Actual source code: ex3.c

petsc-master 2017-05-23
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  2: static char help[] = "Bilinear elements on the unit square for Laplacian.  To test the parallel\n\
  3: matrix assembly, the matrix is intentionally laid out across processors\n\
  4: differently from the way it is assembled.  Input arguments are:\n\
  5:   -m <size> : problem size\n\n";

  7: /*T
  8:    Concepts: KSP^basic parallel example
  9:    Concepts: Matrices^inserting elements by blocks
 10:    Processors: n
 11: T*/

 13: /*
 14:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 15:   automatically includes:
 16:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 17:      petscmat.h - matrices
 18:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 19:      petscviewer.h - viewers               petscpc.h  - preconditioners
 20: */
 21:  #include <petscksp.h>

 23: /* Declare user-defined routines */
 24: extern PetscErrorCode FormElementStiffness(PetscReal,PetscScalar*);
 25: extern PetscErrorCode FormElementRhs(PetscScalar,PetscScalar,PetscReal,PetscScalar*);

 27: int main(int argc,char **args)
 28: {
 29:   Vec            u,b,ustar; /* approx solution, RHS, exact solution */
 30:   Mat            A;           /* linear system matrix */
 31:   KSP            ksp;         /* Krylov subspace method context */
 32:   PetscInt       N;           /* dimension of system (global) */
 33:   PetscInt       M;           /* number of elements (global) */
 34:   PetscMPIInt    rank;        /* processor rank */
 35:   PetscMPIInt    size;        /* size of communicator */
 36:   PetscScalar    Ke[16];      /* element matrix */
 37:   PetscScalar    r[4];        /* element vector */
 38:   PetscReal      h;           /* mesh width */
 39:   PetscReal      norm;        /* norm of solution error */
 40:   PetscScalar    x,y;
 42:   PetscInt       idx[4],count,*rows,i,m = 5,start,end,its;

 44:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 45:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 46:   N    = (m+1)*(m+1);
 47:   M    = m*m;
 48:   h    = 1.0/m;
 49:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 50:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

 52:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 53:          Compute the matrix and right-hand-side vector that define
 54:          the linear system, Au = b.
 55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 57:   /*
 58:      Create stiffness matrix
 59:   */
 60:   MatCreate(PETSC_COMM_WORLD,&A);
 61:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
 62:   MatSetFromOptions(A);
 63:   MatSeqAIJSetPreallocation(A,9,NULL);
 64:   MatMPIAIJSetPreallocation(A,9,NULL,8,NULL);
 65:   start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
 66:   end   = start + M/size + ((M%size) > rank);

 68:   /*
 69:      Assemble matrix
 70:   */
 71:   FormElementStiffness(h*h,Ke);
 72:   for (i=start; i<end; i++) {
 73:     /* node numbers for the four corners of element */
 74:     idx[0] = (m+1)*(i/m) + (i % m);
 75:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
 76:     MatSetValues(A,4,idx,4,idx,Ke,ADD_VALUES);
 77:   }
 78:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 79:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 81:   /*
 82:      Create right-hand-side and solution vectors
 83:   */
 84:   VecCreate(PETSC_COMM_WORLD,&u);
 85:   VecSetSizes(u,PETSC_DECIDE,N);
 86:   VecSetFromOptions(u);
 87:   PetscObjectSetName((PetscObject)u,"Approx. Solution");
 88:   VecDuplicate(u,&b);
 89:   PetscObjectSetName((PetscObject)b,"Right hand side");
 90:   VecDuplicate(b,&ustar);
 91:   VecSet(u,0.0);
 92:   VecSet(b,0.0);

 94:   /*
 95:      Assemble right-hand-side vector
 96:   */
 97:   for (i=start; i<end; i++) {
 98:     /* location of lower left corner of element */
 99:     x = h*(i % m); y = h*(i/m);
100:     /* node numbers for the four corners of element */
101:     idx[0] = (m+1)*(i/m) + (i % m);
102:     idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
103:     FormElementRhs(x,y,h*h,r);
104:     VecSetValues(b,4,idx,r,ADD_VALUES);
105:   }
106:   VecAssemblyBegin(b);
107:   VecAssemblyEnd(b);

