Actual source code: ex25.c

  2: static char help[] ="Minimum surface problem\n\
  3: Uses 2-dimensional distributed arrays.\n\
  4: \n\
  5:   Solves the linear systems via multilevel methods \n\
  6: \n\n";

  8: /*T
  9:    Concepts: SNES^solving a system of nonlinear equations
 10:    Concepts: DA^using distributed arrays
 11:    Concepts: multigrid;
 12:    Processors: n
 13: T*/

 15: /*  
 16:   
 17:     This example models the partial differential equation 
 18:    
 19:          - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0.
 20:        
 21:     
 22:     in the unit square, which is uniformly discretized in each of x and 
 23:     y in this simple encoding.  The degrees of freedom are vertex centered
 24:  
 25:     A finite difference approximation with the usual 5-point stencil 
 26:     is used to discretize the boundary value problem to obtain a 
 27:     nonlinear system of equations. 
 28:  
 29: */

 31:  #include petscsnes.h
 32:  #include petscda.h
 33:  #include petscmg.h
 34:  #include petscdmmg.h


 41: int main(int argc,char **argv)
 42: {
 43:   DMMG           *dmmg;
 44:   SNES           snes;
 46:   PetscInt       its,lits;
 47:   PetscReal      litspit;
 48:   DA             da;

 50:   PetscInitialize(&argc,&argv,PETSC_NULL,help);


 53:   /*
 54:       Create the multilevel DA data structure 
 55:   */
 56:   DMMGCreate(PETSC_COMM_WORLD,3,0,&dmmg);

 58:   /*
 59:       Set the DA (grid structure) for the grids.
 60:   */
 61:   DACreate2d(PETSC_COMM_WORLD,DA_NONPERIODIC,DA_STENCIL_STAR,-5,-5,PETSC_DECIDE,PETSC_DECIDE,1,1,0,0,&da);
 62:   DMMGSetDM(dmmg,(DM)da);
 63:   DADestroy(da);

 65:   /*
 66:        Process adiC(36): FormFunctionLocal FormFunctionLocali

 68:      Create the nonlinear solver, and tell the DMMG structure to use it
 69:   */
 70:   /*  DMMGSetSNES(dmmg,FormFunction,0); */
 71:   DMMGSetSNESLocal(dmmg,FormFunctionLocal,0,ad_FormFunctionLocal,0);

 73:   /*
 74:       PreLoadBegin() means that the following section of code is run twice. The first time
 75:      through the flag PreLoading is on this the nonlinear solver is only run for a single step.
 76:      The second time through (the actually timed code) the maximum iterations is set to 10
 77:      Preload of the executable is done to eliminate from the timing the time spent bring the 
 78:      executable into memory from disk (paging in).
 79:   */
 80:   PreLoadBegin(PETSC_TRUE,"Solve");
 81:     DMMGSolve(dmmg);
 82:   PreLoadEnd();
 83:   snes = DMMGGetSNES(dmmg);
 84:   SNESGetIterationNumber(snes,&its);
 85:   SNESGetNumberLinearIterations(snes,&lits);
 86:   litspit = ((PetscReal)lits)/((PetscReal)its);
 87:   PetscPrintf(PETSC_COMM_WORLD,"Number of Newton iterations = %D\n",its);
 88:   PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %D\n",lits);
 89:   PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / Newton = %e\n",litspit);

 91:   DMMGDestroy(dmmg);
 92:   PetscFinalize();

 94:   return 0;
 95: }
 96: /* --------------------  Evaluate Function F(x) --------------------- */
 99: PetscErrorCode FormFunction(SNES snes,Vec T,Vec F,void* ptr)
100: {
101:   DMMG           dmmg = (DMMG)ptr;
103:   PetscInt       i,j,mx,my,xs,ys,xm,ym;
104:   PetscScalar    hx,hy;
105:   PetscScalar    **t,**f,gradup,graddown,gradleft,gradright,gradx,grady;
106:   PetscScalar    coeffup,coeffdown,coeffleft,coeffright;
107:   Vec            localT;

