1 2 static const char help[] = "Solves PDE optimization problem using full-space method, treats state and adjoint variables separately.\n\n"; 3 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 11 /* 12 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 16 17 U = (w u lambda) 18 19 fu, fw, flambda contain the gradient of L(w,u,lambda) 20 21 FU = (fw fu flambda) 22 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} 29 30 The exact solution for u is given by u(x) = x*x - 1.25*x + .25 31 32 Use the usual centered finite differences. 33 34 Note we treat the problem as non-linear though it happens to be linear 35 36 See ex22.c for the same code, but that interlaces the u and the lambda 37 38 */ 39 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; 46 47 extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*); 48 extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*); 49 50 int main(int argc,char **argv) 51 { 52 PetscInt its; 53 Vec U,FU; 54 SNES snes; 55 UserCtx user; 56 57 PetscFunctionBeginUser; 58 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 59 60 /* Create a global vector that includes a single redundant array and two da arrays */ 61 PetscCall(DMCompositeCreate(PETSC_COMM_WORLD,&user.packer)); 62 PetscCall(DMRedundantCreate(PETSC_COMM_WORLD,0,1,&user.red1)); 63 PetscCall(DMCompositeAddDM(user.packer,user.red1)); 64 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,1,1,NULL,&user.da1)); 65 PetscCall(DMSetFromOptions(user.da1)); 66 PetscCall(DMSetUp(user.da1)); 67 PetscCall(DMCompositeAddDM(user.packer,user.da1)); 68 PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,5,1,1,NULL,&user.da2)); 69 PetscCall(DMSetFromOptions(user.da2)); 70 PetscCall(DMSetUp(user.da2)); 71 PetscCall(DMDASetFieldName(user.da1,0,"u")); 72 PetscCall(DMDASetFieldName(user.da2,0,"lambda")); 73 PetscCall(DMCompositeAddDM(user.packer,user.da2)); 74 PetscCall(DMCreateGlobalVector(user.packer,&U)); 75 PetscCall(VecDuplicate(U,&FU)); 76 77 /* create graphics windows */ 78 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"u - state variables",-1,-1,-1,-1,&user.u_viewer)); 79 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"lambda - Lagrange multipliers",-1,-1,-1,-1,&user.lambda_viewer)); 80 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"fu - derivate w.r.t. state variables",-1,-1,-1,-1,&user.fu_viewer)); 81 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"flambda - derivate w.r.t. Lagrange multipliers",-1,-1,-1,-1,&user.flambda_viewer)); 82 83 /* create nonlinear solver */ 84 PetscCall(SNESCreate(PETSC_COMM_WORLD,&snes)); 85 PetscCall(SNESSetFunction(snes,FU,FormFunction,&user)); 86 PetscCall(SNESSetFromOptions(snes)); 87 PetscCall(SNESMonitorSet(snes,Monitor,&user,0)); 88 PetscCall(SNESSolve(snes,NULL,U)); 89 PetscCall(SNESGetIterationNumber(snes,&its)); 90 PetscCall(SNESDestroy(&snes)); 91 92 PetscCall(DMDestroy(&user.red1)); 93 PetscCall(DMDestroy(&user.da1)); 94 PetscCall(DMDestroy(&user.da2)); 95 PetscCall(DMDestroy(&user.packer)); 96 PetscCall(VecDestroy(&U)); 97 PetscCall(VecDestroy(&FU)); 98 PetscCall(PetscViewerDestroy(&user.u_viewer)); 99 PetscCall(PetscViewerDestroy(&user.lambda_viewer)); 100 PetscCall(PetscViewerDestroy(&user.fu_viewer)); 101 PetscCall(PetscViewerDestroy(&user.flambda_viewer)); 102 PetscCall(PetscFinalize()); 103 return 0; 104 } 105 106 /* 107 Evaluates FU = Gradiant(L(w,u,lambda)) 