Actual source code: ex3.c
2: static char help[] = "Solves 1D heat equation with FEM formulation.\n\
3: Input arguments are\n\
4: -useAlhs: solve Alhs*U' = (Arhs*U + g) \n\
5: otherwise, solve U' = inv(Alhs)*(Arhs*U + g) \n\n";
7: /*--------------------------------------------------------------------------
8: Solves 1D heat equation U_t = U_xx with FEM formulation:
9: Alhs*U' = rhs (= Arhs*U + g)
10: We thank Chris Cox <clcox@clemson.edu> for contributing the original code
11: ----------------------------------------------------------------------------*/
13: #include <petscksp.h>
14: #include <petscts.h>
16: /* special variable - max size of all arrays */
17: #define num_z 10
19: /*
20: User-defined application context - contains data needed by the
21: application-provided call-back routines.
22: */
23: typedef struct {
24: Mat Amat; /* left hand side matrix */
25: Vec ksp_rhs, ksp_sol; /* working vectors for formulating inv(Alhs)*(Arhs*U+g) */
26: int max_probsz; /* max size of the problem */
27: PetscBool useAlhs; /* flag (1 indicates solving Alhs*U' = Arhs*U+g */
28: int nz; /* total number of grid points */
29: PetscInt m; /* total number of interio grid points */
30: Vec solution; /* global exact ts solution vector */
31: PetscScalar *z; /* array of grid points */
32: PetscBool debug; /* flag (1 indicates activation of debugging printouts) */
33: } AppCtx;
35: extern PetscScalar exact(PetscScalar, PetscReal);
36: extern PetscErrorCode Monitor(TS, PetscInt, PetscReal, Vec, void *);
37: extern PetscErrorCode Petsc_KSPSolve(AppCtx *);
38: extern PetscScalar bspl(PetscScalar *, PetscScalar, PetscInt, PetscInt, PetscInt[][2], PetscInt);
39: extern PetscErrorCode femBg(PetscScalar[][3], PetscScalar *, PetscInt, PetscScalar *, PetscReal);
40: extern PetscErrorCode femA(AppCtx *, PetscInt, PetscScalar *);
41: extern PetscErrorCode rhs(AppCtx *, PetscScalar *, PetscInt, PetscScalar *, PetscReal);
42: extern PetscErrorCode RHSfunction(TS, PetscReal, Vec, Vec, void *);
44: int main(int argc, char **argv)
45: {
46: PetscInt i, m, nz, steps, max_steps, k, nphase = 1;
47: PetscScalar zInitial, zFinal, val, *z;
48: PetscReal stepsz[4], T, ftime;
49: TS ts;
50: SNES snes;
51: Mat Jmat;
52: AppCtx appctx; /* user-defined application context */
53: Vec init_sol; /* ts solution vector */
54: PetscMPIInt size;
56: PetscFunctionBeginUser;
57: PetscCall(PetscInitialize(&argc, &argv, (char *)0, help));
58: PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));
59: PetscCheck(size == 1, PETSC_COMM_SELF, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only");
61: /* initializations */
62: zInitial = 0.0;
63: zFinal = 1.0;
64: nz = num_z;
65: m = nz - 2;
66: appctx.nz = nz;
67: max_steps = (PetscInt)10000;
69: appctx.m = m;
70: appctx.max_probsz = nz;
71: appctx.debug = PETSC_FALSE;
72: appctx.useAlhs = PETSC_FALSE;
74: PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "", "");
75: PetscCall(PetscOptionsName("-debug", NULL, NULL, &appctx.debug));
76: PetscCall(PetscOptionsName("-useAlhs", NULL, NULL, &appctx.useAlhs));
77: PetscCall(PetscOptionsRangeInt("-nphase", NULL, NULL, nphase, &nphase, NULL, 1, 3));
78: PetscOptionsEnd();
79: T = 0.014 / nphase;
81: /* create vector to hold ts solution */
82: /*-----------------------------------*/
83: PetscCall(VecCreate(PETSC_COMM_WORLD, &init_sol));
84: PetscCall(VecSetSizes(init_sol, PETSC_DECIDE, m));
85: PetscCall(VecSetFromOptions(init_sol));
87: /* create vector to hold true ts soln for comparison */
88: PetscCall(VecDuplicate(init_sol, &appctx.solution));
90: /* create LHS matrix Amat */
91: /*------------------------*/
92: PetscCall(MatCreateSeqAIJ(PETSC_COMM_WORLD, m, m, 3, NULL, &appctx.Amat));
93: PetscCall(MatSetFromOptions(appctx.Amat));
94: PetscCall(MatSetUp(appctx.Amat));
95: /* set space grid points - interio points only! */
96: PetscCall(PetscMalloc1(nz + 1, &z));
97: for (i = 0; i < nz; i++) z[i] = (i) * ((zFinal - zInitial) / (nz - 1));
98: appctx.z = z;
