Actual source code: ex8.c
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: {
61: Vec x; /* Solution vector */
62: TS ts; /* Time-stepping context */
63: AppCtx user; /* Application context */
64: PetscViewer viewer;
67: PetscInitialize(&argc, &argv, "petscopt_ex8", help);
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 0;
109: }
111: PetscErrorCode PostStep(TS ts)
112: {
113: Vec X;
114: AppCtx *user;
115: PetscReal t;
116: PetscScalar asum;
118: TSGetApplicationContext(ts, &user);
119: TSGetTime(ts, &t);
120: TSGetSolution(ts, &X);
121: /*
122: if (t >= .2) {
123: TSGetSolution(ts,&X);
124: VecView(X,PETSC_VIEWER_BINARY_WORLD);
125: exit(0);
126: results in initial conditions after fault in binaryoutput
127: }*/
129: 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 */
130: else user->Pmax = user->Pmax_s;
132: VecSum(X, &asum);
133: PetscPrintf(PETSC_COMM_WORLD, "sum(p) at t = %f = %f\n", (double)t, (double)(asum));
134: return 0;
135: }
137: PetscErrorCode ini_bou(Vec X, AppCtx *user)
138: {
139: DM cda;
140: DMDACoor2d **coors;
141: PetscScalar **p;
142: Vec gc;
143: PetscInt M, N, Ir, J;
144: PetscMPIInt rank;
147: MPI_Comm_rank(PETSC_COMM_WORLD, &rank);
148: DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
149: user->dx = (user->xmax - user->xmin) / (M - 1);
150: user->dy = (user->ymax - user->ymin) / (N - 1);
151: DMGetCoordinateDM(user->da, &cda);
152: DMGetCoordinates(user->da, &gc);
153: DMDAVecGetArrayRead(cda, gc, &coors);
154: DMDAVecGetArray(user->da, X, &p);
156: /* Point mass at (mux,muy) */
157: PetscPrintf(PETSC_COMM_WORLD, "Original user->mux = %f, user->muy = %f\n", (double)PetscRealPart(user->mux), (double)PetscRealPart(user->muy));
158: DMDAGetLogicalCoordinate(user->da, user->mux, user->muy, 0.0, &Ir, &J, NULL, &user->mux, &user->muy, NULL);
159: user->PM_min = user->Pmax * PetscSinScalar(user->mux);
160: PetscCall(
161: PetscPrintf(PETSC_COMM_WORLD, "Corrected user->mux = %f, user->muy = %f user->PM_min = %f,user->dx = %f\n", (double)PetscRealPart(user->mux), (double)PetscRealPart(user->muy), (double)PetscRealPart(user->PM_min), (double)PetscRealPart(user->dx)));
162: if (Ir > -1 && J > -1) p[J][Ir] = 1.0;
164: DMDAVecRestoreArrayRead(cda, gc, &coors);
165: DMDAVecRestoreArray(user->da, X, &p);
166: return 0;
167: }
169: /* First advection term */
170: PetscErrorCode adv1(PetscScalar **p, PetscScalar y, PetscInt i, PetscInt j, PetscInt M, PetscScalar *p1, AppCtx *user)
171: {
172: PetscScalar f, fpos, fneg;
173: f = (y - user->ws);
174: fpos = PetscMax(f, 0);
175: fneg = PetscMin(f, 0);
176: if (user->st_width == 1) {
177: *p1 = fpos * (p[j][i] - p[j][i - 1]) / user->dx + fneg * (p[j][i + 1] - p[j][i]) / user->dx;
178: } else if (user->st_width == 2) {
179: *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);
180: } else if (user->st_width == 3) {
181: *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);
182: }
183: /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/
184: return 0;
185: }
187: /* Second advection term */
188: PetscErrorCode adv2(PetscScalar **p, PetscScalar x, PetscScalar y, PetscInt i, PetscInt j, PetscInt N, PetscScalar *p2, AppCtx *user)
189: {
190: PetscScalar f, fpos, fneg;
191: f = (user->ws / (2 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(x) - user->D * (y - user->ws));
192: fpos = PetscMax(f, 0);
193: fneg = PetscMin(f, 0);
194: if (user->st_width == 1) {
195: *p2 = fpos * (p[j][i] - p[j - 1][i]) / user->dy + fneg * (p[j + 1][i] - p[j][i]) / user->dy;
