Actual source code: ex2.c

  1: /*
  2:        Formatted test for TS routines.

  4:           Solves U_t=F(t,u)
  5:           Where:

  7:                   [2*u1+u2   ]
  8:           F(t,u)= [u1+2*u2+u3]
  9:                   [   u2+2*u3]

 11:        When run in parallel, each process solves the same set of equations separately.
 12: */

 14: static char help[] = "Solves a linear ODE. \n\n";

 16: #include <petscts.h>
 17: #include <petscpc.h>

 19: extern PetscErrorCode RHSFunction(TS, PetscReal, Vec, Vec, void *);
 20: extern PetscErrorCode RHSJacobian(TS, PetscReal, Vec, Mat, Mat, void *);
 21: extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *);
 22: extern PetscErrorCode Initial(Vec, void *);
 23: extern PetscErrorCode MyMatMult(Mat, Vec, Vec);

 25: extern PetscReal solx(PetscReal);
 26: extern PetscReal soly(PetscReal);
 27: extern PetscReal solz(PetscReal);

 29: int main(int argc, char **argv)
 30: {
 31:   PetscInt  time_steps = 100, steps;
 32:   Vec       global;
 33:   PetscReal dt, ftime;
 34:   TS        ts;
 35:   Mat       A, S;
 36:   PetscBool nest = PETSC_FALSE;

 38:   PetscFunctionBeginUser;
 39:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));
 40:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-time", &time_steps, NULL));
 41:   PetscCall(PetscOptionsGetBool(NULL, NULL, "-nest", &nest, NULL));

 43:   /* create vector to hold state */
 44:   if (nest) {
 45:     Vec g[3];

 47:     PetscCall(VecCreate(PETSC_COMM_WORLD, &g[0]));
 48:     PetscCall(VecSetSizes(g[0], 1, PETSC_DECIDE));
 49:     PetscCall(VecSetFromOptions(g[0]));
 50:     PetscCall(VecDuplicate(g[0], &g[1]));
 51:     PetscCall(VecDuplicate(g[0], &g[2]));
 52:     PetscCall(VecCreateNest(PETSC_COMM_WORLD, 3, NULL, g, &global));
 53:     PetscCall(VecDestroy(&g[0]));
 54:     PetscCall(VecDestroy(&g[1]));
 55:     PetscCall(VecDestroy(&g[2]));
 56:   } else {
 57:     PetscCall(VecCreate(PETSC_COMM_WORLD, &global));
 58:     PetscCall(VecSetSizes(global, 3, PETSC_DECIDE));
 59:     PetscCall(VecSetFromOptions(global));
 60:   }

 62:   /* set initial conditions */
 63:   PetscCall(Initial(global, NULL));

 65:   /* make timestep context */
 66:   PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
 67:   PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
 68:   PetscCall(TSMonitorSet(ts, Monitor, NULL, NULL));
 69:   dt = 0.001;

 71:   /*
 72:     The user provides the RHS and Jacobian
 73:   */
 74:   PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, NULL));
 75:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
 76:   PetscCall(MatSetSizes(A, 3, 3, PETSC_DECIDE, PETSC_DECIDE));
 77:   PetscCall(MatSetFromOptions(A));
 78:   PetscCall(MatSetUp(A));
 79:   PetscCall(RHSJacobian(ts, 0.0, global, A, A, NULL));
 80:   PetscCall(TSSetRHSJacobian(ts, A, A, RHSJacobian, NULL));

 82:   PetscCall(MatCreateShell(PETSC_COMM_WORLD, 3, 3, PETSC_DECIDE, PETSC_DECIDE, NULL, &S));
 83:   PetscCall(MatShellSetOperation(S, MATOP_MULT, (void (*)(void))MyMatMult));
 84:   PetscCall(TSSetRHSJacobian(ts, S, A, RHSJacobian, NULL));

 86:   PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP));
 87:   PetscCall(TSSetFromOptions(ts));

