Actual source code: ex2.c

petsc-master 2015-07-31
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  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_n>       : number of mesh points in y-direction\n\n";

  9: /*T
 10:    Concepts: KSP^basic parallel example;
 11:    Concepts: KSP^Laplacian, 2d
 12:    Concepts: Laplacian, 2d
 13:    Processors: n
 14: T*/

 16: /*
 17:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 18:   automatically includes:
 19:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 20:      petscmat.h - matrices
 21:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 22:      petscviewer.h - viewers               petscpc.h  - preconditioners
 23: */
 24: #include <petscksp.h>

 28: int main(int argc,char **args)
 29: {
 30:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
 31:   Mat            A;        /* linear system matrix */
 32:   KSP            ksp;     /* linear solver context */
 33:   PetscRandom    rctx;     /* random number generator context */
 34:   PetscReal      norm;     /* norm of solution error */
 35:   PetscInt       i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
 37:   PetscBool      flg = PETSC_FALSE;
 38:   PetscScalar    v;
 39: #if defined(PETSC_USE_LOG)
 40:   PetscLogStage stage;
 41: #endif

 43:   PetscInitialize(&argc,&args,(char*)0,help);
 44:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 45:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 47:          Compute the matrix and right-hand-side vector that define
 48:          the linear system, Ax = b.
 49:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 50:   /*
 51:      Create parallel matrix, specifying only its global dimensions.
 52:      When using MatCreate(), the matrix format can be specified at
 53:      runtime. Also, the parallel partitioning of the matrix is
 54:      determined by PETSc at runtime.

 56:      Performance tuning note:  For problems of substantial size,
 57:      preallocation of matrix memory is crucial for attaining good
 58:      performance. See the matrix chapter of the users manual for details.
 59:   */
 60:   MatCreate(PETSC_COMM_WORLD,&A);
 61:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 62:   MatSetFromOptions(A);
 63:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 64:   MatSeqAIJSetPreallocation(A,5,NULL);

 66:   /*
 67:      Currently, all PETSc parallel matrix formats are partitioned by
 68:      contiguous chunks of rows across the processors.  Determine which
 69:      rows of the matrix are locally owned.
 70:   */
 71:   MatGetOwnershipRange(A,&Istart,&Iend);

 73:   /*
 74:      Set matrix elements for the 2-D, five-point stencil in parallel.
 75:       - Each processor needs to insert only elements that it owns
 76:         locally (but any non-local elements will be sent to the
 77:         appropriate processor during matrix assembly).
 78:       - Always specify global rows and columns of matrix entries.

 80:      Note: this uses the less common natural ordering that orders first
 81:      all the unknowns for x = h then for x = 2h etc; Hence you see J = Ii +- n
 82:      instead of J = I +- m as you might expect. The more standard ordering
 83:      would first do all variables for y = h, then y = 2h etc.

 85:    */
 86:   PetscLogStageRegister("Assembly", &stage);
 87:   PetscLogStagePush(stage);
 88:   for (Ii=Istart; Ii<Iend; Ii++) {
 89:     v = -1.0; i = Ii/n; j = Ii - i*n;
 90:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 91:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 92:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 93:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);}
 94:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
 95:   }

 97:   /*
 98:      Assemble matrix, using the 2-step process:
 99:        MatAssemblyBegin(), MatAssemblyEnd()
100:      Computations can be done while messages are in transition
101:      by placing code between these two statements.
102:   */
103:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
104:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
105:   PetscLogStagePop();

107:   /* A is symmetric. Set symmetric flag to enable ICC/Cholesky preconditioner */
108:   MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);

110:   /*
111:      Create parallel vectors.
112:       - We form 1 vector from scratch and then duplicate as needed.
113:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
114:         in this example, we specify only the
115:         vector's global dimension; the parallel partitioning is determined
116:         at runtime.
117:       - When solving a linear system, the vectors and matrices MUST
118:         be partitioned accordingly.  PETSc automatically generates
119:         appropriately partitioned matrices and vectors when MatCreate()
120:         and VecCreate() are used with the same communicator.
121:       - The user can alternatively specify the local vector and matrix
122:         dimensions when more sophisticated partitioning is needed
123:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
124:         below).
125:   */
126:   VecCreate(PETSC_COMM_WORLD,&u);
127:   VecSetSizes(u,PETSC_DECIDE,m*n);
128:   VecSetFromOptions(u);
129:   VecDuplicate(u,&b);
130:   VecDuplicate(b,&x);

132:   /*
133:      Set exact solution; then compute right-hand-side vector.
134:      By default we use an exact solution of a vector with all
135:      elements of 1.0;  Alternatively, using the runtime option
136:      -random_sol forms a solution vector with random components.
137:   */
138:   PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);
139:   if (flg) {
140:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
141:     PetscRandomSetFromOptions(rctx);
142:     VecSetRandom(u,rctx);
143:     PetscRandomDestroy(&rctx);
144:   } else {
145:     VecSet(u,1.0);
146:   }
147:   MatMult(A,u,b);

149:   /*
150:      View the exact solution vector if desired
151:   */
152:   flg  = PETSC_FALSE;
153:   PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);
154:   if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

156:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157:                 Create the linear solver and set various options
158:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

160:   /*
161:      Create linear solver context
162:   */
163:   KSPCreate(PETSC_COMM_WORLD,&ksp);

165:   /*
166:      Set operators. Here the matrix that defines the linear system
167:      also serves as the preconditioning matrix.
168:   */
169:   KSPSetOperators(ksp,A,A);

171:   /*
172:      Set linear solver defaults for this problem (optional).
173:      - By extracting the KSP and PC contexts from the KSP context,
174:        we can then directly call any KSP and PC routines to set
175:        various options.
176:      - The following two statements are optional; all of these
177:        parameters could alternatively be specified at runtime via
178:        KSPSetFromOptions().  All of these defaults can be
179:        overridden at runtime, as indicated below.
180:   */
181:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
182:                           PETSC_DEFAULT);

184:   /*
185:     Set runtime options, e.g.,
186:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
187:     These options will override those specified above as long as
188:     KSPSetFromOptions() is called _after_ any other customization
189:     routines.
190:   */
191:   KSPSetFromOptions(ksp);

193:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
194:                       Solve the linear system
195:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

197:   KSPSolve(ksp,b,x);

199:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
200:                       Check solution and clean up
201:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

203:   /*
204:      Check the error
205:   */
206:   VecAXPY(x,-1.0,u);
207:   VecNorm(x,NORM_2,&norm);
208:   KSPGetIterationNumber(ksp,&its);

210:   /*
211:      Print convergence information.  PetscPrintf() produces a single
212:      print statement from all processes that share a communicator.
213:      An alternative is PetscFPrintf(), which prints to a file.
214:   */
215:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

217:   /*
218:      Free work space.  All PETSc objects should be destroyed when they
219:      are no longer needed.
220:   */
221:   KSPDestroy(&ksp);
222:   VecDestroy(&u);  VecDestroy(&x);
223:   VecDestroy(&b);  MatDestroy(&A);

225:   /*
226:      Always call PetscFinalize() before exiting a program.  This routine
227:        - finalizes the PETSc libraries as well as MPI
228:        - provides summary and diagnostic information if certain runtime
229:          options are chosen (e.g., -log_summary).
230:   */
231:   PetscFinalize();
232:   return 0;
233: }