Actual source code: ex32.c

petsc-3.5.4 2015-05-23
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  1: /*
  2:   Laplacian in 3D. Use for testing BAIJ matrix.
  3:   Modeled by the partial differential equation

  5:    - Laplacian u = 1,0 < x,y,z < 1,

  7:    with boundary conditions
  8:    u = 1 for x = 0, x = 1, y = 0, y = 1, z = 0, z = 1.
  9: */

 11: static char help[] = "Solves 3D Laplacian using wirebasket based multigrid.\n\n";

 13: #include <petscdm.h>
 14: #include <petscdmda.h>
 15: #include <petscksp.h>

 17: extern PetscErrorCode ComputeMatrix(DM,Mat);
 18: extern PetscErrorCode ComputeRHS(DM,Vec);

 22: int main(int argc,char **argv)
 23: {
 25:   KSP            ksp;
 26:   PC             pc;
 27:   Vec            x,b;
 28:   DM             da;
 29:   Mat            A,Atrans;
 30:   PetscInt       dof=1,M=-8;
 31:   PetscBool      flg,trans=PETSC_FALSE;

 33:   PetscInitialize(&argc,&argv,(char*)0,help);
 34:   PetscOptionsGetInt(NULL,"-dof",&dof,NULL);
 35:   PetscOptionsGetInt(NULL,"-M",&M,NULL);
 36:   PetscOptionsGetBool(NULL,"-trans",&trans,NULL);

 38:   DMDACreate(PETSC_COMM_WORLD,&da);
 39:   DMDASetDim(da,3);
 40:   DMDASetBoundaryType(da,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE);
 41:   DMDASetStencilType(da,DMDA_STENCIL_STAR);
 42:   DMDASetSizes(da,M,M,M);
 43:   DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);
 44:   DMDASetDof(da,dof);
 45:   DMDASetStencilWidth(da,1);
 46:   DMDASetOwnershipRanges(da,NULL,NULL,NULL);
 47:   DMSetFromOptions(da);
 48:   DMSetUp(da);

 50:   DMCreateGlobalVector(da,&x);
 51:   DMCreateGlobalVector(da,&b);
 52:   ComputeRHS(da,b);
 53:   DMSetMatType(da,MATBAIJ);
 54:   DMCreateMatrix(da,&A);
 55:   ComputeMatrix(da,A);


 58:   /* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
 59:   MatTranspose(A,MAT_INITIAL_MATRIX,&Atrans);
 60:   MatAXPY(A,1.0,Atrans,DIFFERENT_NONZERO_PATTERN);
 61:   MatScale(A,0.5);
 62:   MatDestroy(&Atrans);

 64:   /* Test sbaij matrix */
 65:   flg  = PETSC_FALSE;
 66:   PetscOptionsGetBool(NULL, "-test_sbaij1", &flg,NULL);
 67:   if (flg) {
 68:     Mat       sA;
 69:     PetscBool issymm;
 70:     MatIsTranspose(A,A,0.0,&issymm);
 71:     if (issymm) {
 72:       MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
 73:     } else printf("Warning: A is non-symmetric\n");
 74:     MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);
 75:     MatDestroy(&A);
 76:     A    = sA;
 77:   }

 79:   KSPCreate(PETSC_COMM_WORLD,&ksp);
 80:   KSPSetFromOptions(ksp);
 81:   KSPSetOperators(ksp,A,A);
 82:   KSPGetPC(ksp,&pc);
 83:   PCSetDM(pc,(DM)da);

 85:   if (trans) {
 86:     KSPSolveTranspose(ksp,b,x);
 87:   } else {
 88:     KSPSolve(ksp,b,x);
 89:   }

 91:   /* check final residual */
 92:   flg  = PETSC_FALSE;
 93:   PetscOptionsGetBool(NULL, "-check_final_residual", &flg,NULL);
 94:   if (flg) {
 95:     Vec       b1;
 96:     PetscReal norm;
 97:     KSPGetSolution(ksp,&x);
 98:     VecDuplicate(b,&b1);
 99:     MatMult(A,x,b1);
100:     VecAXPY(b1,-1.0,b);
101:     VecNorm(b1,NORM_2,&norm);
102:     PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);
103:     VecDestroy(&b1);
104:   }

106:   KSPDestroy(&ksp);
107:   VecDestroy(&x);
108:   VecDestroy(&b);
109:   MatDestroy(&A);
110:   DMDestroy(&da);
111:   PetscFinalize();
112:   return 0;
113: }

117: PetscErrorCode ComputeRHS(DM da,Vec b)
118: {
120:   PetscInt       mx,my,mz;
121:   PetscScalar    h;

124:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
125:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
126:   VecSet(b,h);
127:   return(0);
128: }

132: PetscErrorCode ComputeMatrix(DM da,Mat B)
133: {
135:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,dof,k1,k2,k3;
136:   PetscScalar    *v,*v_neighbor,Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
137:   MatStencil     row,col;

140:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
141:   /* For simplicity, this example only works on mx=my=mz */
142:   if (mx != my || mx != mz) SETERRQ3(PETSC_COMM_SELF,1,"This example only works with mx %d = my %d = mz %d\n",mx,my,mz);

144:   Hx      = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
145:   HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;

147:   PetscMalloc1((2*dof*dof+1),&v);
148:   v_neighbor = v + dof*dof;
149:   PetscMemzero(v,(2*dof*dof+1)*sizeof(PetscScalar));
150:   k3         = 0;
151:   for (k1=0; k1<dof; k1++) {
152:     for (k2=0; k2<dof; k2++) {
153:       if (k1 == k2) {
154:         v[k3]          = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
155:         v_neighbor[k3] = -HxHydHz;
156:       } else {
157:         v[k3]          = k1/(dof*dof);;
158:         v_neighbor[k3] = k2/(dof*dof);
159:       }
160:       k3++;
161:     }
162:   }
163:   DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);

165:   for (k=zs; k<zs+zm; k++) {
166:     for (j=ys; j<ys+ym; j++) {
167:       for (i=xs; i<xs+xm; i++) {
168:         row.i = i; row.j = j; row.k = k;
169:         if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) { /* boudary points */
170:           MatSetValuesBlockedStencil(B,1,&row,1,&row,v,INSERT_VALUES);
171:         } else { /* interior points */
172:           /* center */
173:           col.i = i; col.j = j; col.k = k;
174:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v,INSERT_VALUES);

176:           /* x neighbors */
177:           col.i = i-1; col.j = j; col.k = k;
178:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
179:           col.i = i+1; col.j = j; col.k = k;
180:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);

182:           /* y neighbors */
183:           col.i = i; col.j = j-1; col.k = k;
184:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
185:           col.i = i; col.j = j+1; col.k = k;
186:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);

188:           /* z neighbors */
189:           col.i = i; col.j = j; col.k = k-1;
190:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
191:           col.i = i; col.j = j; col.k = k+1;
192:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
193:         }
194:       }
195:     }
196:   }
197:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
198:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
199:   PetscFree(v);
200:   return(0);
201: }