109:   /*
110:      Modify matrix and right-hand-side for Dirichlet boundary conditions
111:   */
112:   PetscMalloc1(4*m,&rows);
113:   for (i=0; i<m+1; i++) {
114:     rows[i] = i; /* bottom */
115:     rows[3*m - 1 +i] = m*(m+1) + i; /* top */
116:   }
117:   count = m+1; /* left side */
118:   for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
119:   count = 2*m; /* left side */
120:   for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
121:   for (i=0; i<4*m; i++) {
122:     y = h*(rows[i]/(m+1));
123:     VecSetValues(u,1,&rows[i],&y,INSERT_VALUES);
124:     VecSetValues(b,1,&rows[i],&y,INSERT_VALUES);
125:   }
126:   MatZeroRows(A,4*m,rows,1.0,0,0);
127:   PetscFree(rows);

129:   VecAssemblyBegin(u);
130:   VecAssemblyEnd(u);
131:   VecAssemblyBegin(b);
132:   VecAssemblyEnd(b);

134:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
135:                 Create the linear solver and set various options
136:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

138:   KSPCreate(PETSC_COMM_WORLD,&ksp);
139:   KSPSetOperators(ksp,A,A);
140:   KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
141:   KSPSetFromOptions(ksp);

143:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
144:                       Solve the linear system
145:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

147:   KSPSolve(ksp,b,u);

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150:                       Check solution and clean up
151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

153:   /* Check error */
154:   VecGetOwnershipRange(ustar,&start,&end);
155:   for (i=start; i<end; i++) {
156:     y = h*(i/(m+1));
157:     VecSetValues(ustar,1,&i,&y,INSERT_VALUES);
158:   }
159:   VecAssemblyBegin(ustar);
160:   VecAssemblyEnd(ustar);
161:   VecAXPY(u,-1.0,ustar);
162:   VecNorm(u,NORM_2,&norm);
163:   KSPGetIterationNumber(ksp,&its);
164:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)(norm*h),its);

166:   /*
167:      Free work space.  All PETSc objects should be destroyed when they
168:      are no longer needed.
169:   */
170:   KSPDestroy(&ksp); VecDestroy(&u);
171:   VecDestroy(&ustar); VecDestroy(&b);
172:   MatDestroy(&A);

174:   /*
175:      Always call PetscFinalize() before exiting a program.  This routine
176:        - finalizes the PETSc libraries as well as MPI
177:        - provides summary and diagnostic information if certain runtime
178:          options are chosen (e.g., -log_view).
179:   */
180:   PetscFinalize();
181:   return ierr;
182: }

184: /* --------------------------------------------------------------------- */
185: /* element stiffness for Laplacian */
186: PetscErrorCode FormElementStiffness(PetscReal H,PetscScalar *Ke)
187: {
189:   Ke[0]  = H/6.0;    Ke[1]  = -.125*H; Ke[2]  = H/12.0;   Ke[3]  = -.125*H;
190:   Ke[4]  = -.125*H;  Ke[5]  = H/6.0;   Ke[6]  = -.125*H;  Ke[7]  = H/12.0;
191:   Ke[8]  = H/12.0;   Ke[9]  = -.125*H; Ke[10] = H/6.0;    Ke[11] = -.125*H;
192:   Ke[12] = -.125*H;  Ke[13] = H/12.0;  Ke[14] = -.125*H;  Ke[15] = H/6.0;
193:   return(0);
194: }
195: /* --------------------------------------------------------------------- */
196: PetscErrorCode FormElementRhs(PetscScalar x,PetscScalar y,PetscReal H,PetscScalar *r)
197: {
199:   r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
200:   return(0);
201: }