Actual source code: ex23.c
petsc-3.8.4 2018-03-24
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>
21: int main(int argc,char **args)
22: {
23: Vec x, b, u; /* approx solution, RHS, exact solution */
24: Mat A; /* linear system matrix */
25: KSP ksp; /* linear solver context */
26: PC pc; /* preconditioner context */
27: PetscReal norm,tol=1000.*PETSC_MACHINE_EPSILON; /* norm of solution error */
29: PetscInt i,n = 10,col[3],its,rstart,rend,nlocal;
30: PetscScalar one = 1.0,value[3];
32: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
33: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
35: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
36: Compute the matrix and right-hand-side vector that define
37: the linear system, Ax = b.
38: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
40: /*
41: Create vectors. Note that we form 1 vector from scratch and
42: then duplicate as needed. For this simple case let PETSc decide how
43: many elements of the vector are stored on each processor. The second
44: argument to VecSetSizes() below causes PETSc to decide.
45: */
46: VecCreate(PETSC_COMM_WORLD,&x);
47: VecSetSizes(x,PETSC_DECIDE,n);
48: VecSetFromOptions(x);
49: VecDuplicate(x,&b);
50: VecDuplicate(x,&u);
52: /* Identify the starting and ending mesh points on each
53: processor for the interior part of the mesh. We let PETSc decide
54: above. */
56: VecGetOwnershipRange(x,&rstart,&rend);
57: VecGetLocalSize(x,&nlocal);
59: /*
60: Create matrix. When using MatCreate(), the matrix format can
61: be specified at runtime.
63: Performance tuning note: For problems of substantial size,
64: preallocation of matrix memory is crucial for attaining good
65: performance. See the matrix chapter of the users manual for details.
67: We pass in nlocal as the "local" size of the matrix to force it
68: to have the same parallel layout as the vector created above.
69: */
70: MatCreate(PETSC_COMM_WORLD,&A);
71: MatSetSizes(A,nlocal,nlocal,n,n);
72: MatSetFromOptions(A);
73: MatSetUp(A);
75: /*
76: Assemble matrix.
78: The linear system is distributed across the processors by
79: chunks of contiguous rows, which correspond to contiguous
80: sections of the mesh on which the problem is discretized.
81: For matrix assembly, each processor contributes entries for
82: the part that it owns locally.
83: */
86: if (!rstart) {
87: rstart = 1;
88: i = 0; col[0] = 0; col[1] = 1; value[0] = 2.0; value[1] = -1.0;
89: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
90: }
91: if (rend == n) {
92: rend = n-1;
93: i = n-1; col[0] = n-2; col[1] = n-1; value[0] = -1.0; value[1] = 2.0;
94: MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
95: }
97: /* Set entries corresponding to the mesh interior */
98: value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
99: for (i=rstart; i<rend; i++) {
100: col[0] = i-1; col[1] = i; col[2] = i+1;
101: MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
102: }
104: /* Assemble the matrix */
105: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
106: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
108: /*
109: Set exact solution; then compute right-hand-side vector.
110: */
111: VecSet(u,one);
112: MatMult(A,u,b);
114: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
115: Create the linear solver and set various options
116: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
117: /*
118: Create linear solver context
119: */
120: KSPCreate(PETSC_COMM_WORLD,&ksp);
122: /*
123: Set operators. Here the matrix that defines the linear system
124: also serves as the preconditioning matrix.
125: */
126: KSPSetOperators(ksp,A,A);
128: /*
129: Set linear solver defaults for this problem (optional).
130: - By extracting the KSP and PC contexts from the KSP context,
131: we can then directly call any KSP and PC routines to set
132: various options.
133: - The following four statements are optional; all of these
134: parameters could alternatively be specified at runtime via
135: KSPSetFromOptions();
136: */
137: KSPGetPC(ksp,&pc);
138: PCSetType(pc,PCJACOBI);
139: KSPSetTolerances(ksp,1.e-7,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
141: /*
142: Set runtime options, e.g.,
143: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
144: These options will override those specified above as long as
145: KSPSetFromOptions() is called _after_ any other customization
146: routines.
147: */
148: KSPSetFromOptions(ksp);
150: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151: Solve the linear system
152: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: /*
154: Solve linear system
155: */
156: KSPSolve(ksp,b,x);
158: /*
159: View solver info; we could instead use the option -ksp_view to
160: print this info to the screen at the conclusion of KSPSolve().
161: */
162: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
164: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
165: Check solution and clean up
166: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
167: /*
168: Check the error
169: */
170: VecAXPY(x,-1.0,u);
171: VecNorm(x,NORM_2,&norm);
172: KSPGetIterationNumber(ksp,&its);
173: if (norm > tol) {
174: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %D\n",(double)norm,its);
175: }
177: /*
178: Free work space. All PETSc objects should be destroyed when they
179: are no longer needed.
180: */
181: VecDestroy(&x); VecDestroy(&u);
182: VecDestroy(&b); MatDestroy(&A);
183: KSPDestroy(&ksp);
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_view).
190: */
191: PetscFinalize();
192: return ierr;
193: }