Actual source code: ex21.c
petsc-3.13.6 2020-09-29
2: static const char help[] = "Solves PDE optimization problem using full-space method, treats state and adjoint variables separately.\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>
11: /*
13: w - design variables (what we change to get an optimal solution)
14: u - state variables (i.e. the PDE solution)
15: lambda - the Lagrange multipliers
17: U = (w u lambda)
19: fu, fw, flambda contain the gradient of L(w,u,lambda)
21: FU = (fw fu flambda)
23: In this example the PDE is
24: Uxx = 2,
25: u(0) = w(0), thus this is the free parameter
26: u(1) = 0
27: the function we wish to minimize is
28: \integral u^{2}
30: The exact solution for u is given by u(x) = x*x - 1.25*x + .25
32: Use the usual centered finite differences.
34: Note we treat the problem as non-linear though it happens to be linear
36: See ex22.c for the same code, but that interlaces the u and the lambda
38: */
40: typedef struct {
41: DM red1,da1,da2;
42: DM packer;
43: PetscViewer u_viewer,lambda_viewer;
44: PetscViewer fu_viewer,flambda_viewer;
45: } UserCtx;
47: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
48: extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*);
51: int main(int argc,char **argv)
52: {
54: PetscInt its;
55: Vec U,FU;
56: SNES snes;
57: UserCtx user;
59: PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
61: /* Create a global vector that includes a single redundant array and two da arrays */
62: DMCompositeCreate(PETSC_COMM_WORLD,&user.packer);
63: DMRedundantCreate(PETSC_COMM_WORLD,0,1,&user.red1);
64: DMCompositeAddDM(user.packer,user.red1);
65: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,1,1,NULL,&user.da1);
66: DMSetFromOptions(user.da1);
67: DMSetUp(user.da1);
68: DMCompositeAddDM(user.packer,user.da1);
69: DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,1,1,NULL,&user.da2);
70: DMSetFromOptions(user.da2);
71: DMSetUp(user.da2);
72: DMDASetFieldName(user.da1,0,"u");
73: DMDASetFieldName(user.da2,0,"lambda");
74: DMCompositeAddDM(user.packer,user.da2);
75: DMCreateGlobalVector(user.packer,&U);
76: VecDuplicate(U,&FU);
78: /* create graphics windows */
79: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u - state variables",-1,-1,-1,-1,&user.u_viewer);
80: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"lambda - Lagrange multipliers",-1,-1,-1,-1,&user.lambda_viewer);
81: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu - derivate w.r.t. state variables",-1,-1,-1,-1,&user.fu_viewer);
82: PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"flambda - derivate w.r.t. Lagrange multipliers",-1,-1,-1,-1,&user.flambda_viewer);
85: /* create nonlinear solver */
86: SNESCreate(PETSC_COMM_WORLD,&snes);
87: SNESSetFunction(snes,FU,FormFunction,&user);
88: SNESSetFromOptions(snes);
89: SNESMonitorSet(snes,Monitor,&user,0);
90: SNESSolve(snes,NULL,U);
91: SNESGetIterationNumber(snes,&its);
92: SNESDestroy(&snes);
94: DMDestroy(&user.red1);
95: DMDestroy(&user.da1);
96: DMDestroy(&user.da2);
97: DMDestroy(&user.packer);
98: VecDestroy(&U);
99: VecDestroy(&FU);
100: PetscViewerDestroy(&user.u_viewer);
101: PetscViewerDestroy(&user.lambda_viewer);