99: PetscCall(femA(&appctx, nz, z));
101: /* create the jacobian matrix */
102: /*----------------------------*/
103: PetscCall(MatCreate(PETSC_COMM_WORLD, &Jmat));
104: PetscCall(MatSetSizes(Jmat, PETSC_DECIDE, PETSC_DECIDE, m, m));
105: PetscCall(MatSetFromOptions(Jmat));
106: PetscCall(MatSetUp(Jmat));
108: /* create working vectors for formulating rhs=inv(Alhs)*(Arhs*U + g) */
109: PetscCall(VecDuplicate(init_sol, &appctx.ksp_rhs));
110: PetscCall(VecDuplicate(init_sol, &appctx.ksp_sol));
112: /* set initial guess */
113: /*-------------------*/
114: for (i = 0; i < nz - 2; i++) {
115: val = exact(z[i + 1], 0.0);
116: PetscCall(VecSetValue(init_sol, i, (PetscScalar)val, INSERT_VALUES));
117: }
118: PetscCall(VecAssemblyBegin(init_sol));
119: PetscCall(VecAssemblyEnd(init_sol));
121: /*create a time-stepping context and set the problem type */
122: /*--------------------------------------------------------*/
123: PetscCall(TSCreate(PETSC_COMM_WORLD, &ts));
124: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
126: /* set time-step method */
127: PetscCall(TSSetType(ts, TSCN));
129: /* Set optional user-defined monitoring routine */
130: PetscCall(TSMonitorSet(ts, Monitor, &appctx, NULL));
131: /* set the right hand side of U_t = RHSfunction(U,t) */
132: PetscCall(TSSetRHSFunction(ts, NULL, (PetscErrorCode(*)(TS, PetscScalar, Vec, Vec, void *))RHSfunction, &appctx));
134: if (appctx.useAlhs) {
135: /* set the left hand side matrix of Amat*U_t = rhs(U,t) */
137: /* Note: this approach is incompatible with the finite differenced Jacobian set below because we can't restore the
138: * Alhs matrix without making a copy. Either finite difference the entire thing or use analytic Jacobians in both
139: * places.
140: */
141: PetscCall(TSSetIFunction(ts, NULL, TSComputeIFunctionLinear, &appctx));
142: PetscCall(TSSetIJacobian(ts, appctx.Amat, appctx.Amat, TSComputeIJacobianConstant, &appctx));
143: }
145: /* use petsc to compute the jacobian by finite differences */
146: PetscCall(TSGetSNES(ts, &snes));
147: PetscCall(SNESSetJacobian(snes, Jmat, Jmat, SNESComputeJacobianDefault, NULL));
149: /* get the command line options if there are any and set them */
150: PetscCall(TSSetFromOptions(ts));
152: #if defined(PETSC_HAVE_SUNDIALS2)
153: {
154: TSType type;
155: PetscBool sundialstype = PETSC_FALSE;
156: PetscCall(TSGetType(ts, &type));
157: PetscCall(PetscObjectTypeCompare((PetscObject)ts, TSSUNDIALS, &sundialstype));
158: PetscCheck(!sundialstype || !appctx.useAlhs, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot use Alhs formulation for TSSUNDIALS type");
159: }
160: #endif
161: /* Sets the initial solution */
162: PetscCall(TSSetSolution(ts, init_sol));
164: stepsz[0] = 1.0 / (2.0 * (nz - 1) * (nz - 1)); /* (mesh_size)^2/2.0 */
165: ftime = 0.0;
166: for (k = 0; k < nphase; k++) {
167: if (nphase > 1) PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Phase %" PetscInt_FMT " initial time %g, stepsz %g, duration: %g\n", k, (double)ftime, (double)stepsz[k], (double)((k + 1) * T)));
168: PetscCall(TSSetTime(ts, ftime));
169: PetscCall(TSSetTimeStep(ts, stepsz[k]));
170: PetscCall(TSSetMaxSteps(ts, max_steps));
171: PetscCall(TSSetMaxTime(ts, (k + 1) * T));
172: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
174: /* loop over time steps */
175: /*----------------------*/
176: PetscCall(TSSolve(ts, init_sol));
177: PetscCall(TSGetSolveTime(ts, &ftime));
178: PetscCall(TSGetStepNumber(ts, &steps));
179: stepsz[k + 1] = stepsz[k] * 1.5; /* change step size for the next phase */
180: }
182: /* free space */
183: PetscCall(TSDestroy(&ts));
184: PetscCall(MatDestroy(&appctx.Amat));
185: PetscCall(MatDestroy(&Jmat));
186: PetscCall(VecDestroy(&appctx.ksp_rhs));
187: PetscCall(VecDestroy(&appctx.ksp_sol));
188: PetscCall(VecDestroy(&init_sol));
189: PetscCall(VecDestroy(&appctx.solution));
190: PetscCall(PetscFree(z));
192: PetscCall(PetscFinalize());
193: return 0;
194: }
196: /*------------------------------------------------------------------------
