Actual source code: ex24.c
2: static char help[] = "Solves PDE optimization problem of ex22.c with AD for adjoint.\n\n";
4: #include petscda.h
5: #include petscpf.h
6: #include petscmg.h
7: #include petscsnes.h
8: #include petscdmmg.h
10: /*
12: Minimize F(w,u) such that G(w,u) = 0
14: L(w,u,lambda) = F(w,u) + lambda^T G(w,u)
16: w - design variables (what we change to get an optimal solution)
17: u - state variables (i.e. the PDE solution)
18: lambda - the Lagrange multipliers
20: U = (w u lambda)
22: fu, fw, flambda contain the gradient of L(w,u,lambda)
24: FU = (fw fu flambda)
26: In this example the PDE is
27: Uxx - u^2 = 2,
28: u(0) = w(0), thus this is the free parameter
29: u(1) = 0
30: the function we wish to minimize is
31: \integral u^{2}
33: The exact solution for u is given by u(x) = x*x - 1.25*x + .25
35: Use the usual centered finite differences.
37: Note we treat the problem as non-linear though it happens to be linear
39: The lambda and u are NOT interlaced.
41: We optionally provide a preconditioner on each level from the operator
43: (1 0 0)
44: (0 J 0)
45: (0 0 J')
47:
48: */
54: typedef struct {
55: Mat J; /* Jacobian of PDE system */
56: KSP ksp; /* Solver for that Jacobian */
57: } AppCtx;
61: PetscErrorCode myPCApply(DMMG dmmg,Vec x,Vec y)
62: {
63: Vec xu,xlambda,yu,ylambda;
64: PetscScalar *xw,*yw;
66: DMComposite packer = (DMComposite)dmmg->dm;
67: AppCtx *appctx = (AppCtx*)dmmg->user;
70: DMCompositeGetAccess(packer,x,&xw,&xu,&xlambda);
71: DMCompositeGetAccess(packer,y,&yw,&yu,&ylambda);
72: if (yw && xw) {
73: yw[0] = xw[0];
74: }
75: KSPSolve(appctx->ksp,xu,yu);
77: KSPSolveTranspose(appctx->ksp,xlambda,ylambda);
78: /* VecCopy(xu,yu);
79: VecCopy(xlambda,ylambda); */
80: DMCompositeRestoreAccess(packer,x,&xw,&xu,&xlambda);
81: DMCompositeRestoreAccess(packer,y,&yw,&yu,&ylambda);
82: return(0);
83: }
87: PetscErrorCode myPCView(DMMG dmmg,PetscViewer v)
88: {
90: AppCtx *appctx = (AppCtx*)dmmg->user;
93: KSPView(appctx->ksp,v);
94: return(0);
95: }
99: int main(int argc,char **argv)
100: {
102: PetscInt nlevels,i,j;
103: DA da;
104: DMMG *dmmg;
105: DMComposite packer;
106: AppCtx *appctx;
107: ISColoring iscoloring;
108: PetscTruth bdp;
110: PetscInitialize(&argc,&argv,PETSC_NULL,help);
112: /* Hardwire several options; can be changed at command line */
113: PetscOptionsSetValue("-dmmg_grid_sequence",PETSC_NULL);
114: PetscOptionsSetValue("-ksp_type","fgmres");
115: PetscOptionsSetValue("-ksp_max_it","5");
116: PetscOptionsSetValue("-pc_mg_type","full");
117: PetscOptionsSetValue("-mg_coarse_ksp_type","gmres");
118: PetscOptionsSetValue("-mg_levels_ksp_type","gmres");
119: PetscOptionsSetValue("-mg_coarse_ksp_max_it","6");
120: PetscOptionsSetValue("-mg_levels_ksp_max_it","3");
121: PetscOptionsSetValue("-snes_mf_type","wp");
122: PetscOptionsSetValue("-snes_mf_compute_normu","no");
123: PetscOptionsSetValue("-snes_ls","basic");
124: PetscOptionsSetValue("-dmmg_jacobian_mf_fd",0);
125: /* PetscOptionsSetValue("-snes_ls","basicnonorms"); */
126: PetscOptionsInsert(&argc,&argv,PETSC_NULL);