196: } else if (user->st_width == 2) {
197: *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);
198: } else if (user->st_width == 3) {
199: *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);
200: }
202: /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/
203: return 0;
204: }
206: /* Diffusion term */
207: PetscErrorCode diffuse(PetscScalar **p, PetscInt i, PetscInt j, PetscReal t, PetscScalar *p_diff, AppCtx *user)
208: {
210: if (user->st_width == 1) {
211: *p_diff = user->disper_coe * ((p[j - 1][i] - 2 * p[j][i] + p[j + 1][i]) / (user->dy * user->dy));
212: } else if (user->st_width == 2) {
213: *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));
214: } else if (user->st_width == 3) {
215: *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));
216: }
217: return 0;
218: }
220: PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
221: {
222: AppCtx *user = (AppCtx *)ctx;
223: DM cda;
224: DMDACoor2d **coors;
225: PetscScalar **p, **f, **pdot;
226: PetscInt i, j;
227: PetscInt xs, ys, xm, ym, M, N;
228: Vec localX, gc, localXdot;
229: PetscScalar p_adv1 = 0.0, p_adv2 = 0.0, p_diff = 0;
230: PetscScalar diffuse1, gamma;
233: DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
234: DMGetCoordinateDM(user->da, &cda);
235: DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0);
237: DMGetLocalVector(user->da, &localX);
238: DMGetLocalVector(user->da, &localXdot);
240: DMGlobalToLocalBegin(user->da, X, INSERT_VALUES, localX);
241: DMGlobalToLocalEnd(user->da, X, INSERT_VALUES, localX);
242: DMGlobalToLocalBegin(user->da, Xdot, INSERT_VALUES, localXdot);
243: DMGlobalToLocalEnd(user->da, Xdot, INSERT_VALUES, localXdot);
245: DMGetCoordinatesLocal(user->da, &gc);
247: DMDAVecGetArrayRead(cda, gc, &coors);
248: DMDAVecGetArrayRead(user->da, localX, &p);
249: DMDAVecGetArrayRead(user->da, localXdot, &pdot);
250: DMDAVecGetArray(user->da, F, &f);
252: gamma = user->D * user->ws / (2 * user->H);
253: diffuse1 = user->lambda * user->lambda * user->q / (user->lambda * gamma + 1) * (1.0 - PetscExpScalar(-t * (gamma + 1.0) / user->lambda));
254: user->disper_coe = user->ws * user->ws / (4 * user->H * user->H) * diffuse1;
256: for (i = xs; i < xs + xm; i++) {
257: for (j = ys; j < ys + ym; j++) {
258: adv1(p, coors[j][i].y, i, j, M, &p_adv1, user);
259: adv2(p, coors[j][i].x, coors[j][i].y, i, j, N, &p_adv2, user);
260: diffuse(p, i, j, t, &p_diff, user);
261: f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
262: }
263: }
264: DMDAVecRestoreArrayRead(user->da, localX, &p);
265: DMDAVecRestoreArrayRead(user->da, localX, &pdot);
266: DMRestoreLocalVector(user->da, &localX);
267: DMRestoreLocalVector(user->da, &localXdot);
268: DMDAVecRestoreArray(user->da, F, &f);
269: DMDAVecRestoreArrayRead(cda, gc, &coors);
271: return 0;
272: }
274: PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat J, Mat Jpre, void *ctx)
275: {
276: AppCtx *user = (AppCtx *)ctx;
277: DM cda;
278: DMDACoor2d **coors;
279: PetscInt i, j;
280: PetscInt xs, ys, xm, ym, M, N;
281: Vec gc;
282: PetscScalar val[5], xi, yi;
283: MatStencil row, col[5];
284: PetscScalar c1, c3, c5, c1pos, c1neg, c3pos, c3neg;
287: DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
288: DMGetCoordinateDM(user->da, &cda);
289: DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0);
291: DMGetCoordinatesLocal(user->da, &gc);
292: DMDAVecGetArrayRead(cda, gc, &coors);
293: for (i = xs; i < xs + xm; i++) {
294: for (j = ys; j < ys + ym; j++) {