197: Set exact solution
198: u(z,t) = sin(6*PI*z)*exp(-36.*PI*PI*t) + 3.*sin(2*PI*z)*exp(-4.*PI*PI*t)
199: --------------------------------------------------------------------------*/
200: PetscScalar exact(PetscScalar z, PetscReal t)
201: {
202: PetscScalar val, ex1, ex2;
204: ex1 = PetscExpReal(-36. * PETSC_PI * PETSC_PI * t);
205: ex2 = PetscExpReal(-4. * PETSC_PI * PETSC_PI * t);
206: val = PetscSinScalar(6 * PETSC_PI * z) * ex1 + 3. * PetscSinScalar(2 * PETSC_PI * z) * ex2;
207: return val;
208: }
210: /*
211: Monitor - User-provided routine to monitor the solution computed at
212: each timestep. This example plots the solution and computes the
213: error in two different norms.
215: Input Parameters:
216: ts - the timestep context
217: step - the count of the current step (with 0 meaning the
218: initial condition)
219: time - the current time
220: u - the solution at this timestep
221: ctx - the user-provided context for this monitoring routine.
222: In this case we use the application context which contains
223: information about the problem size, workspace and the exact
224: solution.
225: */
226: PetscErrorCode Monitor(TS ts, PetscInt step, PetscReal time, Vec u, void *ctx)
227: {
228: AppCtx *appctx = (AppCtx *)ctx;
229: PetscInt i, m = appctx->m;
230: PetscReal norm_2, norm_max, h = 1.0 / (m + 1);
231: PetscScalar *u_exact;
233: PetscFunctionBeginUser;
234: /* Compute the exact solution */
235: PetscCall(VecGetArrayWrite(appctx->solution, &u_exact));
236: for (i = 0; i < m; i++) u_exact[i] = exact(appctx->z[i + 1], time);
237: PetscCall(VecRestoreArrayWrite(appctx->solution, &u_exact));
239: /* Print debugging information if desired */
240: if (appctx->debug) {
241: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Computed solution vector at time %g\n", (double)time));
242: PetscCall(VecView(u, PETSC_VIEWER_STDOUT_SELF));
243: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Exact solution vector\n"));
244: PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
245: }
247: /* Compute the 2-norm and max-norm of the error */
248: PetscCall(VecAXPY(appctx->solution, -1.0, u));
249: PetscCall(VecNorm(appctx->solution, NORM_2, &norm_2));
251: norm_2 = PetscSqrtReal(h) * norm_2;
252: PetscCall(VecNorm(appctx->solution, NORM_MAX, &norm_max));
253: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Timestep %" PetscInt_FMT ": time = %g, 2-norm error = %6.4f, max norm error = %6.4f\n", step, (double)time, (double)norm_2, (double)norm_max));
255: /*
256: Print debugging information if desired
257: */
258: if (appctx->debug) {
259: PetscCall(PetscPrintf(PETSC_COMM_SELF, "Error vector\n"));
260: PetscCall(VecView(appctx->solution, PETSC_VIEWER_STDOUT_SELF));
261: }
262: PetscFunctionReturn(PETSC_SUCCESS);
263: }
265: /*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
266: Function to solve a linear system using KSP
267: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/
269: PetscErrorCode Petsc_KSPSolve(AppCtx *obj)
270: {
271: KSP ksp;
272: PC pc;
274: PetscFunctionBeginUser;
275: /*create the ksp context and set the operators,that is, associate the system matrix with it*/
276: PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
277: PetscCall(KSPSetOperators(ksp, obj->Amat, obj->Amat));
279: /*get the preconditioner context, set its type and the tolerances*/
280: PetscCall(KSPGetPC(ksp, &pc));
281: PetscCall(PCSetType(pc, PCLU));
282: PetscCall(KSPSetTolerances(ksp, 1.e-7, PETSC_DEFAULT, PETSC_DEFAULT, PETSC_DEFAULT));
284: /*get the command line options if there are any and set them*/
285: PetscCall(KSPSetFromOptions(ksp));
287: /*get the linear system (ksp) solve*/
288: PetscCall(KSPSolve(ksp, obj->ksp_rhs, obj->ksp_sol));
290: PetscCall(KSPDestroy(&ksp));
291: PetscFunctionReturn(PETSC_SUCCESS);
292: }
294: /***********************************************************************
295: Function to return value of basis function or derivative of basis function.
