Actual source code: ex8.c
petsc-3.7.5 2017-01-01
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: static const char *const BoundaryTypes[] = {"NONE","GHOSTED","MIRROR","PERIODIC","DMBoundaryType","DM_BOUNDARY_",0};
25: /*
26: User-defined data structures and routines
27: */
28: typedef struct {
29: PetscScalar ws; /* Synchronous speed */
30: PetscScalar H; /* Inertia constant */
31: PetscScalar D; /* Damping constant */
32: PetscScalar Pmax,Pmax_s; /* Maximum power output of generator */
33: PetscScalar PM_min; /* Mean mechanical power input */
34: PetscScalar lambda; /* correlation time */
35: PetscScalar q; /* noise strength */
36: PetscScalar mux; /* Initial average angle */
37: PetscScalar sigmax; /* Standard deviation of initial angle */
38: PetscScalar muy; /* Average speed */
39: PetscScalar sigmay; /* standard deviation of initial speed */
40: PetscScalar rho; /* Cross-correlation coefficient */
41: PetscScalar xmin; /* left boundary of angle */
42: PetscScalar xmax; /* right boundary of angle */
43: PetscScalar ymin; /* bottom boundary of speed */
44: PetscScalar ymax; /* top boundary of speed */
45: PetscScalar dx; /* x step size */
46: PetscScalar dy; /* y step size */
47: PetscScalar disper_coe; /* Dispersion coefficient */
48: DM da;
49: PetscInt st_width; /* Stencil width */
50: DMBoundaryType bx; /* x boundary type */
51: DMBoundaryType by; /* y boundary type */
52: PetscReal tf,tcl; /* Fault incidence and clearing times */
53: } AppCtx;
55: PetscErrorCode Parameter_settings(AppCtx*);
56: PetscErrorCode ini_bou(Vec,AppCtx*);
57: PetscErrorCode IFunction(TS,PetscReal,Vec,Vec,Vec,void*);
58: PetscErrorCode IJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*);
59: PetscErrorCode PostStep(TS);
63: int main(int argc, char **argv)
64: {
66: Vec x; /* Solution vector */
67: TS ts; /* Time-stepping context */
68: AppCtx user; /* Application context */
69: PetscViewer viewer;
71: PetscInitialize(&argc,&argv,"petscopt_ex8", help);
73: /* Get physics and time parameters */
74: Parameter_settings(&user);
75: /* Create a 2D DA with dof = 1 */
76: 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);
77: /* Set x and y coordinates */
78: DMDASetUniformCoordinates(user.da,user.xmin,user.xmax,user.ymin,user.ymax,0,0);
79: DMDASetCoordinateName(user.da,0,"X - the angle");
80: DMDASetCoordinateName(user.da,1,"Y - the speed");
82: /* Get global vector x from DM */
83: DMCreateGlobalVector(user.da,&x);
85: ini_bou(x,&user);
86: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"ini_x",FILE_MODE_WRITE,&viewer);
87: VecView(x,viewer);
88: PetscViewerDestroy(&viewer);
90: TSCreate(PETSC_COMM_WORLD,&ts);
91: TSSetDM(ts,user.da);
92: TSSetProblemType(ts,TS_NONLINEAR);
93: TSSetType(ts,TSARKIMEX);
94: TSSetIFunction(ts,NULL,IFunction,&user);
95: /* TSSetIJacobian(ts,NULL,NULL,IJacobian,&user); */
96: TSSetApplicationContext(ts,&user);
97: TSSetInitialTimeStep(ts,0.0,.005);
98: TSSetFromOptions(ts);
99: TSSetPostStep(ts,PostStep);
100: TSSolve(ts,x);
102: PetscViewerBinaryOpen(PETSC_COMM_WORLD,"fin_x",FILE_MODE_WRITE,&viewer);
103: VecView(x,viewer);
104: PetscViewerDestroy(&viewer);
106: VecDestroy(&x);
107: DMDestroy(&user.da);
108: TSDestroy(&ts);
109: PetscFinalize();
110: return 0;
111: }
115: PetscErrorCode PostStep(TS ts)
116: {
118: Vec X;
119: AppCtx *user;
120: PetscReal t;
121: PetscScalar asum;
124: TSGetApplicationContext(ts,&user);
125: TSGetTime(ts,&t);
126: TSGetSolution(ts,&X);
127: /*
128: if (t >= .2) {
129: TSGetSolution(ts,&X);
130: VecView(X,PETSC_VIEWER_BINARY_WORLD);
131: exit(0);
132: results in initial conditions after fault in binaryoutput
133: }*/
135: 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 */
136: else user->Pmax = user->Pmax_s;
138: VecSum(X,&asum);
139: PetscPrintf(PETSC_COMM_WORLD,"sum(p) at t = %f = %f\n",(double)t,(double)(asum));
140: return(0);
141: }
145: PetscErrorCode ini_bou(Vec X,AppCtx* user)
146: {
148: DM cda;
149: DMDACoor2d **coors;
150: PetscScalar **p;