295: PetscInt nc = 0;
296: xi = coors[j][i].x;
297: yi = coors[j][i].y;
298: row.i = i;
299: row.j = j;
300: c1 = (yi - user->ws) / user->dx;
301: c1pos = PetscMax(c1, 0);
302: c1neg = PetscMin(c1, 0);
303: c3 = (user->ws / (2.0 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(xi) - user->D * (yi - user->ws)) / user->dy;
304: c3pos = PetscMax(c3, 0);
305: c3neg = PetscMin(c3, 0);
306: c5 = (PetscPowScalar((user->lambda * user->ws) / (2 * user->H), 2) * user->q * (1.0 - PetscExpScalar(-t / user->lambda))) / (user->dy * user->dy);
307: col[nc].i = i - 1;
308: col[nc].j = j;
309: val[nc++] = c1pos;
310: col[nc].i = i + 1;
311: col[nc].j = j;
312: val[nc++] = -c1neg;
313: col[nc].i = i;
314: col[nc].j = j - 1;
315: val[nc++] = c3pos + c5;
316: col[nc].i = i;
317: col[nc].j = j + 1;
318: val[nc++] = -c3neg + c5;
319: col[nc].i = i;
320: col[nc].j = j;
321: val[nc++] = -c1pos + c1neg - c3pos + c3neg - 2 * c5 - a;
322: MatSetValuesStencil(Jpre, 1, &row, nc, col, val, INSERT_VALUES);
323: }
324: }
325: DMDAVecRestoreArrayRead(cda, gc, &coors);
327: MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY);
328: MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY);
329: if (J != Jpre) {
330: MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY);
331: MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY);
332: }
333: return 0;
334: }
336: PetscErrorCode Parameter_settings(AppCtx *user)
337: {
338: PetscBool flg;
341: /* Set default parameters */
342: user->ws = 1.0;
343: user->H = 5.0;
344: user->D = 0.0;
345: user->Pmax = user->Pmax_s = 2.1;
346: user->PM_min = 1.0;
347: user->lambda = 0.1;
348: user->q = 1.0;
349: user->mux = PetscAsinScalar(user->PM_min / user->Pmax);
350: user->sigmax = 0.1;
351: user->sigmay = 0.1;
352: user->rho = 0.0;
353: user->xmin = -PETSC_PI;
354: user->xmax = PETSC_PI;
355: user->bx = DM_BOUNDARY_PERIODIC;
356: user->by = DM_BOUNDARY_GHOSTED;
357: user->tf = user->tcl = -1;
358: user->ymin = -2.0;
359: user->ymax = 2.0;
360: user->st_width = 1;
362: PetscOptionsGetScalar(NULL, NULL, "-ws", &user->ws, &flg);
363: PetscOptionsGetScalar(NULL, NULL, "-Inertia", &user->H, &flg);
364: PetscOptionsGetScalar(NULL, NULL, "-D", &user->D, &flg);
365: PetscOptionsGetScalar(NULL, NULL, "-Pmax", &user->Pmax, &flg);
366: PetscOptionsGetScalar(NULL, NULL, "-PM_min", &user->PM_min, &flg);
367: PetscOptionsGetScalar(NULL, NULL, "-lambda", &user->lambda, &flg);
368: PetscOptionsGetScalar(NULL, NULL, "-q", &user->q, &flg);
369: PetscOptionsGetScalar(NULL, NULL, "-mux", &user->mux, &flg);
370: PetscOptionsGetScalar(NULL, NULL, "-muy", &user->muy, &flg);
371: if (flg == 0) user->muy = user->ws;
372: PetscOptionsGetScalar(NULL, NULL, "-xmin", &user->xmin, &flg);
373: PetscOptionsGetScalar(NULL, NULL, "-xmax", &user->xmax, &flg);
374: PetscOptionsGetScalar(NULL, NULL, "-ymin", &user->ymin, &flg);
375: PetscOptionsGetScalar(NULL, NULL, "-ymax", &user->ymax, &flg);
376: PetscOptionsGetInt(NULL, NULL, "-stencil_width", &user->st_width, &flg);
377: PetscOptionsGetEnum(NULL, NULL, "-bx", DMBoundaryTypes, (PetscEnum *)&user->bx, &flg);
378: PetscOptionsGetEnum(NULL, NULL, "-by", DMBoundaryTypes, (PetscEnum *)&user->by, &flg);
379: PetscOptionsGetReal(NULL, NULL, "-tf", &user->tf, &flg);
380: PetscOptionsGetReal(NULL, NULL, "-tcl", &user->tcl, &flg);
381: return 0;
382: }
384: /*TEST
386: build:
387: requires: !complex x
389: test:
390: args: -ts_max_steps 1
391: localrunfiles: petscopt_ex8
392: timeoutfactor: 3
394: TEST*/