xref: /petsc/src/ts/tutorials/power_grid/ex6.c (revision ebead697dbf761eb322f829370bbe90b3bd93fa3)
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 {
53   Vec            x;  /* Solution vector */
54   TS             ts;   /* Time-stepping context */
55   AppCtx         user; /* Application context */
56   Mat            J;
57   PetscViewer    viewer;
58 
59   PetscFunctionBeginUser;
60   PetscCall(PetscInitialize(&argc,&argv,"petscopt_ex6", help));
61   /* Get physics and time parameters */
62   PetscCall(Parameter_settings(&user));
63   /* Create a 2D DA with dof = 1 */
64   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));
65   PetscCall(DMSetFromOptions(user.da));
66   PetscCall(DMSetUp(user.da));
67   /* Set x and y coordinates */
68   PetscCall(DMDASetUniformCoordinates(user.da,user.xmin,user.xmax,user.ymin,user.ymax,0.0,1.0));
69 
70   /* Get global vector x from DM  */
71   PetscCall(DMCreateGlobalVector(user.da,&x));
72 
73   PetscCall(ini_bou(x,&user));
74   PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,"ini_x",FILE_MODE_WRITE,&viewer));
75   PetscCall(VecView(x,viewer));
76   PetscCall(PetscViewerDestroy(&viewer));
77 
78   /* Get Jacobian matrix structure from the da */
79   PetscCall(DMSetMatType(user.da,MATAIJ));
80   PetscCall(DMCreateMatrix(user.da,&J));
81 
82   PetscCall(TSCreate(PETSC_COMM_WORLD,&ts));
83   PetscCall(TSSetProblemType(ts,TS_NONLINEAR));
84   PetscCall(TSSetIFunction(ts,NULL,IFunction,&user));
85   PetscCall(TSSetIJacobian(ts,J,J,IJacobian,&user));
86   PetscCall(TSSetApplicationContext(ts,&user));
87   PetscCall(TSSetMaxTime(ts,user.tmax));
88   PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP));
89   PetscCall(TSSetTime(ts,user.t0));
90   PetscCall(TSSetTimeStep(ts,.005));
91   PetscCall(TSSetFromOptions(ts));
92   PetscCall(TSSetPostStep(ts,PostStep));
93   PetscCall(TSSolve(ts,x));
94 
95   PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD,"fin_x",FILE_MODE_WRITE,&viewer));
96   PetscCall(VecView(x,viewer));
97   PetscCall(PetscViewerDestroy(&viewer));
98 
99   PetscCall(VecDestroy(&x));
100   PetscCall(MatDestroy(&J));
101   PetscCall(DMDestroy(&user.da));
102   PetscCall(TSDestroy(&ts));
103   PetscCall(PetscFinalize());
104   return 0;
105 }
106 
107 PetscErrorCode PostStep(TS ts)
108 {
109   Vec            X;
110   AppCtx         *user;
111   PetscScalar    sum;
112   PetscReal      t;
113 
114   PetscFunctionBegin;
115   PetscCall(TSGetApplicationContext(ts,&user));
116   PetscCall(TSGetTime(ts,&t));
117   PetscCall(TSGetSolution(ts,&X));
118   PetscCall(VecSum(X,&sum));
119   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"sum(p)*dw*dtheta at t = %3.2f = %3.6f\n",(double)t,(double)(sum*user->dx*user->dy)));
120   PetscFunctionReturn(0);
121 }
122 
123 PetscErrorCode ini_bou(Vec X,AppCtx* user)
124 {
125   DM             cda;
126   DMDACoor2d     **coors;
127   PetscScalar    **p;
128   Vec            gc;
129   PetscInt       i,j;
130   PetscInt       xs,ys,xm,ym,M,N;
131   PetscScalar    xi,yi;
132   PetscScalar    sigmax=user->sigmax,sigmay=user->sigmay;
133   PetscScalar    rho   =user->rho;
134   PetscScalar    mux   =user->mux,muy=user->muy;
135   PetscMPIInt    rank;
136 
137   PetscFunctionBeginUser;
138   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD,&rank));
139   PetscCall(DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL));
140   user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
141   PetscCall(DMGetCoordinateDM(user->da,&cda));
142   PetscCall(DMGetCoordinates(user->da,&gc));
143   PetscCall(DMDAVecGetArray(cda,gc,&coors));
144   PetscCall(DMDAVecGetArray(user->da,X,&p));
145   PetscCall(DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0));
146   for (i=xs; i < xs+xm; i++) {
147     for (j=ys; j < ys+ym; j++) {
148       xi = coors[j][i].x; yi = coors[j][i].y;
149       if (i == 0 || j == 0 || i == M-1 || j == N-1) p[j][i] = 0.0;
150       else 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 {
163   PetscScalar f;
164   /*  PetscScalar v1,v2,v3,v4,v5,s1,s2,s3; */
165   PetscFunctionBegin;
166   /*  if (i > 2 && i < M-2) {
167     v1 = (y-user->ws)*(p[j][i-2] - p[j][i-3])/user->dx;
168     v2 = (y-user->ws)*(p[j][i-1] - p[j][i-2])/user->dx;
169     v3 = (y-user->ws)*(p[j][i] - p[j][i-1])/user->dx;
