Actual source code: ex8.c
petsc-3.12.1 2019-10-22
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;
6: Boundary conditions:
7: Zero dirichlet in y using ghosted values
8: Periodic in x
10: Note that x_t and y_t in the above are given functions of x and y; they are not derivatives of x and y.
11: x_t = (y - ws)
12: y_t = (ws/2H)*(Pm - Pmax*sin(x) - D*(w - ws))
14: In this example, we can see the effect of a fault, that zeroes the electrical power output
15: Pmax*sin(x), on the PDF. The fault on/off times can be controlled by options -tf and -tcl respectively.
17: */
19: #include <petscdm.h>
20: #include <petscdmda.h>
21: #include <petscts.h>
23: /*
24: User-defined data structures and routines
25: */
26: typedef struct {
27: PetscScalar ws; /* Synchronous speed */
28: PetscScalar H; /* Inertia constant */
29: PetscScalar D; /* Damping constant */
30: PetscScalar Pmax,Pmax_s; /* Maximum power output of generator */
31: PetscScalar PM_min; /* Mean mechanical power input */
32: PetscScalar lambda; /* correlation time */
33: PetscScalar q; /* noise strength */
34: PetscScalar mux; /* Initial average angle */
35: PetscScalar sigmax; /* Standard deviation of initial angle */
36: PetscScalar muy; /* Average speed */
37: PetscScalar sigmay; /* standard deviation of initial speed */
38: PetscScalar rho; /* Cross-correlation coefficient */
39: PetscScalar xmin; /* left boundary of angle */
40: PetscScalar xmax; /* right boundary of angle */
41: PetscScalar ymin; /* bottom boundary of speed */
42: PetscScalar ymax; /* top boundary of speed */
43: PetscScalar dx; /* x step size */
44: PetscScalar dy; /* y step size */
45: PetscScalar disper_coe; /* Dispersion coefficient */
46: DM da;
47: PetscInt st_width; /* Stencil width */
48: DMBoundaryType bx; /* x boundary type */
49: DMBoundaryType by; /* y boundary type */
50: PetscReal tf,tcl; /* Fault incidence and clearing times */
51: } AppCtx;
53: PetscErrorCode Parameter_settings(AppCtx*);
54: PetscErrorCode ini_bou(Vec,AppCtx*);
55: PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*);
56: PetscErrorCode IJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
57: PetscErrorCode PostStep(TS);
59: int main(int argc, char **argv)
60: {
62: Vec x; /* Solution vector */
63: TS ts; /* Time-stepping context */
64: AppCtx user; /* Application context */
65: PetscViewer viewer;
67: PetscInitialize(&argc,&argv,"petscopt_ex8", help);if (ierr) return ierr;
69: /* Get physics and time parameters */
70: Parameter_settings(&user);
71: /* Create a 2D DA with dof = 1 */
72: DMDACreate2d(PETSC_COMM_WORLD,user.bx,user.by,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,user.st_width,NULL,NULL,&user.da);
73: DMSetFromOptions(user.da);
74: DMSetUp(user.da);
75: /* Set x and y coordinates */
76: DMDASetUniformCoordinates(user.da,user.xmin,user.xmax,user.ymin,user.ymax,0,0);
77: DMDASetCoordinateName(user.da,0,"X - the angle");
78: DMDASetCoordinateName(user.da,1,"Y - the speed");
80: /* Get global vector x from DM */
81: DMCreateGlobalVector(user.da,&x);
83: ini_bou(x,&user);
84: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"ini_x",FILE_MODE_WRITE,&viewer);
85: VecView(x,viewer);
86: PetscViewerDestroy(&viewer);
88: TSCreate(PETSC_COMM_WORLD,&ts);
89: TSSetDM(ts,user.da);
90: TSSetProblemType(ts,TS_NONLINEAR);
91: TSSetType(ts,TSARKIMEX);
92: TSSetIFunction(ts,NULL,IFunction,&user);
93: /* TSSetIJacobian(ts,NULL,NULL,IJacobian,&user); */
