Actual source code: ex12.c
2: /* Program usage: mpiexec -n <procs> ex12 [-help] [all PETSc options] */
4: static char help[] = "Solves a linear system in parallel with KSP.\n\
5: Input parameters include:\n\
6: -m <mesh_x> : number of mesh points in x-direction\n\
7: -n <mesh_n> : number of mesh points in y-direction\n\n";
9: /*T
10: Concepts: KSP^solving a system of linear equations
11: Concepts: KSP^Laplacian, 2d
12: Concepts: PC^registering preconditioners
13: Processors: n
14: T*/
16: /*
17: Demonstrates registering a new preconditioner (PC) type.
19: To register a PC type whose code is linked into the executable,
20: use PCRegister(). To register a PC type in a dynamic library use PCRegisterDynamic()
22: Also provide the prototype for your PCCreate_XXX() function. In
23: this example we use the PETSc implementation of the Jacobi method,
24: PCCreate_Jacobi() just as an example.
26: See the file src/ksp/pc/impls/jacobi/jacobi.c for details on how to
27: write a new PC component.
29: See the manual page PCRegisterDynamic() for details on how to register a method.
30: */
32: /*
33: Include "petscksp.h" so that we can use KSP solvers. Note that this file
34: automatically includes:
35: petscsys.h - base PETSc routines petscvec.h - vectors
36: petscmat.h - matrices
37: petscis.h - index sets petscksp.h - Krylov subspace methods
38: petscviewer.h - viewers petscpc.h - preconditioners
39: */
40: #include petscksp.h
43: EXTERN PetscErrorCode PCCreate_Jacobi(PC);
48: int main(int argc,char **args)
49: {
50: Vec x,b,u; /* approx solution, RHS, exact solution */
51: Mat A; /* linear system matrix */
52: KSP ksp; /* linear solver context */
53: PetscReal norm; /* norm of solution error */
54: PetscInt i,j,Ii,J,Istart,Iend,m = 8,n = 7,its;
56: PetscScalar v,one = 1.0,neg_one = -1.0;
57: PC pc; /* preconditioner context */
59: PetscInitialize(&argc,&args,(char *)0,help);
60: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
61: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
63: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
64: Compute the matrix and right-hand-side vector that define
65: the linear system, Ax = b.
66: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
67: /*
68: Create parallel matrix, specifying only its global dimensions.
69: When using MatCreate(), the matrix format can be specified at
70: runtime. Also, the parallel partitioning of the matrix can be
71: determined by PETSc at runtime.
72: */
73: MatCreate(PETSC_COMM_WORLD,&A);
74: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
75: MatSetFromOptions(A);
77: /*
78: Currently, all PETSc parallel matrix formats are partitioned by
79: contiguous chunks of rows across the processors. Determine which
80: rows of the matrix are locally owned.
81: */
82: MatGetOwnershipRange(A,&Istart,&Iend);
84: /*
85: Set matrix elements for the 2-D, five-point stencil in parallel.
86: - Each processor needs to insert only elements that it owns
87: locally (but any non-local elements will be sent to the
88: appropriate processor during matrix assembly).
89: - Always specify global rows and columns of matrix entries.
90: */
91: for (Ii=Istart; Ii<Iend; Ii++) {
92: v = -1.0; i = Ii/n; j = Ii - i*n;
93: if (i>0) {J = Ii - n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
94: if (i<m-1) {J = Ii + n; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
95: if (j>0) {J = Ii - 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
96: if (j<n-1) {J = Ii + 1; MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);}
97: v = 4.0; MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
98: }
100: /*
101: Assemble matrix, using the 2-step process:
102: MatAssemblyBegin(), MatAssemblyEnd()
103: Computations can be done while messages are in transition
104: by placing code between these two statements.
105: */
106: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
107: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
109: /*
110: Create parallel vectors.
111: - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
112: we specify only the vector's global
113: dimension; the parallel partitioning is determined at runtime.
114: - When solving a linear system, the vectors and matrices MUST
115: be partitioned accordingly. PETSc automatically generates
116: appropriately partitioned matrices and vectors when MatCreate()
117: and VecCreate() are used with the same communicator.
118: - Note: We form 1 vector from scratch and then duplicate as needed.
119: */
120: VecCreate(PETSC_COMM_WORLD,&u);
121: VecSetSizes(u,PETSC_DECIDE,m*n);
122: VecSetFromOptions(u);
123: VecDuplicate(u,&b);
124: VecDuplicate(b,&x);
126: /*
127: Set exact solution; then compute right-hand-side vector.
128: Use an exact solution of a vector with all elements of 1.0;
129: */
130: VecSet(u,one);
131: MatMult(A,u,b);
133: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134: Create the linear solver and set various options
135: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
137: /*
138: Create linear solver context
139: */
140: KSPCreate(PETSC_COMM_WORLD,&ksp);
142: /*
143: Set operators. Here the matrix that defines the linear system
144: also serves as the preconditioning matrix.
145: */
146: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
148: /*
149: First register a new PC type with the command PCRegister()
150: */
151: PCRegister("ourjacobi",0,"PCCreate_Jacobi",PCCreate_Jacobi);
152:
153: /*
154: Set the PC type to be the new method
155: */
156: KSPGetPC(ksp,&pc);
157: PCSetType(pc,"ourjacobi");
159: /*
160: Set runtime options, e.g.,
161: -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
162: These options will override those specified above as long as
163: KSPSetFromOptions() is called _after_ any other customization
164: routines.
165: */
166: KSPSetFromOptions(ksp);
168: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
169: Solve the linear system
170: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
172: KSPSolve(ksp,b,x);
174: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
175: Check solution and clean up
176: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
178: /*
179: Check the error
180: */
181: VecAXPY(x,neg_one,u);
182: VecNorm(x,NORM_2,&norm);
183: KSPGetIterationNumber(ksp,&its);
184: /* Scale the norm */
185: /* norm *= sqrt(1.0/((m+1)*(n+1))); */
187: /*
188: Print convergence information. PetscPrintf() produces a single
189: print statement from all processes that share a communicator.
190: */
191: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A iterations %D\n",norm,its);
193: /*
194: Free work space. All PETSc objects should be destroyed when they
195: are no longer needed.
196: */
197: KSPDestroy(ksp);
198: VecDestroy(u); VecDestroy(x);
199: VecDestroy(b); MatDestroy(A);
201: /*
202: Always call PetscFinalize() before exiting a program. This routine
203: - finalizes the PETSc libraries as well as MPI
204: - provides summary and diagnostic information if certain runtime
205: options are chosen (e.g., -log_summary).
206: */
207: PetscFinalize();
208: return 0;
209: }