Actual source code: ex3.c
2: static char help[] = "Solves a linear system in parallel with KSP. The matrix\n\
3: uses simple bilinear elements on the unit square. To test the parallel\n\
4: matrix assembly, the matrix is intentionally laid out across processors\n\
5: differently from the way it is assembled. Input arguments are:\n\
6: -m <size> : problem size\n\n";
8: /*T
9: Concepts: KSP^basic parallel example
10: Concepts: Matrices^inserting elements by blocks
11: Processors: n
12: T*/
14: /*
15: Include "petscksp.h" so that we can use KSP solvers. Note that this file
16: automatically includes:
17: petsc.h - base PETSc routines petscvec.h - vectors
18: petscsys.h - system routines petscmat.h - matrices
19: petscis.h - index sets petscksp.h - Krylov subspace methods
20: petscviewer.h - viewers petscpc.h - preconditioners
21: */
22: #include petscksp.h
24: /* Declare user-defined routines */
30: int main(int argc,char **args)
31: {
32: Vec u,b,ustar; /* approx solution, RHS, exact solution */
33: Mat A; /* linear system matrix */
34: KSP ksp; /* Krylov subspace method context */
35: IS is; /* index set - used for boundary conditions */
36: PetscInt N; /* dimension of system (global) */
37: PetscInt M; /* number of elements (global) */
38: PetscMPIInt rank; /* processor rank */
39: PetscMPIInt size; /* size of communicator */
40: PetscScalar Ke[16]; /* element matrix */
41: PetscScalar r[4]; /* element vector */
42: PetscReal h; /* mesh width */
43: PetscReal norm; /* norm of solution error */
44: PetscReal x,y;
45: PetscScalar val,zero = 0.0,one = 1.0,none = -1.0;
47: PetscInt idx[4],count,*rows,i,m = 5,start,end,its;
49: PetscInitialize(&argc,&args,(char *)0,help);
50: PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
51: N = (m+1)*(m+1);
52: M = m*m;
53: h = 1.0/m;
54: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
55: MPI_Comm_size(PETSC_COMM_WORLD,&size);
57: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
58: Compute the matrix and right-hand-side vector that define
59: the linear system, Au = b.
60: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
62: /*
63: Create stiffness matrix
64: */
65: MatCreate(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,N,N,&A);
66: MatSetFromOptions(A);
67: start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
68: end = start + M/size + ((M%size) > rank);
70: /*
71: Assemble matrix
72: */
73: FormElementStiffness(h*h,Ke);
74: for (i=start; i<end; i++) {
75: /* location of lower left corner of element */
76: x = h*(i % m); y = h*(i/m);
77: /* node numbers for the four corners of element */
78: idx[0] = (m+1)*(i/m) + (i % m);
79: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
80: MatSetValues(A,4,idx,4,idx,Ke,ADD_VALUES);
81: }
82: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
83: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
85: /*
86: Create right-hand-side and solution vectors
87: */
88: VecCreate(PETSC_COMM_WORLD,&u);
89: VecSetSizes(u,PETSC_DECIDE,N);
90: VecSetFromOptions(u);
91: PetscObjectSetName((PetscObject)u,"Approx. Solution");
92: VecDuplicate(u,&b);
93: PetscObjectSetName((PetscObject)b,"Right hand side");
94: VecDuplicate(b,&ustar);
95: VecSet(&zero,u);
96: VecSet(&zero,b);
98: /*
99: Assemble right-hand-side vector
100: */
101: for (i=start; i<end; i++) {
102: /* location of lower left corner of element */
103: x = h*(i % m); y = h*(i/m);
104: /* node numbers for the four corners of element */
105: idx[0] = (m+1)*(i/m) + (i % m);
106: idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
107: FormElementRhs(x,y,h*h,r);
108: VecSetValues(b,4,idx,r,ADD_VALUES);
109: }
110: VecAssemblyBegin(b);
111: VecAssemblyEnd(b);
113: /*
114: Modify matrix and right-hand-side for Dirichlet boundary conditions
115: */
116: PetscMalloc(4*m*sizeof(PetscInt),&rows);
117: for (i=0; i<m+1; i++) {
118: rows[i] = i; /* bottom */
119: rows[3*m - 1 +i] = m*(m+1) + i; /* top */
120: }
121: count = m+1; /* left side */
122: for (i=m+1; i<m*(m+1); i+= m+1) {
123: rows[count++] = i;
124: }
125: count = 2*m; /* left side */
126: for (i=2*m+1; i<m*(m+1); i+= m+1) {
127: rows[count++] = i;
128: }
129: ISCreateGeneral(PETSC_COMM_SELF,4*m,rows,&is);
130: for (i=0; i<4*m; i++) {
131: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
132: val = y;
133: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
134: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
135: }
136: PetscFree(rows);
137: VecAssemblyBegin(u);
138: VecAssemblyEnd(u);
139: VecAssemblyBegin(b);
140: VecAssemblyEnd(b);
142: MatZeroRows(A,is,&one);
143: ISDestroy(is);
145: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
146: Create the linear solver and set various options
147: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
149: KSPCreate(PETSC_COMM_WORLD,&ksp);
150: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
151: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
152: KSPSetFromOptions(ksp);
154: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
155: Solve the linear system
156: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
158: KSPSolve(ksp,b,u);
160: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
161: Check solution and clean up
162: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
164: /* Check error */
165: VecGetOwnershipRange(ustar,&start,&end);
166: for (i=start; i<end; i++) {
167: x = h*(i % (m+1)); y = h*(i/(m+1));
168: val = y;
169: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
170: }
171: VecAssemblyBegin(ustar);
172: VecAssemblyEnd(ustar);
173: VecAXPY(&none,ustar,u);
174: VecNorm(u,NORM_2,&norm);
175: KSPGetIterationNumber(ksp,&its);
176: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A Iterations %D\n",norm*h,its);
178: /*
179: Free work space. All PETSc objects should be destroyed when they
180: are no longer needed.
181: */
182: KSPDestroy(ksp); VecDestroy(u);
183: VecDestroy(ustar); VecDestroy(b);
184: MatDestroy(A);
186: /*
187: Always call PetscFinalize() before exiting a program. This routine
188: - finalizes the PETSc libraries as well as MPI
189: - provides summary and diagnostic information if certain runtime
190: options are chosen (e.g., -log_summary).
191: */
192: PetscFinalize();
193: return 0;
194: }
196: /* --------------------------------------------------------------------- */
199: /* element stiffness for Laplacian */
200: PetscErrorCode FormElementStiffness(PetscReal H,PetscScalar *Ke)
201: {
203: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
204: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
205: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
206: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
207: return(0);
208: }
209: /* --------------------------------------------------------------------- */
212: PetscErrorCode FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
213: {
215: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
216: return(0);
217: }