Actual source code: ex16.c

```  2: /* Usage:  mpirun ex16 [-help] [all PETSc options] */

4: static char help[] = "Solves a sequence of linear systems with different right-hand-side vectors.\n\
5: Input parameters include:\n\
6:   -ntimes <ntimes>  : number of linear systems to solve\n\
7:   -view_exact_sol   : write exact solution vector to stdout\n\
8:   -m <mesh_x>       : number of mesh points in x-direction\n\
9:   -n <mesh_n>       : number of mesh points in y-direction\n\n";

11: /*T
12:    Concepts: KSP^repeatedly solving linear systems;
13:    Concepts: KSP^Laplacian, 2d
14:    Concepts: Laplacian, 2d
15:    Processors: n
16: T*/

18: /*
19:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
20:   automatically includes:
21:      petsc.h       - base PETSc routines   petscvec.h - vectors
22:      petscsys.h    - system routines       petscmat.h - matrices
23:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
24:      petscviewer.h - viewers               petscpc.h  - preconditioners
25: */
26:  #include petscksp.h

30: int main(int argc,char **args)
31: {
32:   Vec            x,b,u;  /* approx solution, RHS, exact solution */
33:   Mat            A;        /* linear system matrix */
34:   KSP            ksp;     /* linear solver context */
35:   PetscReal      norm;     /* norm of solution error */
37:   PetscInt       ntimes,i,j,k,Ii,J,Istart,Iend;
38:   PetscInt       m = 8,n = 7,its;
39:   PetscTruth     flg;
40:   PetscScalar    v,one = 1.0,neg_one = -1.0,rhs;

42:   PetscInitialize(&argc,&args,(char *)0,help);
43:   PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
44:   PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);

46:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
47:          Compute the matrix for use in solving a series of
48:          linear systems of the form, A x_i = b_i, for i=1,2,...
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.
55:   */
56:   MatCreate(PETSC_COMM_WORLD,&A);
57:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
58:   MatSetFromOptions(A);

60:   /*
61:      Currently, all PETSc parallel matrix formats are partitioned by
62:      contiguous chunks of rows across the processors.  Determine which
63:      rows of the matrix are locally owned.
64:   */
65:   MatGetOwnershipRange(A,&Istart,&Iend);

67:   /*
68:      Set matrix elements for the 2-D, five-point stencil in parallel.
69:       - Each processor needs to insert only elements that it owns
70:         locally (but any non-local elements will be sent to the
71:         appropriate processor during matrix assembly).
72:       - Always specify global rows and columns of matrix entries.
73:    */
74:   for (Ii=Istart; Ii<Iend; Ii++) {
75:     v = -1.0; i = Ii/n; j = Ii - i*n;
76:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
77:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
78:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
79:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
80:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
81:   }

83:   /*
84:      Assemble matrix, using the 2-step process:
85:        MatAssemblyBegin(), MatAssemblyEnd()
86:      Computations can be done while messages are in transition
87:      by placing code between these two statements.
88:   */
89:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
90:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

92:   /*
93:      Create parallel vectors.
94:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
95:         we specify only the vector's global
96:         dimension; the parallel partitioning is determined at runtime.
97:       - When solving a linear system, the vectors and matrices MUST
98:         be partitioned accordingly.  PETSc automatically generates
99:         appropriately partitioned matrices and vectors when MatCreate()
100:         and VecCreate() are used with the same communicator.
101:       - Note: We form 1 vector from scratch and then duplicate as needed.
102:   */
103:   VecCreate(PETSC_COMM_WORLD,&u);
104:   VecSetSizes(u,PETSC_DECIDE,m*n);
105:   VecSetFromOptions(u);
106:   VecDuplicate(u,&b);
107:   VecDuplicate(b,&x);

109:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
110:                 Create the linear solver and set various options
111:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

113:   /*
114:      Create linear solver context
115:   */
116:   KSPCreate(PETSC_COMM_WORLD,&ksp);

118:   /*
119:      Set operators. Here the matrix that defines the linear system
120:      also serves as the preconditioning matrix.
121:   */
122:   KSPSetOperators(ksp,A,A,SAME_PRECONDITIONER);

124:   /*
125:     Set runtime options, e.g.,
126:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
127:     These options will override those specified above as long as
128:     KSPSetFromOptions() is called _after_ any other customization
129:     routines.
130:   */
131:   KSPSetFromOptions(ksp);

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:        Solve several linear systems of the form  A x_i = b_i
135:        I.e., we retain the same matrix (A) for all systems, but
136:        change the right-hand-side vector (b_i) at each step.

138:        In this case, we simply call KSPSolve() multiple times.  The
139:        preconditioner setup operations (e.g., factorization for ILU)
140:        be done during the first call to KSPSolve() only; such operations
141:        will NOT be repeated for successive solves.
142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

144:   ntimes = 2;
145:   PetscOptionsGetInt(PETSC_NULL,"-ntimes",&ntimes,PETSC_NULL);
146:   for (k=1; k<ntimes+1; k++) {

148:     /*
149:        Set exact solution; then compute right-hand-side vector.  We use
150:        an exact solution of a vector with all elements equal to 1.0*k.
151:     */
152:     rhs = one * (PetscReal)k;
153:     VecSet(u,rhs);
154:     MatMult(A,u,b);

156:     /*
157:        View the exact solution vector if desired
158:     */
159:     PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
160:     if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}

162:     KSPSolve(ksp,b,x);

164:     /*
165:        Check the error
166:     */
167:     VecAXPY(x,neg_one,u);
168:     VecNorm(x,NORM_2,&norm);
169:     KSPGetIterationNumber(ksp,&its);
170:     /*
171:        Print convergence information.  PetscPrintf() produces a single
172:        print statement from all processes that share a communicator.
173:     */
174:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A System %D: iterations %D\n",norm,k,its);
175:   }

177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178:                       Clean up
179:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
180:   /*
181:      Free work space.  All PETSc objects should be destroyed when they
182:      are no longer needed.
183:   */
184:   KSPDestroy(ksp);
185:   VecDestroy(u);  VecDestroy(x);
186:   VecDestroy(b);  MatDestroy(A);

188:   /*
189:      Always call PetscFinalize() before exiting a program.  This routine
190:        - finalizes the PETSc libraries as well as MPI
191:        - provides summary and diagnostic information if certain runtime
192:          options are chosen (e.g., -log_summary).
193:   */
194:   PetscFinalize();
195:   return 0;
196: }
```