Actual source code: ex7.c


  2: static char help[] = "Solves u`` + u^{2} = f with Newton-like methods. Using\n\
  3:  matrix-free techniques with user-provided explicit preconditioner matrix.\n\n";

  5: #include <petscsnes.h>

  7: extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*);
  8: extern PetscErrorCode FormJacobianNoMatrix(SNES,Vec,Mat,Mat,void*);
  9: extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*);
 10: extern PetscErrorCode FormFunctioni(void *,PetscInt,Vec,PetscScalar *);
 11: extern PetscErrorCode OtherFunctionForDifferencing(void*,Vec,Vec);
 12: extern PetscErrorCode FormInitialGuess(SNES,Vec);
 13: extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*);

 15: typedef struct {
 16:   PetscViewer viewer;
 17: } MonitorCtx;

 19: typedef struct {
 20:   PetscBool variant;
 21: } AppCtx;

 23: int main(int argc,char **argv)
 24: {
 25:   SNES           snes;                 /* SNES context */
 26:   SNESType       type = SNESNEWTONLS;        /* default nonlinear solution method */
 27:   Vec            x,r,F,U;              /* vectors */
 28:   Mat            J,B;                  /* Jacobian matrix-free, explicit preconditioner */
 29:   AppCtx         user;                 /* user-defined work context */
 30:   PetscScalar    h,xp = 0.0,v;
 31:   PetscInt       its,n = 5,i;
 32:   PetscBool      puremf = PETSC_FALSE;

 34:   PetscInitialize(&argc,&argv,(char*)0,help);
 35:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 36:   PetscOptionsHasName(NULL,NULL,"-variant",&user.variant);
 37:   h    = 1.0/(n-1);

 39:   /* Set up data structures */
 40:   VecCreateSeq(PETSC_COMM_SELF,n,&x);
 41:   PetscObjectSetName((PetscObject)x,"Approximate Solution");
 42:   VecDuplicate(x,&r);
 43:   VecDuplicate(x,&F);
 44:   VecDuplicate(x,&U);
 45:   PetscObjectSetName((PetscObject)U,"Exact Solution");

 47:   /* create explicit matrix preconditioner */
 48:   MatCreateSeqAIJ(PETSC_COMM_SELF,n,n,3,NULL,&B);

 50:   /* Store right-hand-side of PDE and exact solution */
 51:   for (i=0; i<n; i++) {
 52:     v    = 6.0*xp + PetscPowScalar(xp+1.e-12,6.0); /* +1.e-12 is to prevent 0^6 */
 53:     VecSetValues(F,1,&i,&v,INSERT_VALUES);
 54:     v    = xp*xp*xp;
 55:     VecSetValues(U,1,&i,&v,INSERT_VALUES);
 56:     xp  += h;
 57:   }

 59:   /* Create nonlinear solver */
 60:   SNESCreate(PETSC_COMM_WORLD,&snes);
 61:   SNESSetType(snes,type);

 63:   /* Set various routines and options */
 64:   SNESSetFunction(snes,r,FormFunction,F);
 65:   if (user.variant) {
 66:     /* this approach is not normally needed, one should use the MatCreateSNESMF() below usually */
 67:     MatCreateMFFD(PETSC_COMM_WORLD,n,n,n,n,&J);
 68:     MatMFFDSetFunction(J,(PetscErrorCode (*)(void*, Vec, Vec))SNESComputeFunction,snes);
 69:     MatMFFDSetFunctioni(J,FormFunctioni);
 70:     /* Use the matrix free operator for both the Jacobian used to define the linear system and used to define the preconditioner */
 71:     /* This tests MatGetDiagonal() for MATMFFD */
 72:     PetscOptionsHasName(NULL,NULL,"-puremf",&puremf);
 73:   } else {
 74:     /* create matrix free matrix for Jacobian */
 75:     MatCreateSNESMF(snes,&J);
 76:     /* demonstrates differencing a different function than FormFunction() to apply a matrix operator */
 77:     /* note we use the same context for this function as FormFunction, the F vector */
 78:     MatMFFDSetFunction(J,OtherFunctionForDifferencing,F);
 79:   }

 81:   /* Set various routines and options */
 82:   SNESSetJacobian(snes,J,puremf ? J : B,puremf ? FormJacobianNoMatrix : FormJacobian,&user);
 83:   SNESSetFromOptions(snes);

 85:   /* Solve nonlinear system */
 86:   FormInitialGuess(snes,x);
 87:   SNESSolve(snes,NULL,x);
 88:   SNESGetIterationNumber(snes,&its);
 89:   PetscPrintf(PETSC_COMM_SELF,"number of SNES iterations = %D\n\n",its);

 91:   /* Free data structures */
 92:   VecDestroy(&x));  PetscCall(VecDestroy(&r);
 93:   VecDestroy(&U));  PetscCall(VecDestroy(&F);
 94:   MatDestroy(&J));  PetscCall(MatDestroy(&B);
 95:   SNESDestroy(&snes);
 96:   PetscFinalize();
 97:   return 0;
 98: }
 99: /* --------------------  Evaluate Function F(x) --------------------- */

101: PetscErrorCode  FormFunction(SNES snes,Vec x,Vec f,void *dummy)
102: {
103:   const PetscScalar *xx,*FF;
104:   PetscScalar       *ff,d;
105:   PetscInt          i,n;