170     v4 = (y-user->ws)*(p[j][i+1] - p[j][i])/user->dx;
171     v5 = (y-user->ws)*(p[j][i+1] - p[j][i+2])/user->dx;
172 
173     s1 = v1/3.0 - (7.0/6.0)*v2 + (11.0/6.0)*v3;
174     s2 =-v2/6.0 + (5.0/6.0)*v3 + (1.0/3.0)*v4;
175     s3 = v3/3.0 + (5.0/6.0)*v4 - (1.0/6.0)*v5;
176 
177     *p1 = 0.1*s1 + 0.6*s2 + 0.3*s3;
178     } else *p1 = 0.0; */
179   f   =  (y - user->ws);
180   *p1 = f*(p[j][i+1] - p[j][i-1])/(2*user->dx);
181   PetscFunctionReturn(0);
182 }
183 
184 /* Second advection term */
185 PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user)
186 {
187   PetscScalar f;
188   /*  PetscScalar v1,v2,v3,v4,v5,s1,s2,s3; */
189   PetscFunctionBegin;
190   /*  if (j > 2 && j < N-2) {
191     v1 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j-2][i] - p[j-3][i])/user->dy;
192     v2 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j-1][i] - p[j-2][i])/user->dy;
193     v3 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j][i] - p[j-1][i])/user->dy;
194     v4 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j+1][i] - p[j][i])/user->dy;
195     v5 = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*sin(x))*(p[j+2][i] - p[j+1][i])/user->dy;
196 
197     s1 = v1/3.0 - (7.0/6.0)*v2 + (11.0/6.0)*v3;
198     s2 =-v2/6.0 + (5.0/6.0)*v3 + (1.0/3.0)*v4;
199     s3 = v3/3.0 + (5.0/6.0)*v4 - (1.0/6.0)*v5;
200 
201     *p2 = 0.1*s1 + 0.6*s2 + 0.3*s3;
202     } else *p2 = 0.0; */
203   f   = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x));
204   *p2 = f*(p[j+1][i] - p[j-1][i])/(2*user->dy);
205   PetscFunctionReturn(0);
206 }
207 
208 /* Diffusion term */
209 PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user)
210 {
211   PetscFunctionBeginUser;
212 
213   *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy));
214   PetscFunctionReturn(0);
215 }
216 
217 PetscErrorCode BoundaryConditions(PetscScalar **p,DMDACoor2d **coors,PetscInt i,PetscInt j,PetscInt M, PetscInt N,PetscScalar **f,AppCtx *user)
218 {
219   PetscScalar fwc,fthetac;
220   PetscScalar w=coors[j][i].y,theta=coors[j][i].x;
221 
222   PetscFunctionBeginUser;
223   if (user->bc == 0) { /* Natural boundary condition */
224     f[j][i] = p[j][i];
225   } else { /* Steady state boundary condition */
226     fthetac = user->ws/(2*user->H)*(user->PM_min - user->Pmax*PetscSinScalar(theta));
227     fwc = (w*w/2.0 - user->ws*w);
228     if (i == 0 && j == 0) { /* left bottom corner */
229       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;
230     } else if (i == 0 && j == N-1) { /* right bottom corner */
231       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;
232     } else if (i == M-1 && j == 0) { /* left top corner */
233       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;
234     } else if (i == M-1 && j == N-1) { /* right top corner */
235       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;
236     } else if (i == 0) { /* Bottom edge */
237       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);
238     } else if (i == M-1) { /* Top edge */
239       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);
240     } else if (j == 0) { /* Left edge */
241       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);
242     } else if (j == N-1) { /* Right edge */
243       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);
244     }
245   }
246   PetscFunctionReturn(0);
247 }
248 
249 PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
250 {
251   AppCtx         *user=(AppCtx*)ctx;
252   DM             cda;
253   DMDACoor2d     **coors;
254   PetscScalar    **p,**f,**pdot;
255   PetscInt       i,j;
256   PetscInt       xs,ys,xm,ym,M,N;
257   Vec            localX,gc,localXdot;
258   PetscScalar    p_adv1,p_adv2,p_diff;
259 
260   PetscFunctionBeginUser;
261   PetscCall(DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL));
262   PetscCall(DMGetCoordinateDM(user->da,&cda));
263   PetscCall(DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0));
264 
265   PetscCall(DMGetLocalVector(user->da,&localX));
266   PetscCall(DMGetLocalVector(user->da,&localXdot));
267 
268   PetscCall(DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX));
269   PetscCall(DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX));
270   PetscCall(DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot));
271   PetscCall(DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot));
