Actual source code: ex32.c

petsc-3.7.1 2016-05-15
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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,NULL,"-dof",&dof,NULL);
 35:   PetscOptionsGetInt(NULL,NULL,"-M",&M,NULL);
 36:   PetscOptionsGetBool(NULL,NULL,"-trans",&trans,NULL);

 38:   DMDACreate(PETSC_COMM_WORLD,&da);
 39:   DMSetDimension(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:   DMSetFromOptions(da);
 55:   DMCreateMatrix(da,&A);
 56:   ComputeMatrix(da,A);


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

 65:   /* Test sbaij matrix */
 66:   flg  = PETSC_FALSE;
 67:   PetscOptionsGetBool(NULL,NULL, "-test_sbaij1", &flg,NULL);
 68:   if (flg) {
 69:     Mat       sA;
 70:     PetscBool issymm;
 71:     MatIsTranspose(A,A,0.0,&issymm);
 72:     if (issymm) {
 73:       MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);
 74:     } else printf("Warning: A is non-symmetric\n");
 75:     MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);
 76:     MatDestroy(&A);
 77:     A    = sA;
 78:   }

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

 86:   if (trans) {
 87:     KSPSolveTranspose(ksp,b,x);
 88:   } else {
 89:     KSPSolve(ksp,b,x);
 90:   }

 92:   /* check final residual */
 93:   flg  = PETSC_FALSE;
 94:   PetscOptionsGetBool(NULL,NULL, "-check_final_residual", &flg,NULL);
 95:   if (flg) {
 96:     Vec       b1;
 97:     PetscReal norm;
 98:     KSPGetSolution(ksp,&x);
 99:     VecDuplicate(b,&b1);
100:     MatMult(A,x,b1);
101:     VecAXPY(b1,-1.0,b);
102:     VecNorm(b1,NORM_2,&norm);
103:     PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);
104:     VecDestroy(&b1);
105:   }

107:   KSPDestroy(&ksp);
108:   VecDestroy(&x);
109:   VecDestroy(&b);
110:   MatDestroy(&A);
111:   DMDestroy(&da);
112:   PetscFinalize();
113:   return 0;
114: }

118: PetscErrorCode ComputeRHS(DM da,Vec b)
119: {
121:   PetscInt       mx,my,mz;
122:   PetscScalar    h;

125:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);
126:   h    = 1.0/((mx-1)*(my-1)*(mz-1));
127:   VecSet(b,h);
128:   return(0);
129: }

133: PetscErrorCode ComputeMatrix(DM da,Mat B)
134: {
136:   PetscInt       i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,dof,k1,k2,k3;
137:   PetscScalar    *v,*v_neighbor,Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
138:   MatStencil     row,col;

141:   DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);
142:   /* For simplicity, this example only works on mx=my=mz */
143:   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);

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

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

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

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

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

189:           /* z neighbors */
190:           col.i = i; col.j = j; col.k = k-1;
191:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
192:           col.i = i; col.j = j; col.k = k+1;
193:           MatSetValuesBlockedStencil(B,1,&row,1,&col,v_neighbor,INSERT_VALUES);
194:         }
195:       }
196:     }
197:   }
198:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
199:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
200:   PetscFree(v);
201:   return(0);
202: }