Actual source code: ex18.c

petsc-master 2017-10-19
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  1: static const char help[] = "Solves a (permuted) linear system in parallel with KSP.\n\
  2: Input parameters include:\n\
  3:   -permute <natural,rcm,nd,...> : solve system in permuted indexing\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>

 26: int main(int argc,char **args)
 27: {
 28:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
 29:   Mat            A;        /* linear system matrix */
 30:   KSP            ksp;     /* linear solver context */
 31:   PetscRandom    rctx;     /* random number generator context */
 32:   PetscReal      norm;     /* norm of solution error */
 33:   PetscInt       i,j,Ii,J,Istart,Iend,m,n,its;
 35:   PetscBool      random_exact_sol,view_exact_sol,permute;
 36:   char           ordering[256] = MATORDERINGRCM;
 37:   IS             rowperm       = NULL,colperm = NULL;
 38:   PetscScalar    v;
 39: #if defined(PETSC_USE_LOG)
 40:   PetscLogStage stage;
 41: #endif

 43:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
 44:   PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Poisson example options","");
 45:   {
 46:     m                = 8;
 47:     PetscOptionsInt("-m","Number of grid points in x direction","",m,&m,NULL);
 48:     n                = m-1;
 49:     PetscOptionsInt("-n","Number of grid points in y direction","",n,&n,NULL);
 50:     random_exact_sol = PETSC_FALSE;
 51:     PetscOptionsBool("-random_exact_sol","Choose a random exact solution","",random_exact_sol,&random_exact_sol,NULL);
 52:     view_exact_sol   = PETSC_FALSE;
 53:     PetscOptionsBool("-view_exact_sol","View exact solution","",view_exact_sol,&view_exact_sol,NULL);
 54:     permute          = PETSC_FALSE;
 55:     PetscOptionsFList("-permute","Permute matrix and vector to solving in new ordering","",MatOrderingList,ordering,ordering,sizeof(ordering),&permute);
 56:   }
 57:   PetscOptionsEnd();
 58:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 59:          Compute the matrix and right-hand-side vector that define
 60:          the linear system, Ax = b.
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 62:   /*
 63:      Create parallel matrix, specifying only its global dimensions.
 64:      When using MatCreate(), the matrix format can be specified at
 65:      runtime. Also, the parallel partitioning of the matrix is
 66:      determined by PETSc at runtime.

 68:      Performance tuning note:  For problems of substantial size,
 69:      preallocation of matrix memory is crucial for attaining good
 70:      performance. See the matrix chapter of the users manual for details.
 71:   */
 72:   MatCreate(PETSC_COMM_WORLD,&A);
 73:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
 74:   MatSetFromOptions(A);
 75:   MatMPIAIJSetPreallocation(A,5,NULL,5,NULL);
 76:   MatSeqAIJSetPreallocation(A,5,NULL);
 77:   MatSetUp(A);

 79:   /*
 80:      Currently, all PETSc parallel matrix formats are partitioned by
 81:      contiguous chunks of rows across the processors.  Determine which
 82:      rows of the matrix are locally owned.
 83:   */
 84:   MatGetOwnershipRange(A,&Istart,&Iend);

 86:   /*
 87:      Set matrix elements for the 2-D, five-point stencil in parallel.
 88:       - Each processor needs to insert only elements that it owns
 89:         locally (but any non-local elements will be sent to the
 90:         appropriate processor during matrix assembly).
 91:       - Always specify global rows and columns of matrix entries.

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

 98:    */
 99:   PetscLogStageRegister("Assembly", &stage);
100:   PetscLogStagePush(stage);
101:   for (Ii=Istart; Ii<Iend; Ii++) {
102:     v = -1.0; i = Ii/n; j = Ii - i*n;
103:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
104:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
105:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
106:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
107:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
108:   }

110:   /*
111:      Assemble matrix, using the 2-step process:
112:        MatAssemblyBegin(), MatAssemblyEnd()
113:      Computations can be done while messages are in transition
114:      by placing code between these two statements.
115:   */
116:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
117:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
118:   PetscLogStagePop();

