Actual source code: ex22.c
2: static char help[] = "Solves PDE optimization problem.\n\n";
4: #include petscda.h
5: #include petscpf.h
6: #include petscsnes.h
7: #include petscdmmg.h
9: /*
11: w - design variables (what we change to get an optimal solution)
12: u - state variables (i.e. the PDE solution)
13: lambda - the Lagrange multipliers
15: U = (w u lambda)
17: fu, fw, flambda contain the gradient of L(w,u,lambda)
19: FU = (fw fu flambda)
21: In this example the PDE is
22: Uxx = 2,
23: u(0) = w(0), thus this is the free parameter
24: u(1) = 0
25: the function we wish to minimize is
26: \integral u^{2}
28: The exact solution for u is given by u(x) = x*x - 1.25*x + .25
30: Use the usual centered finite differences.
32: Note we treat the problem as non-linear though it happens to be linear
34: See ex21.c for the same code, but that does NOT interlaces the u and the lambda
36: The vectors u_lambda and fu_lambda contain the u and the lambda interlaced
37: */
39: typedef struct {
40: PetscViewer u_lambda_viewer;
41: PetscViewer fu_lambda_viewer;
42: } UserCtx;
50: int main(int argc,char **argv)
51: {
53: UserCtx user;
54: DA da;
55: DMMG *dmmg;
56: VecPack packer;
58: PetscInitialize(&argc,&argv,PETSC_NULL,help);
60: /* Hardwire several options; can be changed at command line */
61: PetscOptionsSetValue("-dmmg_grid_sequence",PETSC_NULL);
62: PetscOptionsSetValue("-ksp_type","fgmres");
63: PetscOptionsSetValue("-ksp_max_it","5");
64: PetscOptionsSetValue("-pc_mg_type","full");
65: PetscOptionsSetValue("-mg_coarse_ksp_type","gmres");
66: PetscOptionsSetValue("-mg_levels_ksp_type","gmres");
67: PetscOptionsSetValue("-mg_coarse_ksp_max_it","6");
68: PetscOptionsSetValue("-mg_levels_ksp_max_it","3");
69: PetscOptionsSetValue("-snes_mf_type","wp");
70: PetscOptionsSetValue("-snes_mf_compute_norma","no");
71: PetscOptionsSetValue("-snes_mf_compute_normu","no");
72: PetscOptionsSetValue("-snes_ls","basic");
73: PetscOptionsSetValue("-dmmg_jacobian_mf_fd",0);
74: /* PetscOptionsSetValue("-snes_ls","basicnonorms"); */
75: PetscOptionsInsert(&argc,&argv,PETSC_NULL);
77: /* Create a global vector that includes a single redundant array and two da arrays */
78: VecPackCreate(PETSC_COMM_WORLD,&packer);
79: VecPackAddArray(packer,1);
80: DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-5,2,1,PETSC_NULL,&da);
81: VecPackAddDA(packer,da);
83: /* create graphics windows */
84: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u_lambda - state variables and Lagrange multipliers",-1,-1,-1,-1,&user.u_lambda_viewer);
85: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu_lambda - derivate w.r.t. state variables and Lagrange multipliers",-1,-1,-1,-1,&user.fu_lambda_viewer);
87: /* create nonlinear multi-level solver */
88: DMMGCreate(PETSC_COMM_WORLD,2,&user,&dmmg);
89: DMMGSetDM(dmmg,(DM)packer);
90: DMMGSetSNES(dmmg,FormFunction,PETSC_NULL);
91: /*
92: for (i=0; i<DMMGGetLevels(dmmg); i++) {
93: SNESSetMonitor(dmmg[i]->snes,Monitor,dmmg[i],0);
94: }*/
95: DMMGSolve(dmmg);
96: DMMGDestroy(dmmg);
98: DADestroy(da);
99: VecPackDestroy(packer);
100: PetscViewerDestroy(user.u_lambda_viewer);
101: PetscViewerDestroy(user.fu_lambda_viewer);
103: PetscFinalize();
104: return 0;
105: }
107: typedef struct {
108: PetscScalar u;
109: PetscScalar lambda;
110: } ULambda;
111:
112: /*
113: Evaluates FU = Gradiant(L(w,u,lambda))
115: This local function acts on the ghosted version of U (accessed via VecPackGetLocalVectors() and
116: VecPackScatter()) BUT the global, nonghosted version of FU (via VecPackGetAccess()).
