */
26   PetscScalar q;          /* noise strength */
27   PetscScalar mux;        /* Initial average angle */
28   PetscScalar sigmax;     /* Standard deviation of initial angle */
29   PetscScalar muy;        /* Average speed */
30   PetscScalar sigmay;     /* standard deviation of initial speed */
31   PetscScalar rho;        /* Cross-correlation coefficient */
32   PetscScalar t0;         /* Initial time */
33   PetscScalar tmax;       /* Final time */
34   PetscScalar xmin;       /* left boundary of angle */
35   PetscScalar xmax;       /* right boundary of angle */
36   PetscScalar ymin;       /* bottom boundary of speed */
37   PetscScalar ymax;       /* top boundary of speed */
38   PetscScalar dx;         /* x step size */
39   PetscScalar dy;         /* y step size */
40   PetscInt    bc;         /* Boundary conditions */
41   PetscScalar disper_coe; /* Dispersion coefficient */
42   DM          da;
43 } AppCtx;
44 
45 PetscErrorCode Parameter_settings(AppCtx *);
46 PetscErrorCode ini_bou(Vec, AppCtx *);
47 PetscErrorCode IFunction(TS, PetscReal, Vec, Vec, Vec, void *);
48 PetscErrorCode IJacobian(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *);
49 PetscErrorCode PostStep(TS);
50 
51 int main(int argc, char **argv) {
52   Vec         x;    /* Solution vector */
53   TS          ts;   /* Time-stepping context */
54   AppCtx      user; /* Application context */
55   Mat         J;
56   PetscViewer viewer;
57 
58   PetscFunctionBeginUser;
59   PetscCall(PetscInitialize(&argc, &argv, "petscopt_ex6", help));
60   /* Get physics and time parameters */
61   PetscCall(Parameter_settings(&user));
62   /* Create a 2D DA with dof = 1 */
63   PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 1, 1, NULL, NULL, &user.da));
64   PetscCall(DMSetFromOptions(user.da));
65   PetscCall(DMSetUp(user.da));
66   /* Set x and y coordinates */
67   PetscCall(DMDASetUniformCoordinates(user.da, user.xmin, user.xmax, user.ymin, user.ymax, 0.0, 1.0));
68 
69   /* Get global vector x from DM  */
70   PetscCall(DMCreateGlobalVector(user.da, &x));
71 
72   PetscCall(ini_bou(x, &user));
73   PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "ini_x", FILE_MODE_WRITE, &viewer));
74   PetscCall(VecView(x, viewer));
75   PetscCall(PetscViewerDestroy(&viewer));
76 
77   /* Get Jacobian matrix structure from the da */
78   PetscCall(DMSetMatType(user.da, MATAIJ));
79   PetscCall(DMCreateMatrix(user.da, &J));
80 
81   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
82   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
83   PetscCall(TSSetIFunction(ts, NULL, IFunction, &user));
84   PetscCall(TSSetIJacobian(ts, J, J, IJacobian, &user));
85   PetscCall(TSSetApplicationContext(ts, &user));
86   PetscCall(TSSetMaxTime(ts, user.tmax));
87   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
88   PetscCall(TSSetTime(ts, user.t0));
89   PetscCall(TSSetTimeStep(ts, .005));
90   PetscCall(TSSetFromOptions(ts));
91   PetscCall(TSSetPostStep(ts, PostStep));
92   PetscCall(TSSolve(ts, x));
93 
94   PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "fin_x", FILE_MODE_WRITE, &viewer));
95   PetscCall(VecView(x, viewer));
96   PetscCall(PetscViewerDestroy(&viewer));
97 
98   PetscCall(VecDestroy(&x));
99   PetscCall(MatDestroy(&J));
100   PetscCall(DMDestroy(&user.da));
101   PetscCall(TSDestroy(&ts));
102   PetscCall(PetscFinalize());
103   return 0;
104 }
105 
106 PetscErrorCode PostStep(TS ts) {
107   Vec         X;
108   AppCtx     *user;
109   PetscScalar sum;
110   PetscReal   t;
111 
112   PetscFunctionBegin;
113   PetscCall(TSGetApplicationContext(ts, &user));