272 
273   PetscCall(DMGetCoordinatesLocal(user->da,&gc));
274 
275   PetscCall(DMDAVecGetArrayRead(cda,gc,&coors));
276   PetscCall(DMDAVecGetArrayRead(user->da,localX,&p));
277   PetscCall(DMDAVecGetArrayRead(user->da,localXdot,&pdot));
278   PetscCall(DMDAVecGetArray(user->da,F,&f));
279 
280   user->disper_coe = PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda));
281   for (i=xs; i < xs+xm; i++) {
282     for (j=ys; j < ys+ym; j++) {
283       if (i == 0 || j == 0 || i == M-1 || j == N-1) {
284         PetscCall(BoundaryConditions(p,coors,i,j,M,N,f,user));
285       } else {
286         PetscCall(adv1(p,coors[j][i].y,i,j,M,&p_adv1,user));
287         PetscCall(adv2(p,coors[j][i].x,i,j,N,&p_adv2,user));
288         PetscCall(diffuse(p,i,j,t,&p_diff,user));
289         f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
290       }
291     }
292   }
293   PetscCall(DMDAVecRestoreArrayRead(user->da,localX,&p));
294   PetscCall(DMDAVecRestoreArrayRead(user->da,localX,&pdot));
295   PetscCall(DMRestoreLocalVector(user->da,&localX));
296   PetscCall(DMRestoreLocalVector(user->da,&localXdot));
297   PetscCall(DMDAVecRestoreArray(user->da,F,&f));
298   PetscCall(DMDAVecRestoreArrayRead(cda,gc,&coors));
299 
300   PetscFunctionReturn(0);
301 }
302 
303 PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
304 {
305   AppCtx         *user=(AppCtx*)ctx;
306   DM             cda;
307   DMDACoor2d     **coors;
308   PetscInt       i,j;
309   PetscInt       xs,ys,xm,ym,M,N;
310   Vec            gc;
311   PetscScalar    val[5],xi,yi;
312   MatStencil     row,col[5];
313   PetscScalar    c1,c3,c5;
314 
315   PetscFunctionBeginUser;
316   PetscCall(DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL));
317   PetscCall(DMGetCoordinateDM(user->da,&cda));
318   PetscCall(DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0));
319 
320   PetscCall(DMGetCoordinatesLocal(user->da,&gc));
321   PetscCall(DMDAVecGetArrayRead(cda,gc,&coors));
322   for (i=xs; i < xs+xm; i++) {
323     for (j=ys; j < ys+ym; j++) {
324       PetscInt nc = 0;
325       xi = coors[j][i].x; yi = coors[j][i].y;
326       row.i = i; row.j = j;
327       if (i == 0 || j == 0 || i == M-1 || j == N-1) {
328         if (user->bc == 0) {
329           col[nc].i = i; col[nc].j = j; val[nc++] = 1.0;
330         } else {
331           PetscScalar fthetac,fwc;
332           fthetac = user->ws/(2*user->H)*(user->PM_min - user->Pmax*PetscSinScalar(xi));
333           fwc     = (yi*yi/2.0 - user->ws*yi);
334           if (i==0 && j==0) {
335             col[nc].i = i+1; col[nc].j = j;   val[nc++] = fwc/user->dx;
336             col[nc].i = i;   col[nc].j = j+1; val[nc++] = -user->disper_coe/user->dy;
337             col[nc].i = i;   col[nc].j = j;   val[nc++] = -fwc/user->dx + fthetac + user->disper_coe/user->dy;
338           } else if (i==0 && j == N-1) {
339             col[nc].i = i+1; col[nc].j = j;   val[nc++] = fwc/user->dx;
340             col[nc].i = i;   col[nc].j = j-1; val[nc++] = user->disper_coe/user->dy;
341             col[nc].i = i;   col[nc].j = j;   val[nc++] = -fwc/user->dx + fthetac - user->disper_coe/user->dy;
342           } else if (i== M-1 && j == 0) {
343             col[nc].i = i-1; col[nc].j = j;   val[nc++] = -fwc/user->dx;
344             col[nc].i = i;   col[nc].j = j+1; val[nc++] = -user->disper_coe/user->dy;
345             col[nc].i = i;   col[nc].j = j;   val[nc++] =  fwc/user->dx + fthetac + user->disper_coe/user->dy;
346           } else if (i == M-1 && j == N-1) {
347             col[nc].i = i-1; col[nc].j = j;   val[nc++] = -fwc/user->dx;
348             col[nc].i = i;   col[nc].j = j-1; val[nc++] =  user->disper_coe/user->dy;
349             col[nc].i = i;   col[nc].j = j;   val[nc++] =  fwc/user->dx + fthetac - user->disper_coe/user->dy;
350           } else if (i==0) {
351             col[nc].i = i+1; col[nc].j = j;   val[nc++] = fwc/user->dx;
352             col[nc].i = i;   col[nc].j = j+1; val[nc++] = -user->disper_coe/(2*user->dy);
353             col[nc].i = i;   col[nc].j = j-1; val[nc++] =  user->disper_coe/(2*user->dy);
354             col[nc].i = i;   col[nc].j = j;   val[nc++] = -fwc/user->dx + fthetac;
355           } else if (i == M-1) {
356             col[nc].i = i-1; col[nc].j = j;   val[nc++] = -fwc/user->dx;
