Actual source code: ex40.c


  2: static char help[] = "Solves a linear system in parallel with KSP.\n\
  3: Input parameters include:\n\
  4:   -random_exact_sol : use a random exact solution vector\n\
  5:   -view_exact_sol   : write exact solution vector to stdout\n\
  6:   -m <mesh_x>       : number of mesh points in x-direction\n\
  7:   -n <mesh_y>       : number of mesh points in y-direction\n\n";

  9: /*
 10:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 11:   automatically includes:
 12:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 13:      petscmat.h - matrices
 14:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 15:      petscviewer.h - viewers               petscpc.h  - preconditioners
 16: */
 17: #include <petscksp.h>

 19: int main(int argc,char **args)
 20: {
 21:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
 22:   Mat            A;        /* linear system matrix */
 23:   KSP            ksp;     /* linear solver context */
 24:   PetscRandom    rctx;     /* random number generator context */
 25:   PetscReal      norm;     /* norm of solution error */
 26:   PetscInt       i,j,Ii,J,m = 8,n = 7,its;
 28:   PetscBool      flg = PETSC_FALSE;
 29:   PetscScalar    v;
 30:   PetscMPIInt    rank;

 32:   PetscInitialize(&argc,&args,(char*)0,help);
 33:   PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
 34:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 35:   MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
 36:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 37:          Compute the matrix and right-hand-side vector that define
 38:          the linear system, Ax = b.
 39:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 40:   /*
 41:      Create parallel matrix, specifying only its global dimensions.
 42:      When using MatCreate(), the matrix format can be specified at
 43:      runtime. Also, the parallel partitioning of the matrix is
 44:      determined by PETSc at runtime.

 46:      Performance tuning note:  For problems of substantial size,
 47:      preallocation of matrix memory is crucial for attaining good
 48:      performance. See the matrix chapter of the users manual for details.
 49:   */
 50:   MatCreate(PETSC_COMM_WORLD,&A);
 51:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 52:   MatSetType(A,MATELEMENTAL);
 53:   MatSetFromOptions(A);
 54:   MatSetUp(A);
 55:   if (rank==0) {
 56:     PetscInt M,N;
 57:     MatGetSize(A,&M,&N);
 58:     for (Ii=0; Ii<M; Ii++) {
 59:       v = -1.0; i = Ii/n; j = Ii - i*n;
 60:       if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 61:       if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 62:       if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 63:       if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 64:       v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
 65:     }
 66:   }
 67:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 68:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

 70:   /* MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE); */

 72:   /*
 73:      Create parallel vectors.
 74:       - We form 1 vector from scratch and then duplicate as needed.
 75:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
 76:         in this example, we specify only the
 77:         vector's global dimension; the parallel partitioning is determined
 78:         at runtime.
 79:       - When solving a linear system, the vectors and matrices MUST
 80:         be partitioned accordingly.  PETSc automatically generates
 81:         appropriately partitioned matrices and vectors when MatCreate()
 82:         and VecCreate() are used with the same communicator.
 83:       - The user can alternatively specify the local vector and matrix
 84:         dimensions when more sophisticated partitioning is needed
 85:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
 86:         below).
 87:   */
 88:   VecCreate(PETSC_COMM_WORLD,&u);
 89:   VecSetSizes(u,PETSC_DECIDE,m*n);
 90:   VecSetFromOptions(u);
 91:   VecDuplicate(u,&b);
 92:   VecDuplicate(b,&x);

 94:   /*
 95:      Set exact solution; then compute right-hand-side vector.
 96:      By default we use an exact solution of a vector with all
 97:      elements of 1.0;  Alternatively, using the runtime option
 98:      -random_sol forms a solution vector with random components.
 99:   */
100:   PetscOptionsGetBool(NULL,NULL,"-random_exact_sol",&flg,NULL);
101:   if (flg) {
102:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
103:     PetscRandomSetFromOptions(rctx);
104:     VecSetRandom(u,rctx);
105:     PetscRandomDestroy(&rctx);
106:   } else {
107:     VecSet(u,1.0);
108:   }
109:   MatMult(A,u,b);

111:   /*
112:      View the exact solution vector if desired
113:   */
114:   flg  = PETSC_FALSE;
115:   PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
116:   if (flg) VecView(u,PETSC_VIEWER_STDOUT_WORLD);

118:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119:                 Create the linear solver and set various options
120:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

122:   /*
123:      Create linear solver context
124:   */
125:   KSPCreate(PETSC_COMM_WORLD,&ksp);

127:   /*
128:      Set operators. Here the matrix that defines the linear system
129:      also serves as the preconditioning matrix.
130:   */
131:   KSPSetOperators(ksp,A,A);

133:   /*
134:      Set linear solver defaults for this problem (optional).
135:      - By extracting the KSP and PC contexts from the KSP context,
136:        we can then directly call any KSP and PC routines to set
137:        various options.
138:      - The following two statements are optional; all of these
139:        parameters could alternatively be specified at runtime via
140:        KSPSetFromOptions().  All of these defaults can be
141:        overridden at runtime, as indicated below.
142:   */
143:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),PETSC_DEFAULT,PETSC_DEFAULT,
144:                           PETSC_DEFAULT);

146:   /*
147:     Set runtime options, e.g.,
148:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
149:     These options will override those specified above as long as
150:     KSPSetFromOptions() is called _after_ any other customization
151:     routines.
152:   */
153:   KSPSetFromOptions(ksp);

155:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156:                       Solve the linear system
157:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

159:   KSPSolve(ksp,b,x);

161:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
162:                       Check solution and clean up
163:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

165:   /*
166:      Check the error
167:   */
168:   VecAXPY(x,-1.0,u);
169:   VecNorm(x,NORM_2,&norm);
170:   KSPGetIterationNumber(ksp,&its);

172:   /*
173:      Print convergence information.  PetscPrintf() produces a single
174:      print statement from all processes that share a communicator.
175:      An alternative is PetscFPrintf(), which prints to a file.
176:   */
177:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

179:   /*
180:      Free work space.  All PETSc objects should be destroyed when they
181:      are no longer needed.
182:   */
183:   KSPDestroy(&ksp);
184:   VecDestroy(&u));  PetscCall(VecDestroy(&x);
185:   VecDestroy(&b));  PetscCall(MatDestroy(&A);

187:   /*
188:      Always call PetscFinalize() before exiting a program.  This routine
189:        - finalizes the PETSc libraries as well as MPI
190:        - provides summary and diagnostic information if certain runtime
191:          options are chosen (e.g., -log_view).
192:   */
193:   PetscFinalize();
194:   return 0;
195: }

197: /*TEST

199:    test:
200:       nsize: 6
201:       args: -pc_type none
202:       requires: elemental

204:    test:
205:       suffix: 2
206:       nsize: 6
207:       args: -pc_type lu -pc_factor_mat_solver_type elemental
208:       requires: elemental

210: TEST*/