114   PetscCall(TSGetTime(ts, &t));
115   PetscCall(TSGetSolution(ts, &X));
116   PetscCall(VecSum(X, &sum));
117   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "sum(p)*dw*dtheta at t = %3.2f = %3.6f\n", (double)t, (double)(sum * user->dx * user->dy)));
118   PetscFunctionReturn(0);
119 }
120 
121 PetscErrorCode ini_bou(Vec X, AppCtx *user) {
122   DM            cda;
123   DMDACoor2d  **coors;
124   PetscScalar **p;
125   Vec           gc;
126   PetscInt      i, j;
127   PetscInt      xs, ys, xm, ym, M, N;
128   PetscScalar   xi, yi;
129   PetscScalar   sigmax = user->sigmax, sigmay = user->sigmay;
130   PetscScalar   rho = user->rho;
131   PetscScalar   mux = user->mux, muy = user->muy;
132   PetscMPIInt   rank;
133 
134   PetscFunctionBeginUser;
135   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
136   PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
137   user->dx = (user->xmax - user->xmin) / (M - 1);
138   user->dy = (user->ymax - user->ymin) / (N - 1);
139   PetscCall(DMGetCoordinateDM(user->da, &cda));
140   PetscCall(DMGetCoordinates(user->da, &gc));
141   PetscCall(DMDAVecGetArray(cda, gc, &coors));
142   PetscCall(DMDAVecGetArray(user->da, X, &p));
143   PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0));
144   for (i = xs; i < xs + xm; i++) {
145     for (j = ys; j < ys + ym; j++) {
146       xi = coors[j][i].x;
147       yi = coors[j][i].y;
148       if (i == 0 || j == 0 || i == M - 1 || j == N - 1) p[j][i] = 0.0;
149       else
150         p[j][i] = (0.5 / (PETSC_PI * sigmax * sigmay * PetscSqrtScalar(1.0 - rho * rho))) * PetscExpScalar(-0.5 / (1 - rho * rho) * (PetscPowScalar((xi - mux) / sigmax, 2) + PetscPowScalar((yi - muy) / sigmay, 2) - 2 * rho * (xi - mux) * (yi - muy) / (sigmax * sigmay)));
151     }
152   }
153   /*  p[N/2+N%2][M/2+M%2] = 1/(user->dx*user->dy); */
154 
155   PetscCall(DMDAVecRestoreArray(cda, gc, &coors));
156   PetscCall(DMDAVecRestoreArray(user->da, X, &p));
157   PetscFunctionReturn(0);
158 }
159 
160 /* First advection term */
161 PetscErrorCode adv1(PetscScalar **p, PetscScalar y, PetscInt i, PetscInt j, PetscInt M, PetscScalar *p1, AppCtx *user) {
162   PetscScalar f;
163   /*  PetscScalar v1,v2,v3,v4,v5,s1,s2,s3; */
164   PetscFunctionBegin;
165   /*  if (i > 2 && i < M-2) {
166     v1 = (y-user->ws)*(p[j][i-2] - p[j][i-3])/user->dx;
167     v2 = (y-user->ws)*(p[j][i-1] - p[j][i-2])/user->dx;
168     v3 = (y-user->ws)*(p[j][i] - p[j][i-1])/user->dx;
169     v4 = (y-user->ws)*(p[j][i+1] - p[j][i])/user->dx;
170     v5 = (y-user->ws)*(p[j][i+1] - p[j][i+2])/user->dx;
171 
172     s1 = v1/3.0 - (7.0/6.0)*v2 + (11.0/6.0)*v3;
173     s2 =-v2/6.0 + (5.0/6.0)*v3 + (1.0/3.0)*v4;
174     s3 = v3/3.0 + (5.0/6.0)*v4 - (1.0/6.0)*v5;
175 
176     *p1 = 0.1*s1 + 0.6*s2 + 0.3*s3;
177     } else *p1 = 0.0; */
178   f   = (y - user->ws);
179   *p1 = f * (p[j][i + 1] - p[j][i - 1]) / (2 * user->dx);
180   PetscFunctionReturn(0);
181 }
182 
183 /* Second advection term */
184 PetscErrorCode adv2(PetscScalar **p, PetscScalar x, PetscInt i, PetscInt j, PetscInt N, PetscScalar *p2, AppCtx *user) {
185   PetscScalar f;
186   /*  PetscScalar v1,v2,v3,v4,v5,s1,s2,s3; */
187   PetscFunctionBegin;
188   /*  if (j > 2 && j < N-2) {
189     v1 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j-2][i] - p[j-3][i])/user->dy;
190     v2 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j-1][i] - p[j-2][i])/user->dy;
191     v3 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j][i] - p[j-1][i])/user->dy;
192     v4 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j+1][i] - p[j][i])/user->dy;
