Actual source code: ex12.c

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

  4: static char help[] = "Solves a linear system in parallel with KSP.\n\
  5: Input parameters include:\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^solving a system of linear equations
 11:    Concepts: KSP^Laplacian, 2d
 12:    Concepts: PC^registering preconditioners
 13:    Processors: n
 14: T*/

 16: /*
 17:    Demonstrates registering a new preconditioner (PC) type.

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

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

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

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

 32: /* 
 33:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 34:   automatically includes:
 35:      petsc.h       - base PETSc routines   petscvec.h - vectors
 36:      petscsys.h    - system routines       petscmat.h - matrices
 37:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 38:      petscviewer.h - viewers               petscpc.h  - preconditioners
 39: */
 40:  #include petscksp.h

 43: EXTERN PetscErrorCode PCCreate_Jacobi(PC);

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

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

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

 77:   /* 
 78:      Currently, all PETSc parallel matrix formats are partitioned by
 79:      contiguous chunks of rows across the processors.  Determine which
 80:      rows of the matrix are locally owned. 
 81:   */
 82:   MatGetOwnershipRange(A,&Istart,&Iend);

 84:   /* 
 85:      Set matrix elements for the 2-D, five-point stencil in parallel.
 86:       - Each processor needs to insert only elements that it owns
 87:         locally (but any non-local elements will be sent to the
 88:         appropriate processor during matrix assembly). 
 89:       - Always specify global rows and columns of matrix entries.
 90:    */
 91:   for (Ii=Istart; Ii<Iend; Ii++) {
 92:     v = -1.0; i = Ii/n; j = Ii - i*n;
 93:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 94:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 95:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 96:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
 97:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
 98:   }

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

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

126:   /* 
127:      Set exact solution; then compute right-hand-side vector.
128:      Use an exact solution of a vector with all elements of 1.0;  
129:   */
130:   VecSet(u,one);
131:   MatMult(A,u,b);

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
134:                 Create the linear solver and set various options
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

137:   /* 
138:      Create linear solver context
139:   */
140:   KSPCreate(PETSC_COMM_WORLD,&ksp);

142:   /* 
143:      Set operators. Here the matrix that defines the linear system
144:      also serves as the preconditioning matrix.
145:   */
146:   KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);

148:   /*
149:        First register a new PC type with the command PCRegister()
150:   */
151:   PCRegister("ourjacobi",0,"PCCreate_Jacobi",PCCreate_Jacobi);
152: 
153:   /* 
154:      Set the PC type to be the new method
155:   */
156:   KSPGetPC(ksp,&pc);
157:   PCSetType(pc,"ourjacobi");

159:   /* 
160:     Set runtime options, e.g.,
161:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
162:     These options will override those specified above as long as
163:     KSPSetFromOptions() is called _after_ any other customization
164:     routines.
165:   */
166:   KSPSetFromOptions(ksp);

168:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
169:                       Solve the linear system
170:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

172:   KSPSolve(ksp,b,x);

174:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
175:                       Check solution and clean up
176:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

178:   /* 
179:      Check the error
180:   */
181:   VecAXPY(x,neg_one,u);
182:   VecNorm(x,NORM_2,&norm);
183:   KSPGetIterationNumber(ksp,&its);
184:   /* Scale the norm */
185:   /*  norm *= sqrt(1.0/((m+1)*(n+1))); */

187:   /*
188:      Print convergence information.  PetscPrintf() produces a single 
189:      print statement from all processes that share a communicator.
190:   */
191:   PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",norm,its);

193:   /* 
194:      Free work space.  All PETSc objects should be destroyed when they
195:      are no longer needed.
196:   */
197:   KSPDestroy(ksp);
198:   VecDestroy(u);  VecDestroy(x);
199:   VecDestroy(b);  MatDestroy(A);

201:   /*
202:      Always call PetscFinalize() before exiting a program.  This routine
203:        - finalizes the PETSc libraries as well as MPI
204:        - provides summary and diagnostic information if certain runtime
205:          options are chosen (e.g., -log_summary). 
206:   */
207:   PetscFinalize();
208:   return 0;
209: }