108 109 */ 110 PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void *dummy) 111 { 112 UserCtx *user = (UserCtx*)dummy; 113 PetscInt xs,xm,i,N; 114 PetscScalar *u,*lambda,*w,*fu,*fw,*flambda,d,h; 115 Vec vw,vu,vlambda,vfw,vfu,vflambda; 116 117 PetscFunctionBeginUser; 118 PetscCall(DMCompositeGetLocalVectors(user->packer,&vw,&vu,&vlambda)); 119 PetscCall(DMCompositeGetLocalVectors(user->packer,&vfw,&vfu,&vflambda)); 120 PetscCall(DMCompositeScatter(user->packer,U,vw,vu,vlambda)); 121 122 PetscCall(DMDAGetCorners(user->da1,&xs,NULL,NULL,&xm,NULL,NULL)); 123 PetscCall(DMDAGetInfo(user->da1,0,&N,0,0,0,0,0,0,0,0,0,0,0)); 124 PetscCall(VecGetArray(vw,&w)); 125 PetscCall(VecGetArray(vfw,&fw)); 126 PetscCall(DMDAVecGetArray(user->da1,vu,&u)); 127 PetscCall(DMDAVecGetArray(user->da1,vfu,&fu)); 128 PetscCall(DMDAVecGetArray(user->da1,vlambda,&lambda)); 129 PetscCall(DMDAVecGetArray(user->da1,vflambda,&flambda)); 130 d = (N-1.0); 131 h = 1.0/d; 132 133 /* derivative of L() w.r.t. w */ 134 if (xs == 0) { /* only first processor computes this */ 135 fw[0] = -2.*d*lambda[0]; 136 } 137 138 /* derivative of L() w.r.t. u */ 139 for (i=xs; i<xs+xm; i++) { 140 if (i == 0) flambda[0] = h*u[0] + 2.*d*lambda[0] - d*lambda[1]; 141 else if (i == 1) flambda[1] = 2.*h*u[1] + 2.*d*lambda[1] - d*lambda[2]; 142 else if (i == N-1) flambda[N-1] = h*u[N-1] + 2.*d*lambda[N-1] - d*lambda[N-2]; 143 else if (i == N-2) flambda[N-2] = 2.*h*u[N-2] + 2.*d*lambda[N-2] - d*lambda[N-3]; 144 else flambda[i] = 2.*h*u[i] - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]); 145 } 146 147 /* derivative of L() w.r.t. lambda */ 148 for (i=xs; i<xs+xm; i++) { 149 if (i == 0) fu[0] = 2.0*d*(u[0] - w[0]); 150 else if (i == N-1) fu[N-1] = 2.0*d*u[N-1]; 151 else fu[i] = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h); 152 } 153 154 PetscCall(VecRestoreArray(vw,&w)); 155 PetscCall(VecRestoreArray(vfw,&fw)); 156 PetscCall(DMDAVecRestoreArray(user->da1,vu,&u)); 157 PetscCall(DMDAVecRestoreArray(user->da1,vfu,&fu)); 158 PetscCall(DMDAVecRestoreArray(user->da1,vlambda,&lambda)); 159 PetscCall(DMDAVecRestoreArray(user->da1,vflambda,&flambda)); 160 161 PetscCall(DMCompositeGather(user->packer,INSERT_VALUES,FU,vfw,vfu,vflambda)); 162 PetscCall(DMCompositeRestoreLocalVectors(user->packer,&vw,&vu,&vlambda)); 163 PetscCall(DMCompositeRestoreLocalVectors(user->packer,&vfw,&vfu,&vflambda)); 164 PetscFunctionReturn(0); 165 } 166 167 PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy) 168 { 169 UserCtx *user = (UserCtx*)dummy; 170 Vec w,u,lambda,U,F; 171 172 PetscFunctionBeginUser; 173 PetscCall(SNESGetSolution(snes,&U)); 174 PetscCall(DMCompositeGetAccess(user->packer,U,&w,&u,&lambda)); 175 PetscCall(VecView(u,user->u_viewer)); 176 PetscCall(VecView(lambda,user->lambda_viewer)); 177 PetscCall(DMCompositeRestoreAccess(user->packer,U,&w,&u,&lambda)); 178 179 PetscCall(SNESGetFunction(snes,&F,0,0)); 180 PetscCall(DMCompositeGetAccess(user->packer,F,&w,&u,&lambda)); 181 PetscCall(VecView(u,user->fu_viewer)); 182 PetscCall(VecView(lambda,user->flambda_viewer)); 183 PetscCall(DMCompositeRestoreAccess(user->packer,F,&w,&u,&lambda)); 184 PetscFunctionReturn(0); 185 } 186 187 /*TEST 188 189 test: 190 nsize: 4 191 args: -snes_linesearch_monitor -snes_mf -pc_type none -snes_monitor_short -nox -ksp_monitor_short -snes_converged_reason 192 requires: !single 193 194 TEST*/ 195