Actual source code: ex16.c

petsc-3.5.4 2015-05-23
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```  2: /* Usage:  mpiexec 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:      petscsys.h       - base PETSc routines   petscvec.h - vectors
22:      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:   PetscBool      flg = PETSC_FALSE;
40:   PetscScalar    v,one = 1.0,neg_one = -1.0,rhs;

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

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

68:   /*
69:      Set matrix elements for the 2-D, five-point stencil in parallel.
70:       - Each processor needs to insert only elements that it owns
71:         locally (but any non-local elements will be sent to the
72:         appropriate processor during matrix assembly).
73:       - Always specify global rows and columns of matrix entries.
74:    */
75:   for (Ii=Istart; Ii<Iend; Ii++) {
76:     v = -1.0; i = Ii/n; j = Ii - i*n;
77:     if (i>0)   {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
78:     if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
79:     if (j>0)   {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
80:     if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
81:     v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
82:   }

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

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

110:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
111:                 Create the linear solver and set various options
112:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

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

139:        In this case, we simply call KSPSolve() multiple times.  The
140:        preconditioner setup operations (e.g., factorization for ILU)
141:        be done during the first call to KSPSolve() only; such operations
142:        will NOT be repeated for successive solves.
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

163:     KSPSolve(ksp,b,x);

165:     /*
166:        Check the error
167:     */
168:     VecAXPY(x,neg_one,u);
169:     VecNorm(x,NORM_2,&norm);
170:     KSPGetIterationNumber(ksp,&its);
171:     /*
172:        Print convergence information.  PetscPrintf() produces a single
173:        print statement from all processes that share a communicator.
174:     */
175:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g System %D: iterations %D\n",(double)norm,k,its);
176:   }

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

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: }
```