151: Vec gc;
152: PetscInt M,N,I,J;
153: PetscMPIInt rank;
156: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
157: DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
158: user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
159: DMGetCoordinateDM(user->da,&cda);
160: DMGetCoordinates(user->da,&gc);
161: DMDAVecGetArrayRead(cda,gc,&coors);
162: DMDAVecGetArray(user->da,X,&p);
164: /* Point mass at (mux,muy) */
165: PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",user->mux,user->muy);
166: DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&I,&J,NULL,&user->mux,&user->muy,NULL);
167: user->PM_min = user->Pmax*PetscSinScalar(user->mux);
168: 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);
169: if (I > -1 && J > -1) {
170: p[J][I] = 1.0;
171: }
173: DMDAVecRestoreArrayRead(cda,gc,&coors);
174: DMDAVecRestoreArray(user->da,X,&p);
175: return(0);
176: }
178: /* First advection term */
181: PetscErrorCode adv1(PetscScalar **p,PetscScalar y,PetscInt i,PetscInt j,PetscInt M,PetscScalar *p1,AppCtx *user)
182: {
183: PetscScalar f,fpos,fneg;
185: f = (y - user->ws);
186: fpos = PetscMax(f,0);
187: fneg = PetscMin(f,0);
188: if (user->st_width == 1) {
189: *p1 = fpos*(p[j][i] - p[j][i-1])/user->dx + fneg*(p[j][i+1] - p[j][i])/user->dx;
190: } else if (user->st_width == 2) {
191: *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);
192: } else if (user->st_width == 3) {
193: *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);
194: }
195: /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/
196: return(0);
197: }
199: /* Second advection term */
202: PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscScalar y,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user)
203: {
204: PetscScalar f,fpos,fneg;
206: f = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x) - user->D*(y - user->ws));
207: fpos = PetscMax(f,0);
208: fneg = PetscMin(f,0);
209: if (user->st_width == 1) {
210: *p2 = fpos*(p[j][i] - p[j-1][i])/user->dy + fneg*(p[j+1][i] - p[j][i])/user->dy;
211: } else if (user->st_width ==2) {
212: *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);
213: } else if (user->st_width == 3) {
214: *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);
215: }
217: /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/
218: return(0);
219: }
221: /* Diffusion term */
224: PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user)
225: {
227: if (user->st_width == 1) {
228: *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy));
229: } else if (user->st_width == 2) {
230: *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));
231: } else if (user->st_width == 3) {
232: *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));
233: }
234: return(0);
235: }
239: PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
240: {
242: AppCtx *user=(AppCtx*)ctx;
243: DM cda;
244: DMDACoor2d **coors;
245: PetscScalar **p,**f,**pdot;
246: PetscInt i,j;
247: PetscInt xs,ys,xm,ym,M,N;
248: Vec localX,gc,localXdot;
249: PetscScalar p_adv1,p_adv2,p_diff;
252: DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
253: DMGetCoordinateDM(user->da,&cda);
254: DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);
256: DMGetLocalVector(user->da,&localX);
257: DMGetLocalVector(user->da,&localXdot);
259: DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);
260: DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);
261: DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);
262: DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);
264: DMGetCoordinatesLocal(user->da,&gc);
266: DMDAVecGetArrayRead(cda,gc,&coors);
267: DMDAVecGetArrayRead(user->da,localX,&p);
268: DMDAVecGetArrayRead(user->da,localXdot,&pdot);
269: DMDAVecGetArray(user->da,F,&f);
271: PetscScalar diffuse1,gamma;
272: gamma = user->D*user->ws/(2*user->H);
273: diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda));
274: user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1;
276: for (i=xs; i < xs+xm; i++) {
