Actual source code: ex3.c
1: /*$Id: ex3.c,v 1.33 2001/08/07 21:30:54 bsmith Exp $*/
3: static char help[] = "Solves a linear system in parallel with SLES. The matrixn
4: uses simple bilinear elements on the unit square. To test the paralleln
5: matrix assembly, the matrix is intentionally laid out across processorsn
6: differently from the way it is assembled. Input arguments are:n
7: -m <size> : problem sizenn";
9: /*T
10: Concepts: SLES^basic parallel example
11: Concepts: Matrices^inserting elements by blocks
12: Processors: n
13: T*/
15: /*
16: Include "petscsles.h" so that we can use SLES solvers. Note that this file
17: automatically includes:
18: petsc.h - base PETSc routines petscvec.h - vectors
19: petscsys.h - system routines petscmat.h - matrices
20: petscis.h - index sets petscksp.h - Krylov subspace methods
21: petscviewer.h - viewers petscpc.h - preconditioners
22: */
23: #include petscsles.h
25: /* Declare user-defined routines */
26: extern int FormElementStiffness(PetscReal,PetscScalar*);
27: extern int FormElementRhs(PetscReal,PetscReal,PetscReal,PetscScalar*);
29: #undef __FUNCT__
31: int main(int argc,char **args)
32: {
33: Vec u,b,ustar; /* approx solution, RHS, exact solution */
34: Mat A; /* linear system matrix */
35: SLES sles; /* linear solver context */
36: KSP ksp; /* Krylov subspace method context */
37: IS is; /* index set - used for boundary conditions */
38: int N; /* dimension of system (global) */
39: int M; /* number of elements (global) */
40: int rank; /* processor rank */
41: int size; /* size of communicator */
42: PetscScalar Ke[16]; /* element matrix */
43: PetscScalar r[4]; /* element vector */
44: PetscReal h; /* mesh width */
45: PetscReal norm; /* norm of solution error */
46: PetscReal x,y;
47: PetscScalar val,zero = 0.0,one = 1.0,none = -1.0;
48: int ierr,idx[4],count,*rows,i,m = 5,start,end,its;
50: PetscInitialize(&argc,&args,(char *)0,help);
51: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
52: N = (m+1)*(m+1);
53: M = m*m;
54: h = 1.0/m;
55: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
56: MPI_Comm_size(PETSC_COMM_WORLD,&size);
58: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
59: Compute the matrix and right-hand-side vector that define
60: the linear system, Au = b.
61: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
63: /*
64: Create stiffness matrix
65: */
66: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&A);
67: MatSetFromOptions(A);
68: start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
69: end = start + M/size + ((M%size) > rank);
71: /*
72: Assemble matrix
73: */
74: FormElementStiffness(h*h,Ke);
75: for (i=start; i<end; i++) {
76: /* location of lower left corner of element */
77: x = h*(i % m); y = h*(i/m);
78: /* node numbers for the four corners of element */
79: idx[0] = (m+1)*(i/m) + (i % m);
80: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
81: MatSetValues(A,4,idx,4,idx,Ke,ADD_VALUES);
82: }
83: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
84: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
86: /*
87: Create right-hand-side and solution vectors
88: */
89: VecCreate(PETSC_COMM_WORLD,&u);
90: VecSetSizes(u,PETSC_DECIDE,N);
91: VecSetFromOptions(u);
92: PetscObjectSetName((PetscObject)u,"Approx. Solution");
93: VecDuplicate(u,&b);
94: PetscObjectSetName((PetscObject)b,"Right hand side");
95: VecDuplicate(b,&ustar);
96: VecSet(&zero,u);
97: VecSet(&zero,b);
99: /*
100: Assemble right-hand-side vector
101: */
102: for (i=start; i<end; i++) {
103: /* location of lower left corner of element */
104: x = h*(i % m); y = h*(i/m);
105: /* node numbers for the four corners of element */
106: idx[0] = (m+1)*(i/m) + (i % m);
107: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
108: FormElementRhs(x,y,h*h,r);
109: VecSetValues(b,4,idx,r,ADD_VALUES);
110: }
111: VecAssemblyBegin(b);
112: VecAssemblyEnd(b);
114: /*
115: Modify matrix and right-hand-side for Dirichlet boundary conditions
116: */
117: PetscMalloc(4*m*sizeof(int),&rows);
118: for (i=0; i<m+1; i++) {
119: rows[i] = i; /* bottom */
120: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
121: }
122: count = m+1; /* left side */
123: for (i=m+1; i<m*(m+1); i+= m+1) {
124: rows[count++] = i;
125: }
126: count = 2*m; /* left side */
127: for (i=2*m+1; i<m*(m+1); i+= m+1) {
128: rows[count++] = i;
129: }
130: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
131: for (i=0; i<4*m; i++) {
132: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
133: val = y;
134: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
135: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
136: }
137: PetscFree(rows);
138: VecAssemblyBegin(u);
139: VecAssemblyEnd(u);
140: VecAssemblyBegin(b);
141: VecAssemblyEnd(b);
143: MatZeroRows(A,is,&one);
144: ISDestroy(is);
146: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
147: Create the linear solver and set various options
148: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
150: SLESCreate(PETSC_COMM_WORLD,&sles);
151: SLESSetOperators(sles,A,A,DIFFERENT_NONZERO_PATTERN);
152: SLESGetKSP(sles,&ksp);
153: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
154: SLESSetFromOptions(sles);
156: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
157: Solve the linear system
158: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
160: SLESSolve(sles,b,u,&its);
162: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163: Check solution and clean up
164: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
166: /* Check error */
167: VecGetOwnershipRange(ustar,&start,&end);
168: for (i=start; i<end; i++) {
169: x = h*(i % (m+1)); y = h*(i/(m+1));
170: val = y;
171: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
172: }
173: VecAssemblyBegin(ustar);
174: VecAssemblyEnd(ustar);
175: VecAXPY(&none,ustar,u);
176: VecNorm(u,NORM_2,&norm);
177: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %dn",norm*h,its);
179: /*
180: Free work space. All PETSc objects should be destroyed when they
181: are no longer needed.
182: */
183: SLESDestroy(sles); VecDestroy(u);
184: VecDestroy(ustar); VecDestroy(b);
185: 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_summary).
192: */
193: PetscFinalize();
194: return 0;
195: }
197: /* --------------------------------------------------------------------- */
198: #undef __FUNCT__
200: /* element stiffness for Laplacian */
201: int FormElementStiffness(PetscReal H,PetscScalar *Ke)
202: {
204: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
205: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
206: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
207: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
208: return(0);
209: }
210: /* --------------------------------------------------------------------- */
211: #undef __FUNCT__
213: int FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
214: {
216: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
217: return(0);
218: }