296: ***********************************************************************
298: Arguments:
299: x = array of xpoints or nodal values
300: xx = point at which the basis function is to be
301: evaluated.
302: il = interval containing xx.
303: iq = indicates which of the two basis functions in
304: interval intrvl should be used
305: nll = array containing the endpoints of each interval.
306: id = If id ~= 2, the value of the basis function
307: is calculated; if id = 2, the value of the
308: derivative of the basis function is returned.
309: ***********************************************************************/
311: PetscScalar bspl(PetscScalar *x, PetscScalar xx, PetscInt il, PetscInt iq, PetscInt nll[][2], PetscInt id)
312: {
313: PetscScalar x1, x2, bfcn;
314: PetscInt i1, i2, iq1, iq2;
316: /* Determine which basis function in interval intrvl is to be used in */
317: iq1 = iq;
318: if (iq1 == 0) iq2 = 1;
319: else iq2 = 0;
321: /* Determine endpoint of the interval intrvl */
322: i1 = nll[il][iq1];
323: i2 = nll[il][iq2];
325: /* Determine nodal values at the endpoints of the interval intrvl */
326: x1 = x[i1];
327: x2 = x[i2];
329: /* Evaluate basis function */
330: if (id == 2) bfcn = (1.0) / (x1 - x2);
331: else bfcn = (xx - x2) / (x1 - x2);
332: return bfcn;
333: }
335: /*---------------------------------------------------------
336: Function called by rhs function to get B and g
337: ---------------------------------------------------------*/
338: PetscErrorCode femBg(PetscScalar btri[][3], PetscScalar *f, PetscInt nz, PetscScalar *z, PetscReal t)
339: {
340: PetscInt i, j, jj, il, ip, ipp, ipq, iq, iquad, iqq;
341: PetscInt nli[num_z][2], indx[num_z];
342: PetscScalar dd, dl, zip, zipq, zz, b_z, bb_z, bij;
343: PetscScalar zquad[num_z][3], dlen[num_z], qdwt[3];
345: PetscFunctionBeginUser;
346: /* initializing everything - btri and f are initialized in rhs.c */
347: for (i = 0; i < nz; i++) {
348: nli[i][0] = 0;
349: nli[i][1] = 0;
350: indx[i] = 0;
351: zquad[i][0] = 0.0;
352: zquad[i][1] = 0.0;
353: zquad[i][2] = 0.0;
354: dlen[i] = 0.0;
355: } /*end for (i)*/
357: /* quadrature weights */
358: qdwt[0] = 1.0 / 6.0;
359: qdwt[1] = 4.0 / 6.0;
360: qdwt[2] = 1.0 / 6.0;
362: /* 1st and last nodes have Dirichlet boundary condition -
363: set indices there to -1 */
365: for (i = 0; i < nz - 1; i++) indx[i] = i - 1;
366: indx[nz - 1] = -1;
368: ipq = 0;
369: for (il = 0; il < nz - 1; il++) {
370: ip = ipq;
371: ipq = ip + 1;
372: zip = z[ip];
373: zipq = z[ipq];
374: dl = zipq - zip;
375: zquad[il][0] = zip;
376: zquad[il][1] = (0.5) * (zip + zipq);
377: zquad[il][2] = zipq;
378: dlen[il] = PetscAbsScalar(dl);
379: nli[il][0] = ip;
380: nli[il][1] = ipq;
381: }
383: for (il = 0; il < nz - 1; il++) {
384: for (iquad = 0; iquad < 3; iquad++) {
385: dd = (dlen[il]) * (qdwt[iquad]);
386: zz = zquad[il][iquad];
388: for (iq = 0; iq < 2; iq++) {
389: ip = nli[il][iq];