94: TSSetApplicationContext(ts,&user);
95: TSSetTimeStep(ts,.005);
96: TSSetFromOptions(ts);
97: TSSetPostStep(ts,PostStep);
98: TSSolve(ts,x);
100: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"fin_x",FILE_MODE_WRITE,&viewer);
101: VecView(x,viewer);
102: PetscViewerDestroy(&viewer);
104: VecDestroy(&x);
105: DMDestroy(&user.da);
106: TSDestroy(&ts);
107: PetscFinalize();
108: return ierr;
109: }
111: PetscErrorCode PostStep(TS ts)
112: {
114: Vec X;
115: AppCtx *user;
116: PetscReal t;
117: PetscScalar asum;
120: TSGetApplicationContext(ts,&user);
121: TSGetTime(ts,&t);
122: TSGetSolution(ts,&X);
123: /*
124: if (t >= .2) {
125: TSGetSolution(ts,&X);
126: VecView(X,PETSC_VIEWER_BINARY_WORLD);
127: exit(0);
128: results in initial conditions after fault in binaryoutput
129: }*/
131: if ((t > user->tf) && (t < user->tcl)) user->Pmax = 0.0; /* A short-circuit that drives the electrical power output (Pmax*sin(delta)) to zero */
132: else user->Pmax = user->Pmax_s;
134: VecSum(X,&asum);
135: PetscPrintf(PETSC_COMM_WORLD,"sum(p) at t = %f = %f\n",(double)t,(double)(asum));
136: return(0);
137: }
139: PetscErrorCode ini_bou(Vec X,AppCtx* user)
140: {
142: DM cda;
143: DMDACoor2d **coors;
144: PetscScalar **p;
145: Vec gc;
146: PetscInt M,N,Ir,J;
147: PetscMPIInt rank;
150: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
151: DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
152: user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
153: DMGetCoordinateDM(user->da,&cda);
154: DMGetCoordinates(user->da,&gc);
155: DMDAVecGetArrayRead(cda,gc,&coors);
156: DMDAVecGetArray(user->da,X,&p);
158: /* Point mass at (mux,muy) */
159: PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",user->mux,user->muy);
160: DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&Ir,&J,NULL,&user->mux,&user->muy,NULL);
161: user->PM_min = user->Pmax*PetscSinScalar(user->mux);
162: PetscPrintf(PETSC_COMM_WORLD,"Corrected user->mux = %f, user->muy = %f user->PM_min = %f,user->dx = %f\n",user->mux,user->muy,user->PM_min,user->dx);
163: if (Ir > -1 && J > -1) {
164: p[J][Ir] = 1.0;
165: }
167: DMDAVecRestoreArrayRead(cda,gc,&coors);
168: DMDAVecRestoreArray(user->da,X,&p);
169: return(0);
170: }
172: /* First advection term */
173: PetscErrorCode adv1(PetscScalar **p,PetscScalar y,PetscInt i,PetscInt j,PetscInt M,PetscScalar *p1,AppCtx *user)
174: {
175: PetscScalar f,fpos,fneg;
177: f = (y - user->ws);
178: fpos = PetscMax(f,0);
179: fneg = PetscMin(f,0);
180: if (user->st_width == 1) {
181: *p1 = fpos*(p[j][i] - p[j][i-1])/user->dx + fneg*(p[j][i+1] - p[j][i])/user->dx;
182: } else if (user->st_width == 2) {
183: *p1 = fpos*(3*p[j][i] - 4*p[j][i-1] + p[j][i-2])/(2*user->dx) + fneg*(-p[j][i+2] + 4*p[j][i+1] - 3*p[j][i])/(2*user->dx);
184: } else if (user->st_width == 3) {
185: *p1 = fpos*(2*p[j][i+1] + 3*p[j][i] - 6*p[j][i-1] + p[j][i-2])/(6*user->dx) + fneg*(-p[j][i+2] + 6*p[j][i+1] - 3*p[j][i] - 2*p[j][i-1])/(6*user->dx);
186: }
187: /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/
188: return(0);
189: }
191: /* Second advection term */
192: PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscScalar y,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user)
193: {
194: PetscScalar f,fpos,fneg;
196: f = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x) - user->D*(y - user->ws));
197: fpos = PetscMax(f,0);
198: fneg = PetscMin(f,0);
