Actual source code: ex43.c

petsc-3.4.0 2013-05-13
  2: static char help[] = "Newton's method to solve a many-variable system that comes from the 2 variable Rosenbrock function + trivial.\n\n";

  4: /*

  6: ./ex43 -snes_monitor_range -snes_max_it 1000 -snes_rtol 1.e-14 -n 10 -snes_converged_reason -sub_snes_monito -sub_snes_mf -sub_snes_converged_reason -sub_snes_rtol 1.e-10 -sub_snes_max_it 1000 -sub_snes_monitor

  8:   Accelerates Newton's method by solving a small problem defined by those elements with large residual plus one level of overlap

 10:   This is a toy code for playing around

 12:   Counts residual entries as small if they are less then .2 times the maximum
 13:   Decides to solve a reduced problem if the number of large entries is less than 20 percent of all entries (and this has been true for criteria_reduce iterations)
 14: */
 15: #include "ex43-44.h"


 18: extern PetscErrorCode FormJacobian1(SNES,Vec,Mat*,Mat*,MatStructure*,void*);
 19: extern PetscErrorCode FormFunction1(SNES,Vec,Vec,void*);

 21: typedef struct {
 22:   PetscInt n,p;
 23: } Ctx;

 27: int main(int argc,char **argv)
 28: {
 29:   SNES                snes;         /* nonlinear solver context */
 30:   Vec                 x,r;          /* solution, residual vectors */
 31:   Mat                 J;            /* Jacobian matrix */
 32:   PetscErrorCode      ierr;
 33:   PetscScalar         *xx;
 34:   PetscInt            i,max_snes_solves = 20,snes_steps_per_solve = 2,criteria_reduce = 1;
 35:   Ctx                 ctx;
 36:   SNESConvergedReason reason;

 38:   PetscInitialize(&argc,&argv,(char*)0,help);
 39:   ctx.n = 0;
 40:   PetscOptionsGetInt(NULL,"-n",&ctx.n,NULL);
 41:   ctx.p = 0;
 42:   PetscOptionsGetInt(NULL,"-p",&ctx.p,NULL);
 43:   PetscOptionsGetInt(NULL,"-max_snes_solves",&max_snes_solves,NULL);
 44:   PetscOptionsGetInt(NULL,"-snes_steps_per_solve",&snes_steps_per_solve,NULL);
 45:   PetscOptionsGetInt(NULL,"-criteria_reduce",&criteria_reduce,NULL);

 47:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 48:      Create nonlinear solver context
 49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 50:   SNESCreate(PETSC_COMM_WORLD,&snes);

 52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 53:      Create matrix and vector data structures; set corresponding routines
 54:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 55:   /*
 56:      Create vectors for solution and nonlinear function
 57:   */
 58:   VecCreate(PETSC_COMM_WORLD,&x);
 59:   VecSetSizes(x,PETSC_DECIDE,2+ctx.n+ctx.p);
 60:   VecSetFromOptions(x);
 61:   VecDuplicate(x,&r);

 63:   /*
 64:      Create Jacobian matrix data structure
 65:   */
 66:   MatCreate(PETSC_COMM_WORLD,&J);
 67:   MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,2+ctx.p+ctx.n,2+ctx.p+ctx.n);
 68:   MatSetFromOptions(J);

 70:   /*
 71:      Set function evaluation routine and vector.
 72:   */
 73:   SNESSetFunction(snes,r,FormFunction1,(void*)&ctx);

 75:   /*
 76:      Set Jacobian matrix data structure and Jacobian evaluation routine
 77:   */
 78:   SNESSetJacobian(snes,J,J,FormJacobian1,(void*)&ctx);

 80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 81:      Customize nonlinear solver; set runtime options
 82:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 83:   SNESSetFromOptions(snes);

 85:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 86:      Evaluate initial guess; then solve nonlinear system
 87:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 88:   VecSet(x,0.0);
 89:   VecGetArray(x,&xx);
 90:   xx[0] = -1.2;
 91:   for (i=1; i<ctx.p+2; i++) xx[i] = 1.0;
 92:   VecRestoreArray(x,&xx);

 94:   /*
 95:      Note: The user should initialize the vector, x, with the initial guess
 96:      for the nonlinear solver prior to calling SNESSolve().  In particular,
 97:      to employ an initial guess of zero, the user should explicitly set
 98:      this vector to zero by calling VecSet().
 99:   */

101:   SNESMonitorSet(snes,MonitorRange,0,0);
102:   SNESSetTolerances(snes,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,snes_steps_per_solve,PETSC_DEFAULT);
103:   for (i=0; i<max_snes_solves; i++) {
104:     SNESSolve(snes,NULL,x);
105:     SNESGetConvergedReason(snes,&reason);
106:     if (reason && reason != SNES_DIVERGED_MAX_IT) break;
107:     if (CountGood > criteria_reduce) {
108:       SolveSubproblem(snes);
109:       CountGood = 0;
110:     }
111:   }

113:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
114:      Free work space.  All PETSc objects should be destroyed when they
115:      are no longer needed.
116:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

118:   VecDestroy(&x); VecDestroy(&r);
119:   MatDestroy(&J); SNESDestroy(&snes);
120:   PetscFinalize();
121:   return 0;
122: }
123: /* ------------------------------------------------------------------- */
126: /*
127:    FormFunction1 - Evaluates nonlinear function, F(x).