193     v5 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j+2][i] - p[j+1][i])/user->dy;
194 
195     s1 = v1/3.0 - (7.0/6.0)*v2 + (11.0/6.0)*v3;
196     s2 =-v2/6.0 + (5.0/6.0)*v3 + (1.0/3.0)*v4;
197     s3 = v3/3.0 + (5.0/6.0)*v4 - (1.0/6.0)*v5;
198 
199     *p2 = 0.1*s1 + 0.6*s2 + 0.3*s3;
200     } else *p2 = 0.0; */
201   f   = (user->ws / (2 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(x));
202   *p2 = f * (p[j + 1][i] - p[j - 1][i]) / (2 * user->dy);
203   PetscFunctionReturn(0);
204 }
205 
206 /* Diffusion term */
207 PetscErrorCode diffuse(PetscScalar **p, PetscInt i, PetscInt j, PetscReal t, PetscScalar *p_diff, AppCtx *user) {
208   PetscFunctionBeginUser;
209 
210   *p_diff = user->disper_coe * ((p[j - 1][i] - 2 * p[j][i] + p[j + 1][i]) / (user->dy * user->dy));
211   PetscFunctionReturn(0);
212 }
213 
214 PetscErrorCode BoundaryConditions(PetscScalar **p, DMDACoor2d **coors, PetscInt i, PetscInt j, PetscInt M, PetscInt N, PetscScalar **f, AppCtx *user) {
215   PetscScalar fwc, fthetac;
216   PetscScalar w = coors[j][i].y, theta = coors[j][i].x;
217 
218   PetscFunctionBeginUser;
219   if (user->bc == 0) { /* Natural boundary condition */
220     f[j][i] = p[j][i];
221   } else { /* Steady state boundary condition */
222     fthetac = user->ws / (2 * user->H) * (user->PM_min - user->Pmax * PetscSinScalar(theta));
223     fwc     = (w * w / 2.0 - user->ws * w);
224     if (i == 0 && j == 0) { /* left bottom corner */
225       f[j][i] = fwc * (p[j][i + 1] - p[j][i]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j][i]) / user->dy;
226     } else if (i == 0 && j == N - 1) { /* right bottom corner */
227       f[j][i] = fwc * (p[j][i + 1] - p[j][i]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j][i] - p[j - 1][i]) / user->dy;
228     } else if (i == M - 1 && j == 0) { /* left top corner */
229       f[j][i] = fwc * (p[j][i] - p[j][i - 1]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j][i]) / user->dy;
230     } else if (i == M - 1 && j == N - 1) { /* right top corner */
231       f[j][i] = fwc * (p[j][i] - p[j][i - 1]) / user->dx + fthetac * p[j][i] - user->disper_coe * (p[j][i] - p[j - 1][i]) / user->dy;
232     } else if (i == 0) { /* Bottom edge */
233       f[j][i] = fwc * (p[j][i + 1] - p[j][i]) / (user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j - 1][i]) / (2 * user->dy);
234     } else if (i == M - 1) { /* Top edge */
235       f[j][i] = fwc * (p[j][i] - p[j][i - 1]) / (user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j - 1][i]) / (2 * user->dy);
236     } else if (j == 0) { /* Left edge */
237       f[j][i] = fwc * (p[j][i + 1] - p[j][i - 1]) / (2 * user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j + 1][i] - p[j][i]) / (user->dy);
238     } else if (j == N - 1) { /* Right edge */
239       f[j][i] = fwc * (p[j][i + 1] - p[j][i - 1]) / (2 * user->dx) + fthetac * p[j][i] - user->disper_coe * (p[j][i] - p[j - 1][i]) / (user->dy);
240     }
241   }
242   PetscFunctionReturn(0);
243 }
244 
245 PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx) {
246   AppCtx       *user = (AppCtx *)ctx;
247   DM            cda;
248   DMDACoor2d  **coors;
249   PetscScalar **p, **f, **pdot;
250   PetscInt      i, j;
251   PetscInt      xs, ys, xm, ym, M, N;
252   Vec           localX, gc, localXdot;
253   PetscScalar   p_adv1, p_adv2, p_diff;
254 
255   PetscFunctionBeginUser;
256   PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
257   PetscCall(DMGetCoordinateDM(user->da, &cda));
258   PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0));