199: if (user->st_width == 1) {
200: *p2 = fpos*(p[j][i] - p[j-1][i])/user->dy + fneg*(p[j+1][i] - p[j][i])/user->dy;
201: } else if (user->st_width ==2) {
202: *p2 = fpos*(3*p[j][i] - 4*p[j-1][i] + p[j-2][i])/(2*user->dy) + fneg*(-p[j+2][i] + 4*p[j+1][i] - 3*p[j][i])/(2*user->dy);
203: } else if (user->st_width == 3) {
204: *p2 = fpos*(2*p[j+1][i] + 3*p[j][i] - 6*p[j-1][i] + p[j-2][i])/(6*user->dy) + fneg*(-p[j+2][i] + 6*p[j+1][i] - 3*p[j][i] - 2*p[j-1][i])/(6*user->dy);
205: }
207: /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/
208: return(0);
209: }
211: /* Diffusion term */
212: PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user)
213: {
215: if (user->st_width == 1) {
216: *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy));
217: } else if (user->st_width == 2) {
218: *p_diff = user->disper_coe*((-p[j-2][i] + 16*p[j-1][i] - 30*p[j][i] + 16*p[j+1][i] - p[j+2][i])/(12.0*user->dy*user->dy));
219: } else if (user->st_width == 3) {
220: *p_diff = user->disper_coe*((2*p[j-3][i] - 27*p[j-2][i] + 270*p[j-1][i] - 490*p[j][i] + 270*p[j+1][i] - 27*p[j+2][i] + 2*p[j+3][i])/(180.0*user->dy*user->dy));
221: }
222: return(0);
223: }
225: PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
226: {
228: AppCtx *user=(AppCtx*)ctx;
229: DM cda;
230: DMDACoor2d **coors;
231: PetscScalar **p,**f,**pdot;
232: PetscInt i,j;
233: PetscInt xs,ys,xm,ym,M,N;
234: Vec localX,gc,localXdot;
235: PetscScalar p_adv1 = 0.0,p_adv2 = 0.0,p_diff = 0;
236: PetscScalar diffuse1,gamma;
239: DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
240: DMGetCoordinateDM(user->da,&cda);
241: DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);
243: DMGetLocalVector(user->da,&localX);
244: DMGetLocalVector(user->da,&localXdot);
246: DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
247: DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
248: DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);
249: DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);
251: DMGetCoordinatesLocal(user->da,&gc);
253: DMDAVecGetArrayRead(cda,gc,&coors);
254: DMDAVecGetArrayRead(user->da,localX,&p);
255: DMDAVecGetArrayRead(user->da,localXdot,&pdot);
256: DMDAVecGetArray(user->da,F,&f);
258: gamma = user->D*user->ws/(2*user->H);
259: diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda));
260: user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1;
262: for (i=xs; i < xs+xm; i++) {
263: for (j=ys; j < ys+ym; j++) {
264: adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);
265: adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);
266: diffuse(p,i,j,t,&p_diff,user);
267: f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
268: }
269: }
270: DMDAVecRestoreArrayRead(user->da,localX,&p);
271: DMDAVecRestoreArrayRead(user->da,localX,&pdot);
272: DMRestoreLocalVector(user->da,&localX);
273: DMRestoreLocalVector(user->da,&localXdot);
274: DMDAVecRestoreArray(user->da,F,&f);
275: DMDAVecRestoreArrayRead(cda,gc,&coors);
277: return(0);
278: }
280: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
281: {
283: AppCtx *user=(AppCtx*)ctx;
284: DM cda;
285: DMDACoor2d **coors;
286: PetscInt i,j;
287: PetscInt xs,ys,xm,ym,M,N;
288: Vec gc;
289: PetscScalar val[5],xi,yi;
290: MatStencil row,col[5];
291: PetscScalar c1,c3,c5,c1pos,c1neg,c3pos,c3neg;
294: DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
295: DMGetCoordinateDM(user->da,&cda);