128: /* create DMComposite object to manage composite vector */
129: DMCompositeCreate(PETSC_COMM_WORLD,&packer);
130: DMCompositeAddArray(packer,0,1);
131: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,1,1,PETSC_NULL,&da);
132: DMCompositeAddDM(packer,(DM)da);
133: DMCompositeAddDM(packer,(DM)da);
134: DADestroy(da);
136: /* create nonlinear multi-level solver */
137: DMMGCreate(PETSC_COMM_WORLD,2,PETSC_NULL,&dmmg);
138: DMMGSetDM(dmmg,(DM)packer);
139: DMCompositeDestroy(packer);
141: /* Create Jacobian of PDE function for each level */
142: nlevels = DMMGGetLevels(dmmg);
143: for (i=0; i<nlevels; i++) {
144: packer = (DMComposite)dmmg[i]->dm;
145: DMCompositeGetEntries(packer,PETSC_NULL,&da,PETSC_NULL);
146: PetscNew(AppCtx,&appctx);
147: DAGetColoring(da,IS_COLORING_GHOSTED,&iscoloring);
148: DAGetMatrix(da,MATAIJ,&appctx->J);
149: MatSetColoring(appctx->J,iscoloring);
150: ISColoringDestroy(iscoloring);
151: DASetLocalFunction(da,(DALocalFunction1)PDEFormFunctionLocal);
152: DASetLocalAdicFunction(da,ad_PDEFormFunctionLocal);
153: dmmg[i]->user = (void*)appctx;
154: }
156: DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);
157: DMMGSetFromOptions(dmmg);
159: PetscOptionsHasName(PETSC_NULL,"-bdp",&bdp);
160: if (bdp) {
161: for (i=0; i<nlevels; i++) {
162: KSP ksp;
163: PC pc,mpc;
165: appctx = (AppCtx*) dmmg[i]->user;
166: KSPCreate(PETSC_COMM_WORLD,&appctx->ksp);
167: KSPSetOptionsPrefix(appctx->ksp,"bdp_");
168: KSPSetFromOptions(appctx->ksp);
170: SNESGetKSP(dmmg[i]->snes,&ksp);
171: KSPGetPC(ksp,&pc);
172: for (j=0; j<=i; j++) {
173: PCMGGetSmoother(pc,j,&ksp);
174: KSPGetPC(ksp,&mpc);
175: PCSetType(mpc,PCSHELL);
176: PCShellSetContext(mpc,dmmg[j]);
177: PCShellSetApply(mpc,(PetscErrorCode (*)(void*,Vec,Vec))myPCApply);
178: PCShellSetView(mpc,(PetscErrorCode (*)(void*,PetscViewer))myPCView);
179: }
180: }
181: }
183: DMMGSolve(dmmg);
185: for (i=0; i<nlevels; i++) {
186: appctx = (AppCtx*)dmmg[i]->user;
187: MatDestroy(appctx->J);
188: if (appctx->ksp) {KSPDestroy(appctx->ksp);}
189: PetscFree(appctx);
190: }
191: DMMGDestroy(dmmg);
193: PetscFinalize();
194: return 0;
195: }
196:
197: /*
198: Enforces the PDE on the grid
199: This local function acts on the ghosted version of U (accessed via DAGetLocalVector())
200: BUT the global, nonghosted version of FU
202: Process adiC(36): PDEFormFunctionLocal
203: */
206: PetscErrorCode PDEFormFunctionLocal(DALocalInfo *info,PetscScalar *u,PetscScalar *fu,PassiveScalar *w)
207: {
208: PetscInt xs = info->xs,xm = info->xm,i,mx = info->mx;
209: PetscScalar d,h;
212: d = mx-1.0;
213: h = 1.0/d;
215: for (i=xs; i<xs+xm; i++) {
216: if (i == 0) fu[i] = 2.0*d*(u[i] - w[0]) + h*u[i]*u[i];
217: else if (i == mx-1) fu[i] = 2.0*d*u[i] + h*u[i]*u[i];
218: else fu[i] = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h) + h*u[i]*u[i];
219: }
221: PetscLogFlops(9*mx);
222: return 0;
223: }
225: /*
226: Evaluates FU = Gradiant(L(w,u,lambda))
228: This is the function that is usually passed to the SNESSetJacobian() or DMMGSetSNES() and
229: defines the nonlinear set of equations that are to be solved.