129:    Input Parameters:
130: .  snes - the SNES context
131: .  x    - input vector
132: .  ctx  - optional user-defined context

134:    Output Parameter:
135: .  f - function vector
136:  */
137: PetscErrorCode FormFunction1(SNES snes,Vec x,Vec f,void *ictx)
138: {
140:   PetscScalar    *xx,*ff;
141:   PetscInt       i;
142:   Ctx            *ctx = (Ctx*)ictx;

144:   /*
145:     Get pointers to vector data.
146:     - For default PETSc vectors, VecGetArray() returns a pointer to
147:     the data array.  Otherwise, the routine is implementation dependent.
148:     - You MUST call VecRestoreArray() when you no longer need access to
149:     the array.
150:   */
151:   VecGetArray(x,&xx);
152:   VecGetArray(f,&ff);

154:   /* Compute function */
155:   ff[0] = -2.0 + 2.0*xx[0] + 400.0*xx[0]*xx[0]*xx[0] - 400.0*xx[0]*xx[1];
156:   for (i=1; i<1+ctx->p; i++) {
157:     ff[i] = -2.0 + 2.0*xx[i] + 400.0*xx[i]*xx[i]*xx[i] - 400.0*xx[i]*xx[i+1] + 200.0*(xx[i] - xx[i-1]*xx[i-1]);
158:   }
159:   ff[ctx->p+1] = -200.0*xx[ctx->p]*xx[ctx->p] + 200.0*xx[ctx->p+1];
160:   for (i=ctx->p+2; i<2+ctx->p+ctx->n; i++) {
161:     ff[i] = xx[i] - xx[0] + .7*xx[1] - .2*xx[i-1]*xx[i-1];
162:   }

164:   /* Restore vectors */
165:   VecRestoreArray(x,&xx);
166:   VecRestoreArray(f,&ff);
167:   return 0;
168: }
169: /* ------------------------------------------------------------------- */
172: /*
173:    FormJacobian1 - Evaluates Jacobian matrix.

175:    Input Parameters:
176: .  snes - the SNES context
177: .  x - input vector
178: .  dummy - optional user-defined context (not used here)

180:    Output Parameters:
181: .  jac - Jacobian matrix
182: .  B - optionally different preconditioning matrix
183: .  flag - flag indicating matrix structure
184: */
185: PetscErrorCode FormJacobian1(SNES snes,Vec x,Mat *jac,Mat *B,MatStructure *flag,void *ictx)
186: {
187:   PetscScalar    *xx;
189:   PetscInt       i;
190:   Ctx            *ctx = (Ctx*)ictx;

192:   MatZeroEntries(*B);
193:   /*
194:      Get pointer to vector data
195:   */
196:   VecGetArray(x,&xx);

198:   /*
199:      Compute Jacobian entries and insert into matrix.
200:       - Since this is such a small problem, we set all entries for
201:         the matrix at once.
202:   */
203:   MatSetValue(*B,0,0, 2.0 + 1200.0*xx[0]*xx[0] - 400.0*xx[1],ADD_VALUES);
204:   MatSetValue(*B,0,1,-400.0*xx[0],ADD_VALUES);

206:   for (i=1; i<ctx->p+1; i++) {
207:     MatSetValue(*B,i,i-1, -400.0*xx[i-1],ADD_VALUES);
208:     MatSetValue(*B,i,i, 2.0 + 1200.0*xx[i]*xx[i] - 400.0*xx[i+1] + 200.0,ADD_VALUES);
209:     MatSetValue(*B,i,i+1,-400.0*xx[i],ADD_VALUES);
210:   }

212:   MatSetValue(*B,ctx->p+1,ctx->p, -400.0*xx[ctx->p],ADD_VALUES);
213:   MatSetValue(*B,ctx->p+1,ctx->p+1,200,ADD_VALUES);

215:   *flag = SAME_NONZERO_PATTERN;

217:   for (i=ctx->p+2; i<2+ctx->p+ctx->n; i++) {
218:     MatSetValue(*B,i,i,1.0,ADD_VALUES);
219:     MatSetValue(*B,i,0,-1.0,ADD_VALUES);
220:     MatSetValue(*B,i,1,.7,ADD_VALUES);
221:     MatSetValue(*B,i,i-1,-.4*xx[i-1],ADD_VALUES);
222:   }
223:   /*
224:      Restore vector
225:   */
226:   VecRestoreArray(x,&xx);

228:   /*
229:      Assemble matrix
230:   */
231:   MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
232:   MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
233:   if (*jac != *B) {
234:     MatAssemblyBegin(*jac,MAT_FINAL_ASSEMBLY);
235:     MatAssemblyEnd(*jac,MAT_FINAL_ASSEMBLY);
236:   }
237:   return 0;
238: }