259 
260   PetscCall(DMGetLocalVector(user->da, &localX));
261   PetscCall(DMGetLocalVector(user->da, &localXdot));
262 
263   PetscCall(DMGlobalToLocalBegin(user->da, X, INSERT_VALUES, localX));
264   PetscCall(DMGlobalToLocalEnd(user->da, X, INSERT_VALUES, localX));
265   PetscCall(DMGlobalToLocalBegin(user->da, Xdot, INSERT_VALUES, localXdot));
266   PetscCall(DMGlobalToLocalEnd(user->da, Xdot, INSERT_VALUES, localXdot));
267 
268   PetscCall(DMGetCoordinatesLocal(user->da, &gc));
269 
270   PetscCall(DMDAVecGetArrayRead(cda, gc, &coors));
271   PetscCall(DMDAVecGetArrayRead(user->da, localX, &p));
272   PetscCall(DMDAVecGetArrayRead(user->da, localXdot, &pdot));
273   PetscCall(DMDAVecGetArray(user->da, F, &f));
274 
275   user->disper_coe = PetscPowScalar((user->lambda * user->ws) / (2 * user->H), 2) * user->q * (1.0 - PetscExpScalar(-t / user->lambda));
276   for (i = xs; i < xs + xm; i++) {
277     for (j = ys; j < ys + ym; j++) {
278       if (i == 0 || j == 0 || i == M - 1 || j == N - 1) {
279         PetscCall(BoundaryConditions(p, coors, i, j, M, N, f, user));
280       } else {
281         PetscCall(adv1(p, coors[j][i].y, i, j, M, &p_adv1, user));
282         PetscCall(adv2(p, coors[j][i].x, i, j, N, &p_adv2, user));
283         PetscCall(diffuse(p, i, j, t, &p_diff, user));
284         f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
285       }
286     }
287   }
288   PetscCall(DMDAVecRestoreArrayRead(user->da, localX, &p));
289   PetscCall(DMDAVecRestoreArrayRead(user->da, localX, &pdot));
290   PetscCall(DMRestoreLocalVector(user->da, &localX));
291   PetscCall(DMRestoreLocalVector(user->da, &localXdot));
292   PetscCall(DMDAVecRestoreArray(user->da, F, &f));
293   PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors));
294 
295   PetscFunctionReturn(0);
296 }
297 
298 PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat J, Mat Jpre, void *ctx) {
299   AppCtx      *user = (AppCtx *)ctx;
300   DM           cda;
301   DMDACoor2d **coors;
302   PetscInt     i, j;
303   PetscInt     xs, ys, xm, ym, M, N;
304   Vec          gc;
305   PetscScalar  val[5], xi, yi;
306   MatStencil   row, col[5];
307   PetscScalar  c1, c3, c5;
308 
309   PetscFunctionBeginUser;
310   PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
311   PetscCall(DMGetCoordinateDM(user->da, &cda));
312   PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0));
313 
314   PetscCall(DMGetCoordinatesLocal(user->da, &gc));
315   PetscCall(DMDAVecGetArrayRead(cda, gc, &coors));
316   for (i = xs; i < xs + xm; i++) {
317     for (j = ys; j < ys + ym; j++) {
318       PetscInt nc = 0;
319       xi          = coors[j][i].x;
320       yi          = coors[j][i].y;
321       row.i       = i;
322       row.j       = j;
323       if (i == 0 || j == 0 || i == M - 1 || j == N - 1) {
324         if (user->bc == 0) {
325           col[nc].i = i;
326           col[nc].j = j;
327           val[nc++] = 1.0;
328         } else {
329           PetscScalar fthetac, fwc;
330           fthetac = user->ws / (2 * user->H) * (user->PM_min - user->Pmax * PetscSinScalar(xi));
331           fwc     = (yi * yi / 2.0 - user->ws * yi);
332           if (i == 0 && j == 0) {
333             col[nc].i = i + 1;
334             col[nc].j = j;
335             val[nc++] = fwc / user->dx;
336             col[nc].i = i;
337             col[nc].j = j + 1;
338             val[nc++] = -user->disper_coe / user->dy;
339             col[nc].i = i;
340             col[nc].j = j;
341             val[nc++] = -fwc / user->dx + fthetac + user->disper_coe / user->dy;