357             col[nc].i = i;   col[nc].j = j+1; val[nc++] = -user->disper_coe/(2*user->dy);
358             col[nc].i = i;   col[nc].j = j-1; val[nc++] =  user->disper_coe/(2*user->dy);
359             col[nc].i = i;   col[nc].j = j;   val[nc++] = fwc/user->dx + fthetac;
360           } else if (j==0) {
361             col[nc].i = i+1; col[nc].j = j;   val[nc++] = fwc/(2*user->dx);
362             col[nc].i = i-1; col[nc].j = j;   val[nc++] = -fwc/(2*user->dx);
363             col[nc].i = i;   col[nc].j = j+1; val[nc++] = -user->disper_coe/user->dy;
364             col[nc].i = i;   col[nc].j = j;   val[nc++] = user->disper_coe/user->dy + fthetac;
365           } else if (j == N-1) {
366             col[nc].i = i+1; col[nc].j = j;   val[nc++] = fwc/(2*user->dx);
367             col[nc].i = i-1; col[nc].j = j;   val[nc++] = -fwc/(2*user->dx);
368             col[nc].i = i;   col[nc].j = j-1; val[nc++] = user->disper_coe/user->dy;
369             col[nc].i = i;   col[nc].j = j;   val[nc++] = -user->disper_coe/user->dy + fthetac;
370           }
371         }
372       } else {
373         c1        = (yi-user->ws)/(2*user->dx);
374         c3        = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi))/(2*user->dy);
375         c5        = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
376         col[nc].i = i-1; col[nc].j = j;   val[nc++] = c1;
377         col[nc].i = i+1; col[nc].j = j;   val[nc++] = -c1;
378         col[nc].i = i;   col[nc].j = j-1; val[nc++] = c3 + c5;
379         col[nc].i = i;   col[nc].j = j+1; val[nc++] = -c3 + c5;
380         col[nc].i = i;   col[nc].j = j;   val[nc++] = -2*c5 -a;
381       }
382       PetscCall(MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES));
383     }
384   }
385   PetscCall(DMDAVecRestoreArrayRead(cda,gc,&coors));
386 
387   PetscCall(MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY));
388   PetscCall(MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY));
389   if (J != Jpre) {
390     PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY));
391     PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY));
392   }
393   PetscFunctionReturn(0);
394 }
395 
396 PetscErrorCode Parameter_settings(AppCtx *user)
397 {
398   PetscBool      flg;
399 
400   PetscFunctionBeginUser;
401 
402   /* Set default parameters */
403   user->ws     = 1.0;
404   user->H      = 5.0;  user->Pmax   = 2.1;
405   user->PM_min = 1.0;  user->lambda = 0.1;
406   user->q      = 1.0;  user->mux    = PetscAsinScalar(user->PM_min/user->Pmax);
407   user->sigmax = 0.1;
408   user->sigmay = 0.1;  user->rho  = 0.0;
409   user->t0     = 0.0;  user->tmax = 2.0;
410   user->xmin   = -1.0; user->xmax = 10.0;
411   user->ymin   = -1.0; user->ymax = 10.0;
412   user->bc     = 0;
413 
414   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg));
415   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg));
416   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg));
417   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg));
418   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg));
419   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg));
420   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg));
421   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-sigmax",&user->sigmax,&flg));
422   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg));
423   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-sigmay",&user->sigmay,&flg));
424   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-rho",&user->rho,&flg));
425   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-t0",&user->t0,&flg));
426   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-tmax",&user->tmax,&flg));
427   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg));
428   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg));
429   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg));
430   PetscCall(PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg));
431   PetscCall(PetscOptionsGetInt(NULL,NULL,"-bc_type",&user->bc,&flg));
432   user->muy = user->ws;
433   PetscFunctionReturn(0);
434 }
435 
436 /*TEST
437 
438    build:
439       requires: !complex
440 
441    test:
442       args: -nox -ts_max_steps 2
443       localrunfiles: petscopt_ex6
444       timeoutfactor: 4
445 
446 TEST*/
447