Actual source code: ex16.c
petsc-3.10.5 2019-03-28
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_n> : number of mesh points in y-direction\n\n";
11: /*T
12: Concepts: KSP^repeatedly solving linear systems;
13: Concepts: KSP^Laplacian, 2d
14: Concepts: Laplacian, 2d
15: Processors: n
16: T*/
18: /*
19: Include "petscksp.h" so that we can use KSP solvers. Note that this file
20: automatically includes:
21: petscsys.h - base PETSc routines petscvec.h - vectors
22: petscmat.h - matrices
23: petscis.h - index sets petscksp.h - Krylov subspace methods
24: petscviewer.h - viewers petscpc.h - preconditioners
25: */
26: #include <petscksp.h>
28: int main(int argc,char **args)
29: {
30: Vec x,b,u; /* approx solution, RHS, exact solution */
31: Mat A; /* linear system matrix */
32: KSP ksp; /* linear solver context */
33: PetscReal norm; /* norm of solution error */
35: PetscInt ntimes,i,j,k,Ii,J,Istart,Iend;
36: PetscInt m = 8,n = 7,its;
37: PetscBool flg = PETSC_FALSE;
38: PetscScalar v,one = 1.0,rhs;
40: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
41: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
42: PetscOptionsGetInt(NULL,NULL,"-n",&n,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,&A);
55: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
56: MatSetFromOptions(A);
57: MatSetUp(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 (Ii=Istart; Ii<Iend; Ii++) {
74: v = -1.0; i = Ii/n; j = Ii - i*n;
75: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
76: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
77: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
78: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
79: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&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: KSPCreate(PETSC_COMM_WORLD,&ksp);
117: /*
118: Set operators. Here the matrix that defines the linear system
119: also serves as the preconditioning matrix.
120: */
121: KSPSetOperators(ksp,A,A);
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: KSPSetFromOptions() is called _after_ any other customization
128: routines.
129: */
130: KSPSetFromOptions(ksp);
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 KSPSolve() multiple times. The
138: preconditioner setup operations (e.g., factorization for ILU)
139: be done during the first call to KSPSolve() only; such operations
140: will NOT be repeated for successive solves.
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: ntimes = 2;
144: PetscOptionsGetInt(NULL,NULL,"-ntimes",&ntimes,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(u,rhs);
153: MatMult(A,u,b);
155: /*
156: View the exact solution vector if desired
157: */
158: PetscOptionsGetBool(NULL,NULL,"-view_exact_sol",&flg,NULL);
159: if (flg) {VecView(u,PETSC_VIEWER_STDOUT_WORLD);}
161: KSPSolve(ksp,b,x);
163: /*
164: Check the error
165: */
166: VecAXPY(x,-1.0,u);
167: VecNorm(x,NORM_2,&norm);
168: KSPGetIterationNumber(ksp,&its);
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 %g System %D: iterations %D\n",(double)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: KSPDestroy(&ksp);
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_view).
192: */
193: PetscFinalize();
194: return ierr;
195: }
198: /*TEST
200: test:
201: nsize: 2
202: args: -ntimes 4 -ksp_gmres_cgs_refinement_type refine_always
204: TEST*/