Actual source code: ex22.c
petsc-3.7.5 2017-01-01
2: static const char help[] = "Solves PDE optimization problem using full-space method, interlaces state and adjoint variables.\n\n";
4: #include <petscdm.h>
5: #include <petscdmda.h>
6: #include <petscdmredundant.h>
7: #include <petscdmcomposite.h>
8: #include <petscpf.h>
9: #include <petscsnes.h>
10: #include <petsc/private/dmimpl.h>
12: /*
14: w - design variables (what we change to get an optimal solution)
15: u - state variables (i.e. the PDE solution)
16: lambda - the Lagrange multipliers
18: U = (w [u_0 lambda_0 u_1 lambda_1 .....])
20: fu, fw, flambda contain the gradient of L(w,u,lambda)
22: FU = (fw [fu_0 flambda_0 .....])
24: In this example the PDE is
25: Uxx = 2,
26: u(0) = w(0), thus this is the free parameter
27: u(1) = 0
28: the function we wish to minimize is
29: \integral u^{2}
31: The exact solution for u is given by u(x) = x*x - 1.25*x + .25
33: Use the usual centered finite differences.
35: Note we treat the problem as non-linear though it happens to be linear
37: See ex21.c for the same code, but that does NOT interlaces the u and the lambda
39: The vectors u_lambda and fu_lambda contain the u and the lambda interlaced
40: */
42: typedef struct {
43: PetscViewer u_lambda_viewer;
44: PetscViewer fu_lambda_viewer;
45: } UserCtx;
47: extern PetscErrorCode ComputeFunction(SNES,Vec,Vec,void*);
48: extern PetscErrorCode ComputeJacobian_MF(SNES,Vec,Mat,Mat,void*);
49: extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*);
51: /*
52: Uses full multigrid preconditioner with GMRES (with no preconditioner inside the GMRES) as the
53: smoother on all levels. This is because (1) in the matrix free case no matrix entries are
54: available for doing Jacobi or SOR preconditioning and (2) the explicit matrix case the diagonal
55: entry for the control variable is zero which means default SOR will not work.
57: */
58: char common_options[] = "-ksp_type fgmres\
59: -snes_grid_sequence 2 \
60: -pc_type mg\
61: -mg_levels_pc_type none \
62: -mg_coarse_pc_type none \
63: -pc_mg_type full \
64: -mg_coarse_ksp_type gmres \
65: -mg_levels_ksp_type gmres \
66: -mg_coarse_ksp_max_it 6 \
67: -mg_levels_ksp_max_it 3";
69: char matrix_free_options[] = "-mat_mffd_compute_normu no \
70: -mat_mffd_type wp";
72: extern PetscErrorCode DMCreateMatrix_MF(DM,Mat*);
76: int main(int argc,char **argv)
77: {
79: UserCtx user;
80: DM red,da;
81: SNES snes;
82: DM packer;
83: PetscBool use_monitor = PETSC_FALSE;
85: PetscInitialize(&argc,&argv,NULL,help);
86: PetscOptionsSetFromOptions(NULL);
88: /* Hardwire several options; can be changed at command line */
89: PetscOptionsInsertString(NULL,common_options);
90: PetscOptionsInsertString(NULL,matrix_free_options);
91: PetscOptionsInsert(NULL,&argc,&argv,NULL);
92: PetscOptionsGetBool(NULL,NULL,"-use_monitor",&use_monitor,PETSC_IGNORE);
94: /* Create a global vector that includes a single redundant array and two da arrays */
95: DMCompositeCreate(PETSC_COMM_WORLD,&packer);
96: DMRedundantCreate(PETSC_COMM_WORLD,0,1,&red);
97: DMSetOptionsPrefix(red,"red_");
98: DMCompositeAddDM(packer,red);
99: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,-5,2,1,NULL,&da);
100: DMSetOptionsPrefix(red,"da_");
