Actual source code: ex16.c
1: /*$Id: ex16.c,v 1.25 2001/08/07 21:30:54 bsmith Exp $*/
3: /* Usage: mpirun ex16 [-help] [all PETSc options] */
5: static char help[] = "Solves a sequence of linear systems with different right-hand-side vectors.n
6: Input parameters include:n
7: -ntimes <ntimes> : number of linear systems to solven
8: -view_exact_sol : write exact solution vector to stdoutn
9: -m <mesh_x> : number of mesh points in x-directionn
10: -n <mesh_n> : number of mesh points in y-directionnn";
12: /*T
13: Concepts: SLES^repeatedly solving linear systems;
14: Concepts: SLES^Laplacian, 2d
15: Concepts: Laplacian, 2d
16: Processors: n
17: T*/
19: /*
20: Include "petscsles.h" so that we can use SLES solvers. Note that this file
21: automatically includes:
22: petsc.h - base PETSc routines petscvec.h - vectors
23: petscsys.h - system routines petscmat.h - matrices
24: petscis.h - index sets petscksp.h - Krylov subspace methods
25: petscviewer.h - viewers petscpc.h - preconditioners
26: */
27: #include petscsles.h
29: #undef __FUNCT__
31: int main(int argc,char **args)
32: {
33: Vec x,b,u; /* approx solution, RHS, exact solution */
34: Mat A; /* linear system matrix */
35: SLES sles; /* linear solver context */
36: PetscReal norm; /* norm of solution error */
37: int ntimes,i,j,k,I,J,Istart,Iend,ierr;
38: int 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,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
57: MatSetFromOptions(A);
59: /*
60: Currently, all PETSc parallel matrix formats are partitioned by
61: contiguous chunks of rows across the processors. Determine which
62: rows of the matrix are locally owned.
63: */
64: MatGetOwnershipRange(A,&Istart,&Iend);
66: /*
67: Set matrix elements for the 2-D, five-point stencil in parallel.
68: - Each processor needs to insert only elements that it owns
69: locally (but any non-local elements will be sent to the
70: appropriate processor during matrix assembly).
71: - Always specify global rows and columns of matrix entries.
72: */
73: for (I=Istart; I<Iend; I++) {
74: v = -1.0; i = I/n; j = I - i*n;
75: if (i>0) {J = I - n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
76: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
77: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
78: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
79: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_VALUES);
80: }
82: /*
83: Assemble matrix, using the 2-step process:
84: MatAssemblyBegin(), MatAssemblyEnd()
85: Computations can be done while messages are in transition
86: by placing code between these two statements.
87: */
88: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
89: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
91: /*
92: Create parallel vectors.
93: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
94: we specify only the vector's global
95: dimension; the parallel partitioning is determined at runtime.
96: - When solving a linear system, the vectors and matrices MUST
97: be partitioned accordingly. PETSc automatically generates
98: appropriately partitioned matrices and vectors when MatCreate()
99: and VecCreate() are used with the same communicator.
100: - Note: We form 1 vector from scratch and then duplicate as needed.
101: */
102: VecCreate(PETSC_COMM_WORLD,&u);
103: VecSetSizes(u,PETSC_DECIDE,m*n);
104: VecSetFromOptions(u);
105: VecDuplicate(u,&b);
106: VecDuplicate(b,&x);
108: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
109: Create the linear solver and set various options
110: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
112: /*
113: Create linear solver context
114: */
115: SLESCreate(PETSC_COMM_WORLD,&sles);
117: /*
118: Set operators. Here the matrix that defines the linear system
119: also serves as the preconditioning matrix.
120: */
121: SLESSetOperators(sles,A,A,SAME_PRECONDITIONER);
123: /*
124: Set runtime options, e.g.,
125: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
126: These options will override those specified above as long as
127: SLESSetFromOptions() is called _after_ any other customization
128: routines.
129: */
130: SLESSetFromOptions(sles);
132: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133: Solve several linear systems of the form A x_i = b_i
134: I.e., we retain the same matrix (A) for all systems, but
135: change the right-hand-side vector (b_i) at each step.
137: In this case, we simply call SLESSolve() multiple times. The
138: preconditioner setup operations (e.g., factorization for ILU)
139: be done during the first call to SLESSolve() only; such operations
140: will NOT be repeated for successive solves.
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: ntimes = 2;
144: PetscOptionsGetInt(PETSC_NULL,"-ntimes",&ntimes,PETSC_NULL);
145: for (k=1; k<ntimes+1; k++) {
147: /*
148: Set exact solution; then compute right-hand-side vector. We use
149: an exact solution of a vector with all elements equal to 1.0*k.
150: */
151: rhs = one * (PetscReal)k;
152: VecSet(&rhs,u);
153: MatMult(A,u,b);
155: /*
156: View the exact solution vector if desired
157: */
158: PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
159: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
161: SLESSolve(sles,b,x,&its);
163: /*
164: Check the error
165: */
166: VecAXPY(&neg_one,u,x);
167: VecNorm(x,NORM_2,&norm);
169: /*
170: Print convergence information. PetscPrintf() produces a single
171: print statement from all processes that share a communicator.
172: */
173: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A System %d: iterations %dn",norm,k,its);
174: }
176: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177: Clean up
178: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
179: /*
180: Free work space. All PETSc objects should be destroyed when they
181: are no longer needed.
182: */
183: SLESDestroy(sles);
184: VecDestroy(u); VecDestroy(x);
185: VecDestroy(b); MatDestroy(A);
187: /*
188: Always call PetscFinalize() before exiting a program. This routine
189: - finalizes the PETSc libraries as well as MPI
190: - provides summary and diagnostic information if certain runtime
191: options are chosen (e.g., -log_summary).
192: */
193: PetscFinalize();
194: return 0;
195: }