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

123:   /*
124:      Create parallel vectors.
125:       - We form 1 vector from scratch and then duplicate as needed.
126:       - When using VecCreate(), VecSetSizes and VecSetFromOptions()
127:         in this example, we specify only the
128:         vector's global dimension; the parallel partitioning is determined
129:         at runtime.
130:       - When solving a linear system, the vectors and matrices MUST
131:         be partitioned accordingly.  PETSc automatically generates
132:         appropriately partitioned matrices and vectors when MatCreate()
133:         and VecCreate() are used with the same communicator.
134:       - The user can alternatively specify the local vector and matrix
135:         dimensions when more sophisticated partitioning is needed
136:         (replacing the PETSC_DECIDE argument in the VecSetSizes() statement
137:         below).
138:   */
139:   VecCreate(PETSC_COMM_WORLD,&u);
140:   VecSetSizes(u,PETSC_DECIDE,m*n);
141:   VecSetFromOptions(u);
142:   VecDuplicate(u,&b);
143:   VecDuplicate(b,&x);

145:   /*
146:      Set exact solution; then compute right-hand-side vector.
147:      By default we use an exact solution of a vector with all
148:      elements of 1.0;  Alternatively, using the runtime option
149:      -random_sol forms a solution vector with random components.
150:   */
151:   if (random_exact_sol) {
152:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
153:     PetscRandomSetFromOptions(rctx);
154:     VecSetRandom(u,rctx);
155:     PetscRandomDestroy(&rctx);
156:   } else {
157:     VecSet(u,1.0);
158:   }
159:   MatMult(A,u,b);

161:   /*
162:      View the exact solution vector if desired
163:   */
164:   if (view_exact_sol) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

166:   if (permute) {
167:     Mat Aperm;
168:     MatGetOrdering(A,ordering,&rowperm,&colperm);
169:     MatPermute(A,rowperm,colperm,&Aperm);
170:     VecPermute(b,colperm,PETSC_FALSE);
171:     MatDestroy(&A);
172:     A    = Aperm;               /* Replace original operator with permuted version */
173:   }

175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176:                 Create the linear solver and set various options
177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

179:   /*
180:      Create linear solver context
181:   */
182:   KSPCreate(PETSC_COMM_WORLD,&ksp);

184:   /*
185:      Set operators. Here the matrix that defines the linear system
186:      also serves as the preconditioning matrix.
187:   */
188:   KSPSetOperators(ksp,A,A);

190:   /*
191:      Set linear solver defaults for this problem (optional).
192:      - By extracting the KSP and PC contexts from the KSP context,
193:        we can then directly call any KSP and PC routines to set
194:        various options.
195:      - The following two statements are optional; all of these
196:        parameters could alternatively be specified at runtime via
197:        KSPSetFromOptions().  All of these defaults can be
198:        overridden at runtime, as indicated below.
199:   */
200:   KSPSetTolerances(ksp,1.e-2/((m+1)*(n+1)),1.e-50,PETSC_DEFAULT,
201:                           PETSC_DEFAULT);

203:   /*
204:     Set runtime options, e.g.,
205:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
206:     These options will override those specified above as long as
207:     KSPSetFromOptions() is called _after_ any other customization
208:     routines.
209:   */
210:   KSPSetFromOptions(ksp);

212:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
213:                       Solve the linear system
214:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

216:   KSPSolve(ksp,b,x);

218:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
219:                       Check solution and clean up
220:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

222:   if (permute) {VecPermute(x,rowperm,PETSC_TRUE);}

224:   /*
225:      Check the error
226:   */
227:   VecAXPY(x,-1.0,u);
228:   VecNorm(x,NORM_2,&norm);
229:   KSPGetIterationNumber(ksp,&its);

231:   /*
232:      Print convergence information.  PetscPrintf() produces a single
233:      print statement from all processes that share a communicator.
234:      An alternative is PetscFPrintf(), which prints to a file.
235:   */
236:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);

238:   /*
239:      Free work space.  All PETSc objects should be destroyed when they
240:      are no longer needed.
241:   */
242:   KSPDestroy(&ksp);
243:   VecDestroy(&u);  VecDestroy(&x);
244:   VecDestroy(&b);  MatDestroy(&A);
245:   ISDestroy(&rowperm);  ISDestroy(&colperm);

247:   /*
248:      Always call PetscFinalize() before exiting a program.  This routine
249:        - finalizes the PETSc libraries as well as MPI
250:        - provides summary and diagnostic information if certain runtime
251:          options are chosen (e.g., -log_view).
252:   */
253:   PetscFinalize();
254:   return ierr;
255: }