101: DMCompositeAddDM(packer,(DM)da);
102: DMSetApplicationContext(packer,&user);
104: packer->ops->creatematrix = DMCreateMatrix_MF;
106: /* create nonlinear multi-level solver */
107: SNESCreate(PETSC_COMM_WORLD,&snes);
108: SNESSetDM(snes,packer);
109: SNESSetFunction(snes,NULL,ComputeFunction,NULL);
110: SNESSetJacobian(snes,NULL, NULL,ComputeJacobian_MF,NULL);
112: SNESSetFromOptions(snes);
114: if (use_monitor) {
115: /* create graphics windows */
116: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u_lambda - state variables and Lagrange multipliers",-1,-1,-1,-1,&user.u_lambda_viewer);
117: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu_lambda - derivate w.r.t. state variables and Lagrange multipliers",-1,-1,-1,-1,&user.fu_lambda_viewer);
118: SNESMonitorSet(snes,Monitor,0,0);
119: }
121: SNESSolve(snes,NULL,NULL);
122: SNESDestroy(&snes);
124: DMDestroy(&red);
125: DMDestroy(&da);
126: DMDestroy(&packer);
127: if (use_monitor) {
128: PetscViewerDestroy(&user.u_lambda_viewer);
129: PetscViewerDestroy(&user.fu_lambda_viewer);
130: }
131: PetscFinalize();
132: return 0;
133: }
135: typedef struct {
136: PetscScalar u;
137: PetscScalar lambda;
138: } ULambda;
142: /*
143: Evaluates FU = Gradiant(L(w,u,lambda))
145: This local function acts on the ghosted version of U (accessed via DMCompositeGetLocalVectors() and
146: DMCompositeScatter()) BUT the global, nonghosted version of FU (via DMCompositeGetAccess()).
148: */
149: PetscErrorCode ComputeFunction(SNES snes,Vec U,Vec FU,void *ctx)
150: {
152: PetscInt xs,xm,i,N;
153: ULambda *u_lambda,*fu_lambda;
154: PetscScalar d,h,*w,*fw;
155: Vec vw,vfw,vu_lambda,vfu_lambda;
156: DM packer,red,da;
159: VecGetDM(U, &packer);
160: DMCompositeGetEntries(packer,&red,&da);
161: DMCompositeGetLocalVectors(packer,&vw,&vu_lambda);
162: DMCompositeScatter(packer,U,vw,vu_lambda);
163: DMCompositeGetAccess(packer,FU,&vfw,&vfu_lambda);
165: DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);
166: DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);
167: VecGetArray(vw,&w);
168: VecGetArray(vfw,&fw);
169: DMDAVecGetArray(da,vu_lambda,&u_lambda);
170: DMDAVecGetArray(da,vfu_lambda,&fu_lambda);
171: d = N-1.0;
172: h = 1.0/d;
174: /* derivative of L() w.r.t. w */
175: if (xs == 0) { /* only first processor computes this */
176: fw[0] = -2.0*d*u_lambda[0].lambda;
177: }
179: /* derivative of L() w.r.t. u */
180: for (i=xs; i<xs+xm; i++) {
181: if (i == 0) fu_lambda[0].lambda = h*u_lambda[0].u + 2.*d*u_lambda[0].lambda - d*u_lambda[1].lambda;
182: else if (i == 1) fu_lambda[1].lambda = 2.*h*u_lambda[1].u + 2.*d*u_lambda[1].lambda - d*u_lambda[2].lambda;
183: else if (i == N-1) fu_lambda[N-1].lambda = h*u_lambda[N-1].u + 2.*d*u_lambda[N-1].lambda - d*u_lambda[N-2].lambda;
184: else if (i == N-2) fu_lambda[N-2].lambda = 2.*h*u_lambda[N-2].u + 2.*d*u_lambda[N-2].lambda - d*u_lambda[N-3].lambda;
185: else fu_lambda[i].lambda = 2.*h*u_lambda[i].u - d*(u_lambda[i+1].lambda - 2.0*u_lambda[i].lambda + u_lambda[i-1].lambda);
186: }
188: /* derivative of L() w.r.t. lambda */
189: for (i=xs; i<xs+xm; i++) {
190: if (i == 0) fu_lambda[0].u = 2.0*d*(u_lambda[0].u - w[0]);
191: else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