118: */
119: PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void* dummy)
120: {
121: DMMG dmmg = (DMMG)dummy;
123: PetscInt xs,xm,i,N,nredundant;
124: ULambda *u_lambda,*fu_lambda;
125: PetscScalar d,h,*w,*fw;
126: Vec vu_lambda,vfu_lambda;
127: DA da;
128: VecPack packer = (VecPack)dmmg->dm;
131: VecPackGetEntries(packer,&nredundant,&da);
132: VecPackGetLocalVectors(packer,&w,&vu_lambda);
133: VecPackScatter(packer,U,w,vu_lambda);
134: VecPackGetAccess(packer,FU,&fw,&vfu_lambda);
136: DAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);
137: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
138: DAVecGetArray(da,vu_lambda,&u_lambda);
139: DAVecGetArray(da,vfu_lambda,&fu_lambda);
140: d = N-1.0;
141: h = 1.0/d;
143: /* derivative of L() w.r.t. w */
144: if (xs == 0) { /* only first processor computes this */
145: fw[0] = -2.0*d*u_lambda[0].lambda;
146: }
148: /* derivative of L() w.r.t. u */
149: for (i=xs; i<xs+xm; i++) {
150: if (i == 0) fu_lambda[0].lambda = h*u_lambda[0].u + 2.*d*u_lambda[0].lambda - d*u_lambda[1].lambda;
151: 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;
152: 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;
153: 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;
154: 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);
155: }
157: /* derivative of L() w.r.t. lambda */
158: for (i=xs; i<xs+xm; i++) {
159: if (i == 0) fu_lambda[0].u = 2.0*d*(u_lambda[0].u - w[0]);
160: else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
161: 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);
162: }
164: DAVecRestoreArray(da,vu_lambda,&u_lambda);
165: DAVecRestoreArray(da,vfu_lambda,&fu_lambda);
166: VecPackRestoreLocalVectors(packer,&w,&vu_lambda);
167: VecPackRestoreAccess(packer,FU,&fw,&vfu_lambda);
168: PetscLogFlops(13*N);
169: return(0);
170: }
172: /*
173: Computes the exact solution
174: */
175: PetscErrorCode u_solution(void *dummy,PetscInt n,PetscScalar *x,PetscScalar *u)
176: {
177: PetscInt i;
179: for (i=0; i<n; i++) {
180: u[2*i] = x[i]*x[i] - 1.25*x[i] + .25;
181: }
182: return(0);
183: }
185: PetscErrorCode ExactSolution(VecPack packer,Vec U)
186: {
187: PF pf;
188: Vec x,u_global;
189: PetscScalar *w;
190: DA da;
192: PetscInt m;
195: VecPackGetEntries(packer,&m,&da);
197: PFCreate(PETSC_COMM_WORLD,1,1,&pf);
198: PFSetType(pf,PFQUICK,(void*)u_solution);
199: DAGetCoordinates(da,&x);
200: if (!x) {
201: DASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);
202: DAGetCoordinates(da,&x);
203: }
204: VecPackGetAccess(packer,U,&w,&u_global,0);
205: if (w) w[0] = .25;
206: PFApplyVec(pf,x,u_global);
207: PFDestroy(pf);
208: VecPackRestoreAccess(packer,U,&w,&u_global,0);
209: return(0);
210: }
213: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
214: {
215: DMMG dmmg = (DMMG)dummy;
216: UserCtx *user = (UserCtx*)dmmg->user;
218: PetscInt m,N;
219: PetscScalar mone = -1.0,*w,*dw;
220: Vec u_lambda,U,F,Uexact;
221: VecPack packer = (VecPack)dmmg->dm;
222: PetscReal norm;
223: DA da;
226: SNESGetSolution(snes,&U);
227: VecPackGetAccess(packer,U,&w,&u_lambda);
228: VecView(u_lambda,user->u_lambda_viewer);
229: VecPackRestoreAccess(packer,U,&w,&u_lambda);
231: SNESGetFunction(snes,&F,0,0);
232: VecPackGetAccess(packer,F,&w,&u_lambda);
233: /* VecView(u_lambda,user->fu_lambda_viewer); */
234: VecPackRestoreAccess(packer,U,&w,&u_lambda);
236: VecPackGetEntries(packer,&m,&da);
237: DAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0);
238: VecDuplicate(U,&Uexact);
239: ExactSolution(packer,Uexact);
240: VecAXPY(Uexact,mone,U);
241: VecPackGetAccess(packer,Uexact,&dw,&u_lambda);
242: VecStrideNorm(u_lambda,0,NORM_2,&norm);
243: norm = norm/sqrt(N-1.);
244: if (dw) PetscPrintf(dmmg->comm,"Norm of error %g Error at x = 0 %g\n",norm,PetscRealPart(dw[0]));
245: VecView(u_lambda,user->fu_lambda_viewer);
246: VecPackRestoreAccess(packer,Uexact,&dw,&u_lambda);
247: VecDestroy(Uexact);
248: return(0);
249: }