Actual source code: ex12.c

  1: /*$Id: ex12.c,v 1.24 2001/08/07 21:30:54 bsmith Exp $*/

  3: /* Program usage:  mpirun -np <procs> ex12 [-help] [all PETSc options] */

  5: static char help[] = "Solves a linear system in parallel with SLES.n
  6: Input parameters include:n
  7:   -m <mesh_x>       : number of mesh points in x-directionn
  8:   -n <mesh_n>       : number of mesh points in y-directionnn";

 10: /*T
 11:    Concepts: SLES^solving a system of linear equations
 12:    Concepts: SLES^Laplacian, 2d
 13:    Concepts: PC^registering preconditioners
 14:    Processors: n
 15: T*/

 17: /*
 18:    Demonstrates registering a new preconditioner (PC) type.

 20:    To register a PC type whose code is linked into the executable,
 21:    use PCRegister(). To register a PC type in a dynamic library use PCRegisterDynamic()

 23:    Also provide the prototype for your PCCreate_XXX() function. In 
 24:    this example we use the PETSc implementation of the Jacobi method,
 25:    PCCreate_Jacobi() just as an example.

 27:    See the file src/sles/pc/impls/jacobi/jacobi.c for details on how to 
 28:    write a new PC component.

 30:    See the manual page PCRegisterDynamic() for details on how to register a method.
 31: */

 33: /* 
 34:   Include "petscsles.h" so that we can use SLES solvers.  Note that this file
 35:   automatically includes:
 36:      petsc.h       - base PETSc routines   petscvec.h - vectors
 37:      petscsys.h    - system routines       petscmat.h - matrices
 38:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 39:      petscviewer.h - viewers               petscpc.h  - preconditioners
 40: */
 41:  #include petscsles.h

 43: EXTERN_C_BEGIN
 44: extern int PCCreate_Jacobi(PC);
 45: EXTERN_C_END

 47: int main(int argc,char **args)
 48: {
 49:   Vec         x,b,u;  /* approx solution, RHS, exact solution */
 50:   Mat         A;        /* linear system matrix */
 51:   SLES        sles;     /* linear solver context */
 52:   PetscReal   norm;     /* norm of solution error */
 53:   int         i,j,I,J,Istart,Iend,ierr,m = 8,n = 7,its;
 54:   PetscScalar v,one = 1.0,neg_one = -1.0;
 55:   PC          pc;      /* preconditioner context */

 57:   PetscInitialize(&argc,&args,(char *)0,help);
 58:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
 59:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);

 61:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 62:          Compute the matrix and right-hand-side vector that define
 63:          the linear system, Ax = b.
 64:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 65:   /* 
 66:      Create parallel matrix, specifying only its global dimensions.
 67:      When using MatCreate(), the matrix format can be specified at
 68:      runtime. Also, the parallel partitioning of the matrix is
 69:      determined by PETSc at runtime.
 70:   */
 71:   MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
 72:   MatSetFromOptions(A);

 74:   /* 
 75:      Currently, all PETSc parallel matrix formats are partitioned by
 76:      contiguous chunks of rows across the processors.  Determine which
 77:      rows of the matrix are locally owned. 
 78:   */
 79:   MatGetOwnershipRange(A,&Istart,&Iend);

 81:   /* 
 82:      Set matrix elements for the 2-D, five-point stencil in parallel.
 83:       - Each processor needs to insert only elements that it owns
 84:         locally (but any non-local elements will be sent to the
 85:         appropriate processor during matrix assembly). 
 86:       - Always specify global rows and columns of matrix entries.
 87:    */
 88:   for (I=Istart; I<Iend; I++) {
 89:     v = -1.0; i = I/n; j = I - i*n;
 90:     if (i>0)   {J = I - n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
 91:     if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
 92:     if (j>0)   {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
 93:     if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
 94:     v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_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);

106:   /* 
107:      Create parallel vectors.
108:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
109:       we specify only the vector's global
110:         dimension; the parallel partitioning is determined at runtime. 
111:       - When solving a linear system, the vectors and matrices MUST
112:         be partitioned accordingly.  PETSc automatically generates
113:         appropriately partitioned matrices and vectors when MatCreate()
114:         and VecCreate() are used with the same communicator. 
115:       - Note: We form 1 vector from scratch and then duplicate as needed.
116:   */
117:   VecCreate(PETSC_COMM_WORLD,&u);
118:   VecSetSizes(u,PETSC_DECIDE,m*n);
119:   VecSetFromOptions(u);
120:   VecDuplicate(u,&b);
121:   VecDuplicate(b,&x);

123:   /* 
124:      Set exact solution; then compute right-hand-side vector.
125:      Use an exact solution of a vector with all elements of 1.0;  
126:   */
127:   VecSet(&one,u);
128:   MatMult(A,u,b);

130:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
131:                 Create the linear solver and set various options
132:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

134:   /* 
135:      Create linear solver context
136:   */
137:   SLESCreate(PETSC_COMM_WORLD,&sles);

139:   /* 
140:      Set operators. Here the matrix that defines the linear system
141:      also serves as the preconditioning matrix.
142:   */
143:   SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);

145:   /*
146:        First register a new PC type with the command PCRegister()
147:   */
148:   PCRegister("ourjacobi",0,"PCCreate_Jacobi",PCCreate_Jacobi);
149: 
150:   /* 
151:      Set the PC type to be the new method
152:   */
153:   SLESGetPC(sles,&pc);
154:   PCSetType(pc,"ourjacobi");

156:   /* 
157:     Set runtime options, e.g.,
158:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
159:     These options will override those specified above as long as
160:     SLESSetFromOptions() is called _after_ any other customization
161:     routines.
162:   */
163:   SLESSetFromOptions(sles);

165:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
166:                       Solve the linear system
167:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

169:   SLESSolve(sles,b,x,&its);

171:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
172:                       Check solution and clean up
173:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

175:   /* 
176:      Check the error
177:   */
178:   VecAXPY(&neg_one,u,x);
179:   VecNorm(x,NORM_2,&norm);

181:   /* Scale the norm */
182:   /*  norm *= sqrt(1.0/((m+1)*(n+1))); */

184:   /*
185:      Print convergence information.  PetscPrintf() produces a single 
186:      print statement from all processes that share a communicator.
187:   */
188:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %dn",norm,its);

190:   /* 
191:      Free work space.  All PETSc objects should be destroyed when they
192:      are no longer needed.
193:   */
194:   SLESDestroy(sles);
195:   VecDestroy(u);  VecDestroy(x);
196:   VecDestroy(b);  MatDestroy(A);

198:   /*
199:      Always call PetscFinalize() before exiting a program.  This routine
200:        - finalizes the PETSc libraries as well as MPI
201:        - provides summary and diagnostic information if certain runtime
202:          options are chosen (e.g., -log_summary). 
203:   */
204:   PetscFinalize();
205:   return 0;
206: }