342           } else if (i == 0 && j == N - 1) {
343             col[nc].i = i + 1;
344             col[nc].j = j;
345             val[nc++] = fwc / user->dx;
346             col[nc].i = i;
347             col[nc].j = j - 1;
348             val[nc++] = user->disper_coe / user->dy;
349             col[nc].i = i;
350             col[nc].j = j;
351             val[nc++] = -fwc / user->dx + fthetac - user->disper_coe / user->dy;
352           } else if (i == M - 1 && j == 0) {
353             col[nc].i = i - 1;
354             col[nc].j = j;
355             val[nc++] = -fwc / user->dx;
356             col[nc].i = i;
357             col[nc].j = j + 1;
358             val[nc++] = -user->disper_coe / user->dy;
359             col[nc].i = i;
360             col[nc].j = j;
361             val[nc++] = fwc / user->dx + fthetac + user->disper_coe / user->dy;
362           } else if (i == M - 1 && j == N - 1) {
363             col[nc].i = i - 1;
364             col[nc].j = j;
365             val[nc++] = -fwc / user->dx;
366             col[nc].i = i;
367             col[nc].j = j - 1;
368             val[nc++] = user->disper_coe / user->dy;
369             col[nc].i = i;
370             col[nc].j = j;
371             val[nc++] = fwc / user->dx + fthetac - user->disper_coe / user->dy;
372           } else if (i == 0) {
373             col[nc].i = i + 1;
374             col[nc].j = j;
375             val[nc++] = fwc / user->dx;
376             col[nc].i = i;
377             col[nc].j = j + 1;
378             val[nc++] = -user->disper_coe / (2 * user->dy);
379             col[nc].i = i;
380             col[nc].j = j - 1;
381             val[nc++] = user->disper_coe / (2 * user->dy);
382             col[nc].i = i;
383             col[nc].j = j;
384             val[nc++] = -fwc / user->dx + fthetac;
385           } else if (i == M - 1) {
386             col[nc].i = i - 1;
387             col[nc].j = j;
388             val[nc++] = -fwc / user->dx;
389             col[nc].i = i;
390             col[nc].j = j + 1;
391             val[nc++] = -user->disper_coe / (2 * user->dy);
392             col[nc].i = i;
393             col[nc].j = j - 1;
394             val[nc++] = user->disper_coe / (2 * user->dy);
395             col[nc].i = i;
396             col[nc].j = j;
397             val[nc++] = fwc / user->dx + fthetac;
398           } else if (j == 0) {
399             col[nc].i = i + 1;
400             col[nc].j = j;
401             val[nc++] = fwc / (2 * user->dx);
402             col[nc].i = i - 1;
403             col[nc].j = j;
404             val[nc++] = -fwc / (2 * user->dx);
405             col[nc].i = i;
406             col[nc].j = j + 1;
407             val[nc++] = -user->disper_coe / user->dy;
408             col[nc].i = i;
409             col[nc].j = j;
410             val[nc++] = user->disper_coe / user->dy + fthetac;
411           } else if (j == N - 1) {
412             col[nc].i = i + 1;
413             col[nc].j = j;
414             val[nc++] = fwc / (2 * user->dx);
415             col[nc].i = i - 1;
416             col[nc].j = j;
417             val[nc++] = -fwc / (2 * user->dx);
418             col[nc].i = i;
419             col[nc].j = j - 1;
420             val[nc++] = user->disper_coe / user->dy;
421             col[nc].i = i;
422             col[nc].j = j;
423             val[nc++] = -user->disper_coe / user->dy + fthetac;
424           }
425         }
426       } else {
427         c1        = (yi - user->ws) / (2 * user->dx);
428         c3        = (user->ws / (2.0 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(xi)) / (2 * user->dy);
