Actual source code: ex25.c

  1: /* $Id: ex18.c,v 1.23 2001/08/07 21:31:17 bsmith Exp $ */


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

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

 17: /*  
 18:   
 19:     This example models the partial differential equation 
 20:    
 21:          - Div((1 + ||GRAD T||^2)^(1/2) (GRAD T)) = 0.
 22:        
 23:     
 24:     in the unit square, which is uniformly discretized in each of x and 
 25:     y in this simple encoding.  The degrees of freedom are vertex centered
 26:  
 27:     A finite difference approximation with the usual 5-point stencil 
 28:     is used to discretize the boundary value problem to obtain a 
 29:     nonlinear system of equations. 
 30:  
 31: */

 33:  #include petscsnes.h
 34:  #include petscda.h
 35:  #include petscmg.h

 37: extern int FormFunction(SNES,Vec,Vec,void*);
 38: extern int FormFunctionLocal(DALocalInfo*,PetscScalar**,PetscScalar**,void*);

 40: #undef __FUNCT__
 42: int main(int argc,char **argv)
 43: {
 44:   DMMG        *dmmg;
 45:   SNES        snes;
 46:   int         ierr,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: 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 = %dn",its);
 88:   PetscPrintf(PETSC_COMM_WORLD,"Number of Linear iterations = %dn",lits);
 89:   PetscPrintf(PETSC_COMM_WORLD,"Average Linear its / Newton = %en",litspit);

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

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

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

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

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

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

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

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

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

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

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

148:     }
149:   }
150:   DAVecRestoreArray((DA)dmmg->dm,localT,(void**)&t);
151:   DAVecRestoreArray((DA)dmmg->dm,F,(void**)&f);
152:   DARestoreLocalVector((DA)dmmg->dm,&localT);
153:   return(0);
154: }

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

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

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

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

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

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

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

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

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

194:     }
195:   }
196:   return(0);
197: }