390: b_z = bspl(z, zz, il, iq, nli, 2);
391: i = indx[ip];
393: if (i > -1) {
394: for (iqq = 0; iqq < 2; iqq++) {
395: ipp = nli[il][iqq];
396: bb_z = bspl(z, zz, il, iqq, nli, 2);
397: j = indx[ipp];
398: bij = -b_z * bb_z;
400: if (j > -1) {
401: jj = 1 + j - i;
402: btri[i][jj] += bij * dd;
403: } else {
404: f[i] += bij * dd * exact(z[ipp], t);
405: /* f[i] += 0.0; */
406: /* if (il==0 && j==-1) { */
407: /* f[i] += bij*dd*exact(zz,t); */
408: /* }*/ /*end if*/
409: } /*end else*/
410: } /*end for (iqq)*/
411: } /*end if (i>0)*/
412: } /*end for (iq)*/
413: } /*end for (iquad)*/
414: } /*end for (il)*/
415: PetscFunctionReturn(PETSC_SUCCESS);
416: }
418: PetscErrorCode femA(AppCtx *obj, PetscInt nz, PetscScalar *z)
419: {
420: PetscInt i, j, il, ip, ipp, ipq, iq, iquad, iqq;
421: PetscInt nli[num_z][2], indx[num_z];
422: PetscScalar dd, dl, zip, zipq, zz, bb, bbb, aij;
423: PetscScalar rquad[num_z][3], dlen[num_z], qdwt[3], add_term;
425: PetscFunctionBeginUser;
426: /* initializing everything */
427: for (i = 0; i < nz; i++) {
428: nli[i][0] = 0;
429: nli[i][1] = 0;
430: indx[i] = 0;
431: rquad[i][0] = 0.0;
432: rquad[i][1] = 0.0;
433: rquad[i][2] = 0.0;
434: dlen[i] = 0.0;
435: } /*end for (i)*/
437: /* quadrature weights */
438: qdwt[0] = 1.0 / 6.0;
439: qdwt[1] = 4.0 / 6.0;
440: qdwt[2] = 1.0 / 6.0;
442: /* 1st and last nodes have Dirichlet boundary condition -
443: set indices there to -1 */
445: for (i = 0; i < nz - 1; i++) indx[i] = i - 1;
446: indx[nz - 1] = -1;
448: ipq = 0;
450: for (il = 0; il < nz - 1; il++) {
451: ip = ipq;
452: ipq = ip + 1;
453: zip = z[ip];
454: zipq = z[ipq];
455: dl = zipq - zip;
456: rquad[il][0] = zip;
457: rquad[il][1] = (0.5) * (zip + zipq);
458: rquad[il][2] = zipq;
459: dlen[il] = PetscAbsScalar(dl);
460: nli[il][0] = ip;
461: nli[il][1] = ipq;
462: } /*end for (il)*/
464: for (il = 0; il < nz - 1; il++) {
465: for (iquad = 0; iquad < 3; iquad++) {
466: dd = (dlen[il]) * (qdwt[iquad]);
467: zz = rquad[il][iquad];
469: for (iq = 0; iq < 2; iq++) {
470: ip = nli[il][iq];
471: bb = bspl(z, zz, il, iq, nli, 1);
472: i = indx[ip];
473: if (i > -1) {
474: for (iqq = 0; iqq < 2; iqq++) {
475: ipp = nli[il][iqq];
476: bbb = bspl(z, zz, il, iqq, nli, 1);
477: j = indx[ipp];
478: aij = bb * bbb;
479: if (j > -1) {
480: add_term = aij * dd;
481: PetscCall(MatSetValue(obj->Amat, i, j, add_term, ADD_VALUES));
482: } /*endif*/
483: } /*end for (iqq)*/
484: } /*end if (i>0)*/
485: } /*end for (iq)*/
486: } /*end for (iquad)*/
487: } /*end for (il)*/
488: PetscCall(MatAssemblyBegin(obj->Amat, MAT_FINAL_ASSEMBLY));
489: PetscCall(MatAssemblyEnd(obj->Amat, MAT_FINAL_ASSEMBLY));
490: PetscFunctionReturn(PETSC_SUCCESS);
491: }
493: /*---------------------------------------------------------
494: Function to fill the rhs vector with
495: By + g values ****
496: ---------------------------------------------------------*/
497: PetscErrorCode rhs(AppCtx *obj, PetscScalar *y, PetscInt nz, PetscScalar *z, PetscReal t)