192: else fu_lambda[i].u = -(d*(u_lambda[i+1].u - 2.0*u_lambda[i].u + u_lambda[i-1].u) - 2.0*h);
193: }
195: VecRestoreArray(vw,&w);
196: VecRestoreArray(vfw,&fw);
197: DMDAVecRestoreArray(da,vu_lambda,&u_lambda);
198: DMDAVecRestoreArray(da,vfu_lambda,&fu_lambda);
199: DMCompositeRestoreLocalVectors(packer,&vw,&vu_lambda);
200: DMCompositeRestoreAccess(packer,FU,&vfw,&vfu_lambda);
201: PetscLogFlops(13.0*N);
202: return(0);
203: }
207: /*
208: Computes the exact solution
209: */
210: PetscErrorCode u_solution(void *dummy,PetscInt n,const PetscScalar *x,PetscScalar *u)
211: {
212: PetscInt i;
215: for (i=0; i<n; i++) u[2*i] = x[i]*x[i] - 1.25*x[i] + .25;
216: return(0);
217: }
221: PetscErrorCode ExactSolution(DM packer,Vec U)
222: {
223: PF pf;
224: Vec x,u_global;
225: PetscScalar *w;
226: DM da;
228: PetscInt m;
231: DMCompositeGetEntries(packer,&m,&da);
233: PFCreate(PETSC_COMM_WORLD,1,2,&pf);
234: /* The cast through PETSC_UINTPTR_T is so that compilers will warn about casting to void * from void(*)(void) */
235: PFSetType(pf,PFQUICK,(void*)(PETSC_UINTPTR_T)u_solution);
236: DMGetCoordinates(da,&x);
237: if (!x) {
238: DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);
239: DMGetCoordinates(da,&x);
240: }
241: DMCompositeGetAccess(packer,U,&w,&u_global,0);
242: if (w) w[0] = .25;
243: PFApplyVec(pf,x,u_global);
244: PFDestroy(&pf);
245: DMCompositeRestoreAccess(packer,U,&w,&u_global,0);
246: return(0);
247: }
251: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
252: {
253: UserCtx *user;
255: PetscInt m,N;
256: PetscScalar *w,*dw;
257: Vec u_lambda,U,F,Uexact;
258: DM packer;
259: PetscReal norm;
260: DM da;
263: SNESGetDM(snes,&packer);
264: DMGetApplicationContext(packer,&user);
265: SNESGetSolution(snes,&U);
266: DMCompositeGetAccess(packer,U,&w,&u_lambda);
267: VecView(u_lambda,user->u_lambda_viewer);
268: DMCompositeRestoreAccess(packer,U,&w,&u_lambda);
270: SNESGetFunction(snes,&F,0,0);
271: DMCompositeGetAccess(packer,F,&w,&u_lambda);
272: /* VecView(u_lambda,user->fu_lambda_viewer); */
273: DMCompositeRestoreAccess(packer,U,&w,&u_lambda);
275: DMCompositeGetEntries(packer,&m,&da);
276: DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);
277: VecDuplicate(U,&Uexact);
278: ExactSolution(packer,Uexact);
279: VecAXPY(Uexact,-1.0,U);
280: DMCompositeGetAccess(packer,Uexact,&dw,&u_lambda);
281: VecStrideNorm(u_lambda,0,NORM_2,&norm);
282: norm = norm/PetscSqrtReal((PetscReal)N-1.);
283: if (dw) PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Error at x = 0 %g\n",(double)norm,(double)PetscRealPart(dw[0]));
284: VecView(u_lambda,user->fu_lambda_viewer);
285: DMCompositeRestoreAccess(packer,Uexact,&dw,&u_lambda);
286: VecDestroy(&Uexact);
287: return(0);
288: }
292: PetscErrorCode DMCreateMatrix_MF(DM packer,Mat *A)
293: {
295: Vec t;
296: PetscInt m;
299: DMGetGlobalVector(packer,&t);
300: VecGetLocalSize(t,&m);
301: DMRestoreGlobalVector(packer,&t);
302: MatCreateMFFD(PETSC_COMM_WORLD,m,m,PETSC_DETERMINE,PETSC_DETERMINE,A);
303: MatSetUp(*A);
304: return(0);
305: }
309: PetscErrorCode ComputeJacobian_MF(SNES snes,Vec x,Mat A,Mat B,void *ctx)
310: {
314: MatMFFDSetFunction(A,(PetscErrorCode (*)(void*,Vec,Vec))SNESComputeFunction,snes);
315: MatMFFDSetBase(A,x,NULL);
316: return(0);
317: }