Actual source code: ex2.c

petsc-master 2014-12-19
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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);
 65:   MatSetUp(A);

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

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

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

 86:    */
 87:   PetscLogStageRegister("Assembly", &stage);
 88:   PetscLogStagePush(stage);
 89:   for (Ii=Istart; Ii<Iend; Ii++) {
 90:     v = -1.0; i = Ii/n; j = Ii - i*n;
 91:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 92:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 93:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 94:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 95:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 96:   }

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

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

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

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

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

157:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
158:                 Create the linear solver and set various options
159:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

194:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195:                       Solve the linear system
196:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

198:   KSPSolve(ksp,b,x);

200:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
201:                       Check solution and clean up
202:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

226:   /*
227:      Always call PetscFinalize() before exiting a program.  This routine
228:        - finalizes the PETSc libraries as well as MPI
229:        - provides summary and diagnostic information if certain runtime
230:          options are chosen (e.g., -log_summary).
231:   */
232:   PetscFinalize();
233:   return 0;
234: }