498: {
499: PetscInt i, j, js, je, jj;
500: PetscScalar val, g[num_z], btri[num_z][3], add_term;
502: PetscFunctionBeginUser;
503: for (i = 0; i < nz - 2; i++) {
504: for (j = 0; j <= 2; j++) btri[i][j] = 0.0;
505: g[i] = 0.0;
506: }
508: /* call femBg to set the tri-diagonal b matrix and vector g */
509: PetscCall(femBg(btri, g, nz, z, t));
511: /* setting the entries of the right hand side vector */
512: for (i = 0; i < nz - 2; i++) {
513: val = 0.0;
514: js = 0;
515: if (i == 0) js = 1;
516: je = 2;
517: if (i == nz - 2) je = 1;
519: for (jj = js; jj <= je; jj++) {
520: j = i + jj - 1;
521: val += (btri[i][jj]) * (y[j]);
522: }
523: add_term = val + g[i];
524: PetscCall(VecSetValue(obj->ksp_rhs, (PetscInt)i, (PetscScalar)add_term, INSERT_VALUES));
525: }
526: PetscCall(VecAssemblyBegin(obj->ksp_rhs));
527: PetscCall(VecAssemblyEnd(obj->ksp_rhs));
528: PetscFunctionReturn(PETSC_SUCCESS);
529: }
531: /*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
532: %% Function to form the right hand side of the time-stepping problem. %%
533: %% -------------------------------------------------------------------------------------------%%
534: if (useAlhs):
535: globalout = By+g
536: else if (!useAlhs):
537: globalout = f(y,t)=Ainv(By+g),
538: in which the ksp solver to transform the problem A*ydot=By+g
539: to the problem ydot=f(y,t)=inv(A)*(By+g)
540: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/
542: PetscErrorCode RHSfunction(TS ts, PetscReal t, Vec globalin, Vec globalout, void *ctx)
543: {
544: AppCtx *obj = (AppCtx *)ctx;
545: PetscScalar soln[num_z];
546: const PetscScalar *soln_ptr;
547: PetscInt i, nz = obj->nz;
548: PetscReal time;
550: PetscFunctionBeginUser;
551: /* get the previous solution to compute updated system */
552: PetscCall(VecGetArrayRead(globalin, &soln_ptr));
553: for (i = 0; i < num_z - 2; i++) soln[i] = soln_ptr[i];
554: PetscCall(VecRestoreArrayRead(globalin, &soln_ptr));
555: soln[num_z - 1] = 0.0;
556: soln[num_z - 2] = 0.0;
558: /* clear out the matrix and rhs for ksp to keep things straight */
559: PetscCall(VecSet(obj->ksp_rhs, (PetscScalar)0.0));
561: time = t;
562: /* get the updated system */
563: PetscCall(rhs(obj, soln, nz, obj->z, time)); /* setup of the By+g rhs */
565: /* do a ksp solve to get the rhs for the ts problem */
566: if (obj->useAlhs) {
567: /* ksp_sol = ksp_rhs */
568: PetscCall(VecCopy(obj->ksp_rhs, globalout));
569: } else {
570: /* ksp_sol = inv(Amat)*ksp_rhs */
571: PetscCall(Petsc_KSPSolve(obj));
572: PetscCall(VecCopy(obj->ksp_sol, globalout));
573: }
574: PetscFunctionReturn(PETSC_SUCCESS);
575: }
577: /*TEST
579: build:
580: requires: !complex
582: test:
583: suffix: euler
584: output_file: output/ex3.out
586: test:
587: suffix: 2
588: args: -useAlhs
589: output_file: output/ex3.out
590: TODO: Broken because SNESComputeJacobianDefault is incompatible with TSComputeIJacobianConstant
592: TEST*/