231: This local function acts on the ghosted version of U (accessed via DMCompositeGetLocalVectors() and
232: DMCompositeScatter()) BUT the global, nonghosted version of FU (via DMCompositeAccess()).
234: This function uses PDEFormFunction() to enforce the PDE constraint equations and its adjoint
235: for the Lagrange multiplier equations
237: */
240: PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
241: {
242: DMMG dmmg = (DMMG)dummy;
244: PetscInt xs,xm,i,N,nredundant;
245: PetscScalar *u,*w,*fw,*fu,*lambda,*flambda,d,h,h2;
246: Vec vu,vlambda,vfu,vflambda,vglambda;
247: DA da;
248: DMComposite packer = (DMComposite)dmmg->dm;
249: PetscTruth useadic = PETSC_TRUE;
250: #if defined(PETSC_HAVE_ADIC)
251: AppCtx *appctx = (AppCtx*)dmmg->user;
252: #endif
256: #if defined(PETSC_HAVE_ADIC)
257: PetscOptionsHasName(0,"-useadic",&skipadic);
258: #endif
260: DMCompositeGetEntries(packer,&nredundant,&da,PETSC_IGNORE);
261: DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
262: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
263: d = (N-1.0);
264: h = 1.0/d;
265: h2 = 2.0*h;
267: DMCompositeGetLocalVectors(packer,&w,&vu,&vlambda);
268: DMCompositeScatter(packer,U,w,vu,vlambda);
269: DMCompositeGetAccess(packer,FU,&fw,&vfu,&vflambda);
270: DMCompositeGetAccess(packer,U,0,0,&vglambda);
272: /* G() */
273: DAFormFunction1(da,vu,vfu,w);
275: #if defined(PETSC_HAVE_ADIC)
276: if (useadic) {
277: /* lambda^T G_u() */
278: DAComputeJacobian1WithAdic(da,vu,appctx->J,w);
279: if (appctx->ksp) {
280: KSPSetOperators(appctx->ksp,appctx->J,appctx->J,SAME_NONZERO_PATTERN);
281: }
282: MatMultTranspose(appctx->J,vglambda,vflambda);
283: }
284: #endif
286: DAVecGetArray(da,vu,&u);
287: DAVecGetArray(da,vfu,&fu);
288: DAVecGetArray(da,vlambda,&lambda);
289: DAVecGetArray(da,vflambda,&flambda);
291: /* L_w */
292: if (xs == 0) { /* only first processor computes this */
293: fw[0] = -2.*d*lambda[0];
294: }
296: /* lambda^T G_u() */
297: if (!useadic) {
298: for (i=xs; i<xs+xm; i++) {
299: if (i == 0) flambda[0] = 2.*d*lambda[0] - d*lambda[1] + h2*lambda[0]*u[0];
300: else if (i == 1) flambda[1] = 2.*d*lambda[1] - d*lambda[2] + h2*lambda[1]*u[1];
301: else if (i == N-1) flambda[N-1] = 2.*d*lambda[N-1] - d*lambda[N-2] + h2*lambda[N-1]*u[N-1];
302: else if (i == N-2) flambda[N-2] = 2.*d*lambda[N-2] - d*lambda[N-3] + h2*lambda[N-2]*u[N-2];
303: else flambda[i] = - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]) + h2*lambda[i]*u[i];
304: }
305: }
307: /* F_u */
308: for (i=xs; i<xs+xm; i++) {
309: if (i == 0) flambda[0] += h*u[0];
310: else if (i == 1) flambda[1] += h2*u[1];
311: else if (i == N-1) flambda[N-1] += h*u[N-1];
312: else if (i == N-2) flambda[N-2] += h2*u[N-2];
313: else flambda[i] += h2*u[i];
314: }
316: DAVecRestoreArray(da,vu,&u);
317: DAVecRestoreArray(da,vfu,&fu);
318: DAVecRestoreArray(da,vlambda,&lambda);
319: DAVecRestoreArray(da,vflambda,&flambda);
321: DMCompositeRestoreLocalVectors(packer,&w,&vu,&vlambda);
322: DMCompositeRestoreAccess(packer,FU,&fw,&vfu,&vflambda);
323: DMCompositeRestoreAccess(packer,U,0,0,&vglambda);
325: PetscLogFlops(9*N);
326: return(0);
327: }