277: for (j=ys; j < ys+ym; j++) {
278: adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);
279: adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);
280: diffuse(p,i,j,t,&p_diff,user);
281: f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
282: }
283: }
284: DMDAVecRestoreArrayRead(user->da,localX,&p);
285: DMDAVecRestoreArrayRead(user->da,localX,&pdot);
286: DMRestoreLocalVector(user->da,&localX);
287: DMRestoreLocalVector(user->da,&localXdot);
288: DMDAVecRestoreArray(user->da,F,&f);
289: DMDAVecRestoreArrayRead(cda,gc,&coors);
291: return(0);
292: }
296: PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx)
297: {
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,c1pos,c1neg,c3pos,c3neg;
310: DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
311: DMGetCoordinateDM(user->da,&cda);
312: DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);
314: DMGetCoordinatesLocal(user->da,&gc);
315: 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; yi = coors[j][i].y;
320: row.i = i; row.j = j;
321: c1 = (yi-user->ws)/user->dx;
322: c1pos = PetscMax(c1,0);
323: c1neg = PetscMin(c1,0);
324: c3 = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(xi) - user->D*(yi - user->ws))/user->dy;
325: c3pos = PetscMax(c3,0);
326: c3neg = PetscMin(c3,0);
327: c5 = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
328: col[nc].i = i-1; col[nc].j = j; val[nc++] = c1pos;
329: col[nc].i = i+1; col[nc].j = j; val[nc++] = -c1neg;
330: col[nc].i = i; col[nc].j = j-1; val[nc++] = c3pos + c5;
331: col[nc].i = i; col[nc].j = j+1; val[nc++] = -c3neg + c5;
332: col[nc].i = i; col[nc].j = j; val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
333: MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES);
334: }
335: }
336: DMDAVecRestoreArrayRead(cda,gc,&coors);
338: MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);
339: MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);
340: if (J != Jpre) {
341: MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);
342: MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);
343: }
344: return(0);
345: }
349: PetscErrorCode Parameter_settings(AppCtx *user)
350: {
352: PetscBool flg;
356: /* Set default parameters */
357: user->ws = 1.0;
358: user->H = 5.0;
359: user->D = 0.0;
360: user->Pmax = user->Pmax_s = 2.1;
361: user->PM_min = 1.0;
362: user->lambda = 0.1;
363: user->q = 1.0;
364: user->mux = PetscAsinScalar(user->PM_min/user->Pmax);
365: user->sigmax = 0.1;
366: user->sigmay = 0.1;
367: user->rho = 0.0;
368: user->xmin = -PETSC_PI;
369: user->xmax = PETSC_PI;
370: user->bx = DM_BOUNDARY_PERIODIC;
371: user->by = DM_BOUNDARY_GHOSTED;
372: user->tf = user->tcl = -1;
373: user->ymin = -2.0;
374: user->ymax = 2.0;
375: user->st_width = 1;
377: PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg);
378: PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg);
379: PetscOptionsGetScalar(NULL,NULL,"-D",&user->D,&flg);
380: PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg);
381: PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg);
382: PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg);
383: PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg);
384: PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg);
385: PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg);
386: if (flg == 0) {
387: user->muy = user->ws;
388: }
389: PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg);
390: PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg);
391: PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg);
392: PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg);
393: PetscOptionsGetInt(NULL,NULL,"-stencil_width",&user->st_width,&flg);
394: PetscOptionsGetEnum("","-bx",BoundaryTypes,(PetscEnum*)&user->bx,&flg);
395: PetscOptionsGetEnum("","-by",BoundaryTypes,(PetscEnum*)&user->by,&flg);
396: PetscOptionsGetReal(NULL,"-tf",&user->tf,&flg);
397: PetscOptionsGetReal(NULL,"-tcl",&user->tcl,&flg);
398: return(0);
399: }