296: DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);
298: DMGetCoordinatesLocal(user->da,&gc);
299: DMDAVecGetArrayRead(cda,gc,&coors);
300: for (i=xs; i < xs+xm; i++) {
301: for (j=ys; j < ys+ym; j++) {
302: PetscInt nc = 0;
303: xi = coors[j][i].x; yi = coors[j][i].y;
304: row.i = i; row.j = j;
305: c1 = (yi-user->ws)/user->dx;
306: c1pos = PetscMax(c1,0);
307: c1neg = PetscMin(c1,0);
308: c3 = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi) - user->D*(yi - user->ws))/user->dy;
309: c3pos = PetscMax(c3,0);
310: c3neg = PetscMin(c3,0);
311: c5 = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
312: col[nc].i = i-1; col[nc].j = j; val[nc++] = c1pos;
313: col[nc].i = i+1; col[nc].j = j; val[nc++] = -c1neg;
314: col[nc].i = i; col[nc].j = j-1; val[nc++] = c3pos + c5;
315: col[nc].i = i; col[nc].j = j+1; val[nc++] = -c3neg + c5;
316: col[nc].i = i; col[nc].j = j; val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
317: MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);
318: }
319: }
320: DMDAVecRestoreArrayRead(cda,gc,&coors);
322: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
323: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
324: if (J != Jpre) {
325: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
326: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
327: }
328: return(0);
329: }
331: PetscErrorCode Parameter_settings(AppCtx *user)
332: {
334: PetscBool flg;
338: /* Set default parameters */
339: user->ws = 1.0;
340: user->H = 5.0;
341: user->D = 0.0;
342: user->Pmax = user->Pmax_s = 2.1;
343: user->PM_min = 1.0;
344: user->lambda = 0.1;
345: user->q = 1.0;
346: user->mux = PetscAsinScalar(user->PM_min/user->Pmax);
347: user->sigmax = 0.1;
348: user->sigmay = 0.1;
349: user->rho = 0.0;
350: user->xmin = -PETSC_PI;
351: user->xmax = PETSC_PI;
352: user->bx = DM_BOUNDARY_PERIODIC;
353: user->by = DM_BOUNDARY_GHOSTED;
354: user->tf = user->tcl = -1;
355: user->ymin = -2.0;
356: user->ymax = 2.0;
357: user->st_width = 1;
359: PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg);
360: PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg);
361: PetscOptionsGetScalar(NULL,NULL,"-D",&user->D,&flg);
362: PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg);
363: PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg);
364: PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg);
365: PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg);
366: PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg);
367: PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg);
368: if (flg == 0) {
369: user->muy = user->ws;
370: }
371: PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg);
372: PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg);
373: PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg);
374: PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg);
375: PetscOptionsGetInt(NULL,NULL,"-stencil_width",&user->st_width,&flg);
376: PetscOptionsGetEnum(NULL,NULL,"-bx",DMBoundaryTypes,(PetscEnum*)&user->bx,&flg);
377: PetscOptionsGetEnum(NULL,NULL,"-by",DMBoundaryTypes,(PetscEnum*)&user->by,&flg);
378: PetscOptionsGetReal(NULL,NULL,"-tf",&user->tf,&flg);
379: PetscOptionsGetReal(NULL,NULL,"-tcl",&user->tcl,&flg);
380: return(0);
381: }
383: /*TEST
385: build:
386: requires: !complex x
388: test:
389: args: -ts_max_steps 1
390: localrunfiles: petscopt_ex8
391: timeoutfactor: 3
393: TEST*/