Actual source code: ex23.c
petsc-3.7.5 2017-01-01
2: static char help[] = "Solves a tridiagonal linear system.\n\n";
4: /*T
5: Concepts: KSP^basic parallel example;
6: Processors: n
7: T*/
9: /*
10: Include "petscksp.h" so that we can use KSP solvers. Note that this file
11: automatically includes:
12: petscsys.h - base PETSc routines petscvec.h - vectors
13: petscmat.h - matrices
14: petscis.h - index sets petscksp.h - Krylov subspace methods
15: petscviewer.h - viewers petscpc.h - preconditioners
17: Note: The corresponding uniprocessor example is ex1.c
18: */
19: #include <petscksp.h>
23: int main(int argc,char **args)
24: {
25: Vec x, b, u; /* approx solution, RHS, exact solution */
26: Mat A; /* linear system matrix */
27: KSP ksp; /* linear solver context */
28: PC pc; /* preconditioner context */
29: PetscReal norm,tol=1000.*PETSC_MACHINE_EPSILON; /* norm of solution error */
31: PetscInt i,n = 10,col[3],its,rstart,rend,nlocal;
32: PetscScalar neg_one = -1.0,one = 1.0,value[3];
34: PetscInitialize(&argc,&args,(char*)0,help);
35: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
37: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
38: Compute the matrix and right-hand-side vector that define
39: the linear system, Ax = b.
40: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
42: /*
43: Create vectors. Note that we form 1 vector from scratch and
44: then duplicate as needed. For this simple case let PETSc decide how
45: many elements of the vector are stored on each processor. The second
46: argument to VecSetSizes() below causes PETSc to decide.
47: */
48: VecCreate(PETSC_COMM_WORLD,&x);
49: VecSetSizes(x,PETSC_DECIDE,n);
50: VecSetFromOptions(x);
51: VecDuplicate(x,&b);
52: VecDuplicate(x,&u);
54: /* Identify the starting and ending mesh points on each
55: processor for the interior part of the mesh. We let PETSc decide
56: above. */
58: VecGetOwnershipRange(x,&rstart,&rend);
59: VecGetLocalSize(x,&nlocal);
61: /*
62: Create matrix. When using MatCreate(), the matrix format can
63: be specified at runtime.
65: Performance tuning note: For problems of substantial size,
66: preallocation of matrix memory is crucial for attaining good
67: performance. See the matrix chapter of the users manual for details.
69: We pass in nlocal as the "local" size of the matrix to force it
70: to have the same parallel layout as the vector created above.
71: */
72: MatCreate(PETSC_COMM_WORLD,&A);
73: MatSetSizes(A,nlocal,nlocal,n,n);
74: MatSetFromOptions(A);
75: MatSetUp(A);
77: /*
78: Assemble matrix.
80: The linear system is distributed across the processors by
81: chunks of contiguous rows, which correspond to contiguous
82: sections of the mesh on which the problem is discretized.
83: For matrix assembly, each processor contributes entries for
84: the part that it owns locally.
85: */
88: if (!rstart) {
89: rstart = 1;
90: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
91: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
92: }
93: if (rend == n) {
94: rend = n-1;
95: i = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
96: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
97: }
99: /* Set entries corresponding to the mesh interior */
100: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
101: for (i=rstart; i<rend; i++) {
102: col[0] = i-1; col[1] = i; col[2] = i+1;
103: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
104: }
106: /* Assemble the matrix */
107: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
108: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
110: /*
111: Set exact solution; then compute right-hand-side vector.
112: */
113: VecSet(u,one);
114: MatMult(A,u,b);
116: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
117: Create the linear solver and set various options
118: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
119: /*
120: Create linear solver context
121: */
122: KSPCreate(PETSC_COMM_WORLD,&ksp);
124: /*
125: Set operators. Here the matrix that defines the linear system
126: also serves as the preconditioning matrix.
127: */
128: KSPSetOperators(ksp,A,A);
130: /*
131: Set linear solver defaults for this problem (optional).
132: - By extracting the KSP and PC contexts from the KSP context,
133: we can then directly call any KSP and PC routines to set
134: various options.
135: - The following four statements are optional; all of these
136: parameters could alternatively be specified at runtime via
137: KSPSetFromOptions();
138: */
139: KSPGetPC(ksp,&pc);
140: PCSetType(pc,PCJACOBI);
141: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
143: /*
144: Set runtime options, e.g.,
145: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
146: These options will override those specified above as long as
147: KSPSetFromOptions() is called _after_ any other customization
148: routines.
149: */
150: KSPSetFromOptions(ksp);
152: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
153: Solve the linear system
154: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
155: /*
156: Solve linear system
157: */
158: KSPSolve(ksp,b,x);
160: /*
161: View solver info; we could instead use the option -ksp_view to
162: print this info to the screen at the conclusion of KSPSolve().
163: */
164: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
166: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167: Check solution and clean up
168: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
169: /*
170: Check the error
171: */
172: VecAXPY(x,neg_one,u);
173: VecNorm(x,NORM_2,&norm);
174: KSPGetIterationNumber(ksp,&its);
175: if (norm > tol) {
176: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
177: }
179: /*
180: Free work space. All PETSc objects should be destroyed when they
181: are no longer needed.
182: */
183: VecDestroy(&x); VecDestroy(&u);
184: VecDestroy(&b); MatDestroy(&A);
185: KSPDestroy(&ksp);
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: }