107:   VecGetArrayRead(x,&xx);
108:   VecGetArray(f,&ff);
109:   VecGetArrayRead((Vec) dummy,&FF);
110:   VecGetSize(x,&n);
111:   d     = (PetscReal)(n - 1); d = d*d;
112:   ff[0] = xx[0];
113:   for (i=1; i<n-1; i++) ff[i] = d*(xx[i-1] - 2.0*xx[i] + xx[i+1]) + xx[i]*xx[i] - FF[i];
114:   ff[n-1] = xx[n-1] - 1.0;
115:   VecRestoreArrayRead(x,&xx);
116:   VecRestoreArray(f,&ff);
117:   VecRestoreArrayRead((Vec)dummy,&FF);
118:   return 0;
119: }

121: PetscErrorCode  FormFunctioni(void *dummy,PetscInt i,Vec x,PetscScalar *s)
122: {
123:   const PetscScalar *xx,*FF;
124:   PetscScalar       d;
125:   PetscInt          n;
126:   SNES              snes = (SNES) dummy;
127:   Vec               F;

129:   SNESGetFunction(snes,NULL,NULL,(void**)&F);
130:   VecGetArrayRead(x,&xx);
131:   VecGetArrayRead(F,&FF);
132:   VecGetSize(x,&n);
133:   d     = (PetscReal)(n - 1); d = d*d;
134:   if (i == 0) {
135:     *s = xx[0];
136:   } else if (i == n-1) {
137:     *s = xx[n-1] - 1.0;
138:   } else {
139:     *s = d*(xx[i-1] - 2.0*xx[i] + xx[i+1]) + xx[i]*xx[i] - FF[i];
140:   }
141:   VecRestoreArrayRead(x,&xx);
142:   VecRestoreArrayRead(F,&FF);
143:   return 0;
144: }

146: /*

148:    Example function that when differenced produces the same matrix free Jacobian as FormFunction()
149:    this is provided to show how a user can provide a different function
150: */
151: PetscErrorCode  OtherFunctionForDifferencing(void *dummy,Vec x,Vec f)
152: {

154:   FormFunction(NULL,x,f,dummy);
155:   VecShift(f,1.0);
156:   return 0;
157: }

159: /* --------------------  Form initial approximation ----------------- */

161: PetscErrorCode  FormInitialGuess(SNES snes,Vec x)
162: {
163:   PetscScalar    pfive = .50;
164:   VecSet(x,pfive);
165:   return 0;
166: }
167: /* --------------------  Evaluate Jacobian F'(x) -------------------- */
168: /*  Evaluates a matrix that is used to precondition the matrix-free
169:     jacobian. In this case, the explicit preconditioner matrix is
170:     also EXACTLY the Jacobian. In general, it would be some lower
171:     order, simplified apprioximation */

173: PetscErrorCode  FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
174: {
175:   const PetscScalar *xx;
176:   PetscScalar       A[3],d;
177:   PetscInt          i,n,j[3];
178:   AppCtx            *user = (AppCtx*) dummy;

180:   VecGetArrayRead(x,&xx);
181:   VecGetSize(x,&n);
182:   d    = (PetscReal)(n - 1); d = d*d;

184:   i    = 0; A[0] = 1.0;
185:   MatSetValues(B,1,&i,1,&i,&A[0],INSERT_VALUES);
186:   for (i=1; i<n-1; i++) {
187:     j[0] = i - 1; j[1] = i;                   j[2] = i + 1;
188:     A[0] = d;     A[1] = -2.0*d + 2.0*xx[i];  A[2] = d;
189:     MatSetValues(B,1,&i,3,j,A,INSERT_VALUES);
190:   }
191:   i     = n-1; A[0] = 1.0;
192:   MatSetValues(B,1,&i,1,&i,&A[0],INSERT_VALUES);
193:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
194:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
195:   VecRestoreArrayRead(x,&xx);

197:   if (user->variant) {
198:     MatMFFDSetBase(jac,x,NULL);
199:   }
200:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
201:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
202:   return 0;
203: }

205: PetscErrorCode  FormJacobianNoMatrix(SNES snes,Vec x,Mat jac,Mat B,void *dummy)
206: {
207:   AppCtx            *user = (AppCtx*) dummy;

209:   if (user->variant) {
210:     MatMFFDSetBase(jac,x,NULL);
211:   }
212:   MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);
213:   MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);
214:   return 0;
215: }

217: /* --------------------  User-defined monitor ----------------------- */

219: PetscErrorCode  Monitor(SNES snes,PetscInt its,PetscReal fnorm,void *dummy)
220: {
221:   MonitorCtx     *monP = (MonitorCtx*) dummy;
222:   Vec            x;
223:   MPI_Comm       comm;

225:   PetscObjectGetComm((PetscObject)snes,&comm);
226:   PetscFPrintf(comm,stdout,"iter = %D, SNES Function norm %g \n",its,(double)fnorm);
227:   SNESGetSolution(snes,&x);
228:   VecView(x,monP->viewer);
229:   return 0;
230: }

232: /*TEST

234:    test:
235:       args: -ksp_gmres_cgs_refinement_type refine_always -snes_monitor_short

237:    test:
238:       suffix: 2
239:       args: -variant -ksp_gmres_cgs_refinement_type refine_always  -snes_monitor_short
240:       output_file: output/ex7_1.out

242:    # uses AIJ matrix to define diagonal matrix for Jacobian preconditioning
243:    test:
244:       suffix: 3
245:       args: -variant -pc_type jacobi -snes_view -ksp_monitor

247:    # uses MATMFFD matrix to define diagonal matrix for Jacobian preconditioning
248:    test:
249:       suffix: 4
250:       args: -variant -pc_type jacobi -puremf  -snes_view -ksp_monitor

252: TEST*/