Actual source code: ex16.c
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_y> : number of mesh points in y-direction\n\n";
11: /*
12: Include "petscksp.h" so that we can use KSP solvers. Note that this file
13: automatically includes:
14: petscsys.h - base PETSc routines petscvec.h - vectors
15: petscmat.h - matrices
16: petscis.h - index sets petscksp.h - Krylov subspace methods
17: petscviewer.h - viewers petscpc.h - preconditioners
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: PetscReal norm; /* norm of solution error */
27: PetscInt ntimes,i,j,k,Ii,J,Istart,Iend;
28: PetscInt m = 8,n = 7,its;
29: PetscBool flg = PETSC_FALSE;
30: PetscScalar v,one = 1.0,rhs;
32: PetscInitialize(&argc,&args,(char*)0,help);
33: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
34: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
36: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
37: Compute the matrix for use in solving a series of
38: linear systems of the form, A x_i = b_i, for i=1,2,...
39: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
40: /*
41: Create parallel matrix, specifying only its global dimensions.
42: When using MatCreate(), the matrix format can be specified at
43: runtime. Also, the parallel partitioning of the matrix is
44: determined by PETSc at runtime.
45: */
46: MatCreate(PETSC_COMM_WORLD,&A);
47: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
48: MatSetFromOptions(A);
49: MatSetUp(A);
51: /*
52: Currently, all PETSc parallel matrix formats are partitioned by
53: contiguous chunks of rows across the processors. Determine which
54: rows of the matrix are locally owned.
55: */
56: MatGetOwnershipRange(A,&Istart,&Iend);
58: /*
59: Set matrix elements for the 2-D, five-point stencil in parallel.
60: - Each processor needs to insert only elements that it owns
61: locally (but any non-local elements will be sent to the
62: appropriate processor during matrix assembly).
63: - Always specify global rows and columns of matrix entries.
64: */
65: for (Ii=Istart; Ii<Iend; Ii++) {
66: v = -1.0; i = Ii/n; j = Ii - i*n;
67: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
68: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
69: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
70: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
71: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
72: }
74: /*
75: Assemble matrix, using the 2-step process:
76: MatAssemblyBegin(), MatAssemblyEnd()
77: Computations can be done while messages are in transition
78: by placing code between these two statements.
79: */
80: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
81: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
83: /*
84: Create parallel vectors.
85: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
86: we specify only the vector's global
87: dimension; the parallel partitioning is determined at runtime.
88: - When solving a linear system, the vectors and matrices MUST
89: be partitioned accordingly. PETSc automatically generates
90: appropriately partitioned matrices and vectors when MatCreate()
91: and VecCreate() are used with the same communicator.
92: - Note: We form 1 vector from scratch and then duplicate as needed.
93: */
94: VecCreate(PETSC_COMM_WORLD,&u);
95: VecSetSizes(u,PETSC_DECIDE,m*n);
96: VecSetFromOptions(u);
97: VecDuplicate(u,&b);
98: VecDuplicate(b,&x);
100: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
101: Create the linear solver and set various options
102: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
104: /*
105: Create linear solver context
106: */
107: KSPCreate(PETSC_COMM_WORLD,&ksp);
109: /*
110: Set operators. Here the matrix that defines the linear system
111: also serves as the preconditioning matrix.
112: */
113: KSPSetOperators(ksp,A,A);
115: /*
116: Set runtime options, e.g.,
117: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
118: These options will override those specified above as long as
119: KSPSetFromOptions() is called _after_ any other customization
120: routines.
121: */
122: KSPSetFromOptions(ksp);
124: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
125: Solve several linear systems of the form A x_i = b_i
126: I.e., we retain the same matrix (A) for all systems, but
127: change the right-hand-side vector (b_i) at each step.
129: In this case, we simply call KSPSolve() multiple times. The
130: preconditioner setup operations (e.g., factorization for ILU)
131: be done during the first call to KSPSolve() only; such operations
132: will NOT be repeated for successive solves.
133: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
135: ntimes = 2;
136: PetscOptionsGetInt(NULL,NULL,"-ntimes",&ntimes,NULL);
137: for (k=1; k<ntimes+1; k++) {
139: /*
140: Set exact solution; then compute right-hand-side vector. We use
141: an exact solution of a vector with all elements equal to 1.0*k.
142: */
143: rhs = one * (PetscReal)k;
144: VecSet(u,rhs);
145: MatMult(A,u,b);
147: /*
148: View the exact solution vector if desired
149: */
150: PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
151: if (flg) VecView(u,PETSC_VIEWER_STDOUT_WORLD);
153: KSPSolve(ksp,b,x);
155: /*
156: Check the error
157: */
158: VecAXPY(x,-1.0,u);
159: VecNorm(x,NORM_2,&norm);
160: KSPGetIterationNumber(ksp,&its);
161: /*
162: Print convergence information. PetscPrintf() produces a single
163: print statement from all processes that share a communicator.
164: */
165: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g System %D: iterations %D\n",(double)norm,k,its);
166: }
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Clean up
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
171: /*
172: Free work space. All PETSc objects should be destroyed when they
173: are no longer needed.
174: */
175: KSPDestroy(&ksp);
176: VecDestroy(&u)); PetscCall(VecDestroy(&x);
177: VecDestroy(&b)); PetscCall(MatDestroy(&A);
179: /*
180: Always call PetscFinalize() before exiting a program. This routine
181: - finalizes the PETSc libraries as well as MPI
182: - provides summary and diagnostic information if certain runtime
183: options are chosen (e.g., -log_view).
184: */
185: PetscFinalize();
186: return 0;
187: }
189: /*TEST
191: test:
192: nsize: 2
193: args: -ntimes 4 -ksp_gmres_cgs_refinement_type refine_always
195: TEST*/