 89:   PetscCall(TSSetTimeStep(ts, dt));
 90:   PetscCall(TSSetMaxSteps(ts, time_steps));
 91:   PetscCall(TSSetMaxTime(ts, 1));
 92:   PetscCall(TSSetSolution(ts, global));

 94:   PetscCall(TSSolve(ts, global));
 95:   PetscCall(TSGetSolveTime(ts, &ftime));
 96:   PetscCall(TSGetStepNumber(ts, &steps));

 98:   /* free the memory */
 99:   PetscCall(TSDestroy(&ts));
100:   PetscCall(VecDestroy(&global));
101:   PetscCall(MatDestroy(&A));
102:   PetscCall(MatDestroy(&S));

104:   PetscCall(PetscFinalize());
105:   return 0;
106: }

108: PetscErrorCode MyMatMult(Mat S, Vec x, Vec y)
109: {
110:   const PetscScalar *inptr;
111:   PetscScalar       *outptr;

113:   PetscFunctionBeginUser;
114:   PetscCall(VecGetArrayRead(x, &inptr));
115:   PetscCall(VecGetArrayWrite(y, &outptr));

117:   outptr[0] = 2.0 * inptr[0] + inptr[1];
118:   outptr[1] = inptr[0] + 2.0 * inptr[1] + inptr[2];
119:   outptr[2] = inptr[1] + 2.0 * inptr[2];

121:   PetscCall(VecRestoreArrayRead(x, &inptr));
122:   PetscCall(VecRestoreArrayWrite(y, &outptr));
123:   PetscFunctionReturn(PETSC_SUCCESS);
124: }

126: PetscErrorCode Initial(Vec global, void *ctx)
127: {
128:   PetscScalar *localptr;

130:   PetscFunctionBeginUser;
131:   PetscCall(VecGetArrayWrite(global, &localptr));
132:   localptr[0] = solx(0.0);
133:   localptr[1] = soly(0.0);
134:   localptr[2] = solz(0.0);
135:   PetscCall(VecRestoreArrayWrite(global, &localptr));
136:   PetscFunctionReturn(PETSC_SUCCESS);
137: }

139: PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec global, void *ctx)
140: {
141:   const PetscScalar *tmp;
142:   PetscScalar        exact[] = {solx(time), soly(time), solz(time)};

144:   PetscFunctionBeginUser;
145:   PetscCall(VecGetArrayRead(global, &tmp));
146:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "At t =%14.6e u = %14.6e  %14.6e  %14.6e \n", (double)time, (double)PetscRealPart(tmp[0]), (double)PetscRealPart(tmp[1]), (double)PetscRealPart(tmp[2])));
147:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "At t =%14.6e errors = %14.6e  %14.6e  %14.6e \n", (double)time, (double)PetscRealPart(tmp[0] - exact[0]), (double)PetscRealPart(tmp[1] - exact[1]), (double)PetscRealPart(tmp[2] - exact[2])));
148:   PetscCall(VecRestoreArrayRead(global, &tmp));
149:   PetscFunctionReturn(PETSC_SUCCESS);
150: }

152: PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx)
153: {
154:   PetscScalar       *outptr;
155:   const PetscScalar *inptr;

157:   PetscFunctionBeginUser;
158:   /*Extract income array */
159:   PetscCall(VecGetArrayRead(globalin, &inptr));

161:   /* Extract outcome array*/
162:   PetscCall(VecGetArrayWrite(globalout, &outptr));

164:   outptr[0] = 2.0 * inptr[0] + inptr[1];
165:   outptr[1] = inptr[0] + 2.0 * inptr[1] + inptr[2];
166:   outptr[2] = inptr[1] + 2.0 * inptr[2];

168:   PetscCall(VecRestoreArrayRead(globalin, &inptr));
169:   PetscCall(VecRestoreArrayWrite(globalout, &outptr));
170:   PetscFunctionReturn(PETSC_SUCCESS);
171: }