429         c5        = (PetscPowScalar((user->lambda * user->ws) / (2 * user->H), 2) * user->q * (1.0 - PetscExpScalar(-t / user->lambda))) / (user->dy * user->dy);
430         col[nc].i = i - 1;
431         col[nc].j = j;
432         val[nc++] = c1;
433         col[nc].i = i + 1;
434         col[nc].j = j;
435         val[nc++] = -c1;
436         col[nc].i = i;
437         col[nc].j = j - 1;
438         val[nc++] = c3 + c5;
439         col[nc].i = i;
440         col[nc].j = j + 1;
441         val[nc++] = -c3 + c5;
442         col[nc].i = i;
443         col[nc].j = j;
444         val[nc++] = -2 * c5 - a;
445       }
446       PetscCall(MatSetValuesStencil(Jpre, 1, &row, nc, col, val, INSERT_VALUES));
447     }
448   }
449   PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors));
450 
451   PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY));
452   PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY));
453   if (J != Jpre) {
454     PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY));
455     PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY));
456   }
457   PetscFunctionReturn(0);
458 }
459 
460 PetscErrorCode Parameter_settings(AppCtx *user) {
461   PetscBool flg;
462 
463   PetscFunctionBeginUser;
464 
465   /* Set default parameters */
466   user->ws     = 1.0;
467   user->H      = 5.0;
468   user->Pmax   = 2.1;
469   user->PM_min = 1.0;
470   user->lambda = 0.1;
471   user->q      = 1.0;
472   user->mux    = PetscAsinScalar(user->PM_min / user->Pmax);
473   user->sigmax = 0.1;
474   user->sigmay = 0.1;
475   user->rho    = 0.0;
476   user->t0     = 0.0;
477   user->tmax   = 2.0;
478   user->xmin   = -1.0;
479   user->xmax   = 10.0;
480   user->ymin   = -1.0;
481   user->ymax   = 10.0;
482   user->bc     = 0;
483 
484   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ws", &user->ws, &flg));
485   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-Inertia", &user->H, &flg));
486   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-Pmax", &user->Pmax, &flg));
487   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-PM_min", &user->PM_min, &flg));
488   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-lambda", &user->lambda, &flg));
489   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-q", &user->q, &flg));
490   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-mux", &user->mux, &flg));
491   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-sigmax", &user->sigmax, &flg));
492   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-muy", &user->muy, &flg));
493   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-sigmay", &user->sigmay, &flg));
494   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-rho", &user->rho, &flg));
495   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-t0", &user->t0, &flg));
496   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-tmax", &user->tmax, &flg));
497   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-xmin", &user->xmin, &flg));
498   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-xmax", &user->xmax, &flg));
499   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ymin", &user->ymin, &flg));
500   PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ymax", &user->ymax, &flg));
501   PetscCall(PetscOptionsGetInt(NULL, NULL, "-bc_type", &user->bc, &flg));
502   user->muy = user->ws;
503   PetscFunctionReturn(0);
504 }
505 
506 /*TEST
507 
508    build:
509       requires: !complex
510 
511    test:
512       args: -nox -ts_max_steps 2
513       localrunfiles: petscopt_ex6
514       timeoutfactor: 4
515 
516 TEST*/
517