Actual source code: ex23.c

  1: /*$Id: ex23.c,v 1.11 2001/08/07 21:30:54 bsmith Exp $*/

  3: /* Program usage:  mpirun ex23 [-help] [all PETSc options] */

  5: static char help[] = "Solves a tridiagonal linear system.nn";

  7: /*T
  8:    Concepts: SLES^basic parallel example;
  9:    Processors: n
 10: T*/

 12: /* 
 13:   Include "petscsles.h" so that we can use SLES solvers.  Note that this file
 14:   automatically includes:
 15:      petsc.h       - base PETSc routines   petscvec.h - vectors
 16:      petscsys.h    - system routines       petscmat.h - matrices
 17:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 18:      petscviewer.h - viewers               petscpc.h  - preconditioners

 20:   Note:  The corresponding uniprocessor example is ex1.c
 21: */
 22:  #include petscsles.h

 24: int main(int argc,char **args)
 25: {
 26:   Vec         x, b, u;      /* approx solution, RHS, exact solution */
 27:   Mat         A;            /* linear system matrix */
 28:   SLES        sles;         /* linear solver context */
 29:   PC          pc;           /* preconditioner context */
 30:   KSP         ksp;          /* Krylov subspace method context */
 31:   PetscReal   norm;         /* norm of solution error */
 32:   int         ierr,i,n = 10,col[3],its,rstart,rend,nlocal;
 33:   PetscScalar neg_one = -1.0,one = 1.0,value[3];

 35:   PetscInitialize(&argc,&args,(char *)0,help);
 36:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);

 38:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 39:          Compute the matrix and right-hand-side vector that define
 40:          the linear system, Ax = b.
 41:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 43:   /* 
 44:      Create vectors.  Note that we form 1 vector from scratch and
 45:      then duplicate as needed. For this simple case let PETSc decide how
 46:      many elements of the vector are stored on each processor. The second
 47:      argument to VecSetSizes() below causes PETSc to decide.
 48:   */
 49:   VecCreate(PETSC_COMM_WORLD,&x);
 50:   VecSetSizes(x,PETSC_DECIDE,n);
 51:   VecSetFromOptions(x);
 52:   VecDuplicate(x,&b);
 53:   VecDuplicate(x,&u);

 55:   /* Identify the starting and ending mesh points on each
 56:      processor for the interior part of the mesh. We let PETSc decide
 57:      above. */

 59:   VecGetOwnershipRange(x,&rstart,&rend);
 60:   VecGetLocalSize(x,&nlocal);

 62:   /* 
 63:      Create matrix.  When using MatCreate(), the matrix format can
 64:      be specified at runtime.

 66:      Performance tuning note:  For problems of substantial size,
 67:      preallocation of matrix memory is crucial for attaining good 
 68:      performance.  Since preallocation is not possible via the generic
 69:      matrix creation routine MatCreate(), we recommend for practical 
 70:      problems instead to use the creation routine for a particular matrix
 71:      format, e.g.,
 72:          MatCreateMPIAIJ() - sequential AIJ (compressed sparse row)
 73:          MatCreateMPIBAIJ() - block AIJ
 74:      See the matrix chapter of the users manual for details.

 76:      We pass in nlocal as the "local" size of the matrix to force it
 77:      to have the same parallel layout as the vector created above.
 78:   */
 79:   MatCreate(PETSC_COMM_WORLD,nlocal,nlocal,n,n,&A);
 80:   MatSetFromOptions(A);

 82:   /* 
 83:      Assemble matrix.  

 85:      The linear system is distributed across the processors by 
 86:      chunks of contiguous rows, which correspond to contiguous
 87:      sections of the mesh on which the problem is discretized.  
 88:      For matrix assembly, each processor contributes entries for
 89:      the part that it owns locally.
 90:   */


 93:   if (!rstart) {
 94:     rstart = 1;
 95:     i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
 96:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
 97:   }
 98:   if (rend == n) {
 99:     rend = n-1;
100:     i = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
101:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
102:   }

104:   /* Set entries corresponding to the mesh interior */
105:   value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
106:   for (i=rstart; i<rend; i++) {
107:     col[0] = i-1; col[1] = i; col[2] = i+1;
108:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
109:   }

111:   /* Assemble the matrix */
112:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
113:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

115:   /* 
116:      Set exact solution; then compute right-hand-side vector.
117:   */
118:   VecSet(&one,u);
119:   MatMult(A,u,b);

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
122:                 Create the linear solver and set various options
123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
124:   /* 
125:      Create linear solver context
126:   */
127:   SLESCreate(PETSC_COMM_WORLD,&sles);

129:   /* 
130:      Set operators. Here the matrix that defines the linear system
131:      also serves as the preconditioning matrix.
132:   */
133:   SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);

135:   /* 
136:      Set linear solver defaults for this problem (optional).
137:      - By extracting the KSP and PC contexts from the SLES context,
138:        we can then directly call any KSP and PC routines to set
139:        various options.
140:      - The following four statements are optional; all of these
141:        parameters could alternatively be specified at runtime via
142:        SLESSetFromOptions();
143:   */
144:   SLESGetKSP(sles,&ksp);
145:   SLESGetPC(sles,&pc);
146:   PCSetType(pc,PCJACOBI);
147:   KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);

149:   /* 
150:     Set runtime options, e.g.,
151:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
152:     These options will override those specified above as long as
153:     SLESSetFromOptions() is called _after_ any other customization
154:     routines.
155:   */
156:   SLESSetFromOptions(sles);
157: 
158:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
159:                       Solve the linear system
160:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
161:   /* 
162:      Solve linear system
163:   */
164:   SLESSolve(sles,b,x,&its);

166:   /* 
167:      View solver info; we could instead use the option -sles_view to
168:      print this info to the screen at the conclusion of SLESSolve().
169:   */
170:   SLESView(sles,PETSC_VIEWER_STDOUT_WORLD);

172:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
173:                       Check solution and clean up
174:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
175:   /* 
176:      Check the error
177:   */
178:   VecAXPY(&neg_one,u,x);
179:   ierr  = VecNorm(x,NORM_2,&norm);
180:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A, Iterations %dn",norm,its);
181:   /* 
182:      Free work space.  All PETSc objects should be destroyed when they
183:      are no longer needed.
184:   */
185:   VecDestroy(x); VecDestroy(u);
186:   VecDestroy(b); MatDestroy(A);
187:   SLESDestroy(sles);

189:   /*
190:      Always call PetscFinalize() before exiting a program.  This routine
191:        - finalizes the PETSc libraries as well as MPI
192:        - provides summary and diagnostic information if certain runtime
193:          options are chosen (e.g., -log_summary).
194:   */
195:   PetscFinalize();
196:   return 0;
197: }