173: PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec x, Mat A, Mat BB, void *ctx)
174: {
175:   PetscScalar v[3];
176:   PetscInt    idx[3], rst;

178:   PetscFunctionBeginUser;
179:   PetscCall(VecGetOwnershipRange(x, &rst, NULL));
180:   idx[0] = 0 + rst;
181:   idx[1] = 1 + rst;
182:   idx[2] = 2 + rst;

184:   v[0] = 2.0;
185:   v[1] = 1.0;
186:   v[2] = 0.0;
187:   PetscCall(MatSetValues(BB, 1, idx, 3, idx, v, INSERT_VALUES));

189:   v[0] = 1.0;
190:   v[1] = 2.0;
191:   v[2] = 1.0;
192:   PetscCall(MatSetValues(BB, 1, idx + 1, 3, idx, v, INSERT_VALUES));

194:   v[0] = 0.0;
195:   v[1] = 1.0;
196:   v[2] = 2.0;
197:   PetscCall(MatSetValues(BB, 1, idx + 2, 3, idx, v, INSERT_VALUES));

199:   PetscCall(MatAssemblyBegin(BB, MAT_FINAL_ASSEMBLY));
200:   PetscCall(MatAssemblyEnd(BB, MAT_FINAL_ASSEMBLY));

202:   if (A != BB) {
203:     PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
204:     PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
205:   }
206:   PetscFunctionReturn(PETSC_SUCCESS);
207: }

209: /*
210:       The exact solutions
211: */
212: PetscReal solx(PetscReal t)
213: {
214:   return PetscExpReal((2.0 - PetscSqrtReal(2.0)) * t) / 2.0 - PetscExpReal((2.0 - PetscSqrtReal(2.0)) * t) / (2.0 * PetscSqrtReal(2.0)) + PetscExpReal((2.0 + PetscSqrtReal(2.0)) * t) / 2.0 + PetscExpReal((2.0 + PetscSqrtReal(2.0)) * t) / (2.0 * PetscSqrtReal(2.0));
215: }

217: PetscReal soly(PetscReal t)
218: {
219:   return PetscExpReal((2.0 - PetscSqrtReal(2.0)) * t) / 2.0 - PetscExpReal((2.0 - PetscSqrtReal(2.0)) * t) / PetscSqrtReal(2.0) + PetscExpReal((2.0 + PetscSqrtReal(2.0)) * t) / 2.0 + PetscExpReal((2.0 + PetscSqrtReal(2.0)) * t) / PetscSqrtReal(2.0);
220: }

222: PetscReal solz(PetscReal t)
223: {
224:   return PetscExpReal((2.0 - PetscSqrtReal(2.0)) * t) / 2.0 - PetscExpReal((2.0 - PetscSqrtReal(2.0)) * t) / (2.0 * PetscSqrtReal(2.0)) + PetscExpReal((2.0 + PetscSqrtReal(2.0)) * t) / 2.0 + PetscExpReal((2.0 + PetscSqrtReal(2.0)) * t) / (2.0 * PetscSqrtReal(2.0));
225: }

227: /*TEST

229:     test:
230:       suffix: euler
231:       args: -ts_type euler -nest {{0 1}}
232:       requires: !single

234:     test:
235:       suffix: beuler
236:       args: -ts_type beuler -nest {{0 1}}
237:       requires: !single

239:     test:
240:       suffix: rk
241:       args: -ts_type rk -nest {{0 1}} -ts_adapt_monitor
242:       requires: !single

244:     test:
245:       diff_args: -j
246:       requires: double !complex
247:       output_file: output/ex2_be_adapt.out
248:       suffix: bdf_1_adapt
249:       args: -ts_type bdf -ts_bdf_order 1 -ts_adapt_type basic -ts_adapt_clip 0,2

251:     test:
252:       diff_args: -j
253:       requires: double !complex
254:       suffix: be_adapt
255:       args: -ts_type beuler -ts_adapt_type basic -ts_adapt_clip 0,2

257: TEST*/