110:   DAGetLocalVector((DA)dmmg->dm,&localT);
111:   DAGetInfo((DA)dmmg->dm,PETSC_NULL,&mx,&my,0,0,0,0,0,0,0,0);
112:   hx    = 1.0/(PetscReal)(mx-1);  hy    = 1.0/(PetscReal)(my-1);
113: 
114:   /* Get ghost points */
115:   DAGlobalToLocalBegin((DA)dmmg->dm,T,INSERT_VALUES,localT);
116:   DAGlobalToLocalEnd((DA)dmmg->dm,T,INSERT_VALUES,localT);
117:   DAGetCorners((DA)dmmg->dm,&xs,&ys,0,&xm,&ym,0);
118:   DAVecGetArray((DA)dmmg->dm,localT,&t);
119:   DAVecGetArray((DA)dmmg->dm,F,&f);

121:   /* Evaluate function */
122:   for (j=ys; j<ys+ym; j++) {
123:     for (i=xs; i<xs+xm; i++) {

125:       if (i == 0 || i == mx-1 || j == 0 || j == my-1) {

127:         f[j][i] = t[j][i] - (1.0 - (2.0*hx*(PetscReal)i - 1.0)*(2.0*hx*(PetscReal)i - 1.0));
128: 
129:       } else {

131:         gradup     = (t[j+1][i] - t[j][i])/hy;
132:         graddown   = (t[j][i] - t[j-1][i])/hy;
133:         gradright  = (t[j][i+1] - t[j][i])/hx;
134:         gradleft   = (t[j][i] - t[j][i-1])/hx;

136:         gradx      = .5*(t[j][i+1] - t[j][i-1])/hx;
137:         grady      = .5*(t[j+1][i] - t[j-1][i])/hy;

139:         coeffup    = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx);
140:         coeffdown  = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx);

142:         coeffleft  = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady);
143:         coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady);

145:         f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy;
146: 
147:       }

149:     }
150:   }
151:   DAVecRestoreArray((DA)dmmg->dm,localT,&t);
152:   DAVecRestoreArray((DA)dmmg->dm,F,&f);
153:   DARestoreLocalVector((DA)dmmg->dm,&localT);
154:   return(0);
155: }

157: PetscErrorCode FormFunctionLocal(DALocalInfo *info,PetscScalar **t,PetscScalar **f,void *ptr)
158: {
159:   PetscInt     i,j;
160:   PetscScalar  hx,hy;
161:   PetscScalar  gradup,graddown,gradleft,gradright,gradx,grady;
162:   PetscScalar  coeffup,coeffdown,coeffleft,coeffright;

165:   hx    = 1.0/(PetscReal)(info->mx-1);  hy    = 1.0/(PetscReal)(info->my-1);
166: 
167:   /* Evaluate function */
168:   for (j=info->ys; j<info->ys+info->ym; j++) {
169:     for (i=info->xs; i<info->xs+info->xm; i++) {

171:       if (i == 0 || i == info->mx-1 || j == 0 || j == info->my-1) {

173:         f[j][i] = t[j][i] - (1.0 - (2.0*hx*(PetscReal)i - 1.0)*(2.0*hx*(PetscReal)i - 1.0));
174: 
175:       } else {

177:         gradup     = (t[j+1][i] - t[j][i])/hy;
178:         graddown   = (t[j][i] - t[j-1][i])/hy;
179:         gradright  = (t[j][i+1] - t[j][i])/hx;
180:         gradleft   = (t[j][i] - t[j][i-1])/hx;

182:         gradx      = .5*(t[j][i+1] - t[j][i-1])/hx;
183:         grady      = .5*(t[j+1][i] - t[j-1][i])/hy;

185:         coeffup    = 1.0/PetscSqrtScalar(1.0 + gradup*gradup + gradx*gradx);
186:         coeffdown  = 1.0/PetscSqrtScalar(1.0 + graddown*graddown + gradx*gradx);

188:         coeffleft  = 1.0/PetscSqrtScalar(1.0 + gradleft*gradleft + grady*grady);
189:         coeffright = 1.0/PetscSqrtScalar(1.0 + gradright*gradright + grady*grady);

191:         f[j][i] = (coeffup*gradup - coeffdown*graddown)*hx + (coeffright*gradright - coeffleft*gradleft)*hy;
192: 
193:       }

195:     }
196:   }
197:   return(0);
198: }