102: PetscViewerDestroy(&user.fu_viewer);
103: PetscViewerDestroy(&user.flambda_viewer);
104: PetscFinalize();
105: return ierr;
106: }
108: /*
109: Evaluates FU = Gradiant(L(w,u,lambda))
111: */
112: PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void *dummy)
113: {
114: UserCtx *user = (UserCtx*)dummy;
116: PetscInt xs,xm,i,N;
117: PetscScalar *u,*lambda,*w,*fu,*fw,*flambda,d,h;
118: Vec vw,vu,vlambda,vfw,vfu,vflambda;
121: DMCompositeGetLocalVectors(user->packer,&vw,&vu,&vlambda);
122: DMCompositeGetLocalVectors(user->packer,&vfw,&vfu,&vflambda);
123: DMCompositeScatter(user->packer,U,vw,vu,vlambda);
125: DMDAGetCorners(user->da1,&xs,NULL,NULL,&xm,NULL,NULL);
126: DMDAGetInfo(user->da1,0,&N,0,0,0,0,0,0,0,0,0,0,0);
127: VecGetArray(vw,&w);
128: VecGetArray(vfw,&fw);
129: DMDAVecGetArray(user->da1,vu,&u);
130: DMDAVecGetArray(user->da1,vfu,&fu);
131: DMDAVecGetArray(user->da1,vlambda,&lambda);
132: DMDAVecGetArray(user->da1,vflambda,&flambda);
133: d = (N-1.0);
134: h = 1.0/d;
136: /* derivative of L() w.r.t. w */
137: if (xs == 0) { /* only first processor computes this */
138: fw[0] = -2.*d*lambda[0];
139: }
141: /* derivative of L() w.r.t. u */
142: for (i=xs; i<xs+xm; i++) {
143: if (i == 0) flambda[0] = h*u[0] + 2.*d*lambda[0] - d*lambda[1];
144: else if (i == 1) flambda[1] = 2.*h*u[1] + 2.*d*lambda[1] - d*lambda[2];
145: else if (i == N-1) flambda[N-1] = h*u[N-1] + 2.*d*lambda[N-1] - d*lambda[N-2];
146: else if (i == N-2) flambda[N-2] = 2.*h*u[N-2] + 2.*d*lambda[N-2] - d*lambda[N-3];
147: else flambda[i] = 2.*h*u[i] - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]);
148: }
150: /* derivative of L() w.r.t. lambda */
151: for (i=xs; i<xs+xm; i++) {
152: if (i == 0) fu[0] = 2.0*d*(u[0] - w[0]);
153: else if (i == N-1) fu[N-1] = 2.0*d*u[N-1];
154: else fu[i] = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h);
155: }
157: VecRestoreArray(vw,&w);
158: VecRestoreArray(vfw,&fw);
159: DMDAVecRestoreArray(user->da1,vu,&u);
160: DMDAVecRestoreArray(user->da1,vfu,&fu);
161: DMDAVecRestoreArray(user->da1,vlambda,&lambda);
162: DMDAVecRestoreArray(user->da1,vflambda,&flambda);
164: DMCompositeGather(user->packer,INSERT_VALUES,FU,vfw,vfu,vflambda);
165: DMCompositeRestoreLocalVectors(user->packer,&vw,&vu,&vlambda);
166: DMCompositeRestoreLocalVectors(user->packer,&vfw,&vfu,&vflambda);
167: return(0);
168: }
170: PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
171: {
172: UserCtx *user = (UserCtx*)dummy;
174: Vec w,u,lambda,U,F;
177: SNESGetSolution(snes,&U);
178: DMCompositeGetAccess(user->packer,U,&w,&u,&lambda);
179: VecView(u,user->u_viewer);
180: VecView(lambda,user->lambda_viewer);
181: DMCompositeRestoreAccess(user->packer,U,&w,&u,&lambda);
183: SNESGetFunction(snes,&F,0,0);
184: DMCompositeGetAccess(user->packer,F,&w,&u,&lambda);
185: VecView(u,user->fu_viewer);
186: VecView(lambda,user->flambda_viewer);
187: DMCompositeRestoreAccess(user->packer,F,&w,&u,&lambda);
188: return(0);
189: }
191: /*TEST
193: test:
194: nsize: 4
195: args: -snes_linesearch_monitor -snes_mf -pc_type none -snes_monitor_short -nox -ksp_monitor_short -snes_converged_reason
196: requires: !single
198: TEST*/