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: int main(int argc,char **args)
30: {
31: Vec x,b,u; /* approx solution, RHS, exact solution */
32: Mat A; /* linear system matrix */
33: SLES sles; /* linear solver context */
34: PetscReal norm; /* norm of solution error */
35: int ntimes,i,j,k,I,J,Istart,Iend,ierr;
36: int m = 8,n = 7,its;
37: PetscTruth flg;
38: PetscScalar v,one = 1.0,neg_one = -1.0,rhs;
40: PetscInitialize(&argc,&args,(char *)0,help);
41: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
42: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
44: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
45: Compute the matrix for use in solving a series of
46: linear systems of the form, A x_i = b_i, for i=1,2,...
47: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
48: /*
49: Create parallel matrix, specifying only its global dimensions.
50: When using MatCreate(), the matrix format can be specified at
51: runtime. Also, the parallel partitioning of the matrix is
52: determined by PETSc at runtime.
53: */
54: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n,&A);
55: MatSetFromOptions(A);
57: /*
58: Currently, all PETSc parallel matrix formats are partitioned by
59: contiguous chunks of rows across the processors. Determine which
60: rows of the matrix are locally owned.
61: */
62: MatGetOwnershipRange(A,&Istart,&Iend);
64: /*
65: Set matrix elements for the 2-D, five-point stencil in parallel.
66: - Each processor needs to insert only elements that it owns
67: locally (but any non-local elements will be sent to the
68: appropriate processor during matrix assembly).
69: - Always specify global rows and columns of matrix entries.
70: */
71: for (I=Istart; I<Iend; I++) {
72: v = -1.0; i = I/n; j = I - i*n;
73: if (i>0) {J = I - n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
74: if (i<m-1) {J = I + n; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
75: if (j>0) {J = I - 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
76: if (j<n-1) {J = I + 1; MatSetValues(A,1,&I,1,&J,&v,INSERT_VALUES);}
77: v = 4.0; MatSetValues(A,1,&I,1,&I,&v,INSERT_VALUES);
78: }
80: /*
81: Assemble matrix, using the 2-step process:
82: MatAssemblyBegin(), MatAssemblyEnd()
83: Computations can be done while messages are in transition
84: by placing code between these two statements.
85: */
86: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
87: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
89: /*
90: Create parallel vectors.
91: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
92: we specify only the vector's global
93: dimension; the parallel partitioning is determined at runtime.
94: - When solving a linear system, the vectors and matrices MUST
95: be partitioned accordingly. PETSc automatically generates
96: appropriately partitioned matrices and vectors when MatCreate()
97: and VecCreate() are used with the same communicator.
98: - Note: We form 1 vector from scratch and then duplicate as needed.
99: */
100: VecCreate(PETSC_COMM_WORLD,&u);
101: VecSetSizes(u,PETSC_DECIDE,m*n);
102: VecSetFromOptions(u);
103: VecDuplicate(u,&b);
104: VecDuplicate(b,&x);
106: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
107: Create the linear solver and set various options
108: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
110: /*
111: Create linear solver context
112: */
113: SLESCreate(PETSC_COMM_WORLD,&sles);
115: /*
116: Set operators. Here the matrix that defines the linear system
117: also serves as the preconditioning matrix.
118: */
119: SLESSetOperators(sles,A,A,SAME_PRECONDITIONER);
121: /*
122: Set runtime options, e.g.,
123: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
124: These options will override those specified above as long as
125: SLESSetFromOptions() is called _after_ any other customization
126: routines.
127: */
128: SLESSetFromOptions(sles);
130: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
131: Solve several linear systems of the form A x_i = b_i
132: I.e., we retain the same matrix (A) for all systems, but
133: change the right-hand-side vector (b_i) at each step.
135: In this case, we simply call SLESSolve() multiple times. The
136: preconditioner setup operations (e.g., factorization for ILU)
137: be done during the first call to SLESSolve() only; such operations
138: will NOT be repeated for successive solves.
139: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
141: ntimes = 2;
142: PetscOptionsGetInt(PETSC_NULL,"-ntimes",&ntimes,PETSC_NULL);
143: for (k=1; k<ntimes+1; k++) {
145: /*
146: Set exact solution; then compute right-hand-side vector. We use
147: an exact solution of a vector with all elements equal to 1.0*k.
148: */
149: rhs = one * (PetscReal)k;
150: VecSet(&rhs,u);
151: MatMult(A,u,b);
153: /*
154: View the exact solution vector if desired
155: */
156: PetscOptionsHasName(PETSC_NULL,"-view_exact_sol",&flg);
157: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
159: SLESSolve(sles,b,x,&its);
161: /*
162: Check the error
163: */
164: VecAXPY(&neg_one,u,x);
165: VecNorm(x,NORM_2,&norm);
167: /*
168: Print convergence information. PetscPrintf() produces a single
169: print statement from all processes that share a communicator.
170: */
171: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A System %d: iterations %dn",norm,k,its);
172: }
174: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: Clean up
176: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
177: /*
178: Free work space. All PETSc objects should be destroyed when they
179: are no longer needed.
180: */
181: SLESDestroy(sles);
182: VecDestroy(u); VecDestroy(x);
183: VecDestroy(b); MatDestroy(A);
185: /*
186: Always call PetscFinalize() before exiting a program. This routine
187: - finalizes the PETSc libraries as well as MPI
188: - provides summary and diagnostic information if certain runtime
189: options are chosen (e.g., -log_summary).
190: */
191: PetscFinalize();
192: return 0;
193: }