Actual source code: ex3.c
petsc-3.7.5 2017-01-01
2: static char help[] = "Bilinear elements on the unit square for Laplacian. To test the parallel\n\
3: matrix assembly, the matrix is intentionally laid out across processors\n\
4: differently from the way it is assembled. Input arguments are:\n\
5: -m <size> : problem size\n\n";
7: /*T
8: Concepts: KSP^basic parallel example
9: Concepts: Matrices^inserting elements by blocks
10: Processors: n
11: T*/
13: /*
14: Include "petscksp.h" so that we can use KSP solvers. Note that this file
15: automatically includes:
16: petscsys.h - base PETSc routines petscvec.h - vectors
17: petscmat.h - matrices
18: petscis.h - index sets petscksp.h - Krylov subspace methods
19: petscviewer.h - viewers petscpc.h - preconditioners
20: */
21: #include <petscksp.h>
23: /* Declare user-defined routines */
24: extern PetscErrorCode FormElementStiffness(PetscReal,PetscScalar*);
25: extern PetscErrorCode FormElementRhs(PetscReal,PetscReal,PetscReal,PetscScalar*);
29: int main(int argc,char **args)
30: {
31: Vec u,b,ustar; /* approx solution, RHS, exact solution */
32: Mat A; /* linear system matrix */
33: KSP ksp; /* Krylov subspace method context */
34: PetscInt N; /* dimension of system (global) */
35: PetscInt M; /* number of elements (global) */
36: PetscMPIInt rank; /* processor rank */
37: PetscMPIInt size; /* size of communicator */
38: PetscScalar Ke[16]; /* element matrix */
39: PetscScalar r[4]; /* element vector */
40: PetscReal h; /* mesh width */
41: PetscReal norm; /* norm of solution error */
42: PetscReal x,y;
43: PetscScalar val;
45: PetscInt idx[4],count,*rows,i,m = 5,start,end,its;
47: PetscInitialize(&argc,&args,(char*)0,help);
48: PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);
49: N = (m+1)*(m+1);
50: M = m*m;
51: h = 1.0/m;
52: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
53: MPI_Comm_size(PETSC_COMM_WORLD,&size);
55: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
56: Compute the matrix and right-hand-side vector that define
57: the linear system, Au = b.
58: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
60: /*
61: Create stiffness matrix
62: */
63: MatCreate(PETSC_COMM_WORLD,&A);
64: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);
65: MatSetFromOptions(A);
66: MatSeqAIJSetPreallocation(A,9,NULL);
67: MatMPIAIJSetPreallocation(A,9,NULL,8,NULL);
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(u,0.0);
97: VecSet(b,0.0);
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: PetscMalloc1(4*m,&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) rows[count++] = i;
124: count = 2*m; /* left side */
125: for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
126: for (i=0; i<4*m; i++) {
127: x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
128: val = y;
129: VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);
130: VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);
131: }
132: MatZeroRows(A,4*m,rows,1.0,0,0);
133: PetscFree(rows);
135: VecAssemblyBegin(u);
136: VecAssemblyEnd(u);
137: VecAssemblyBegin(b);
138: VecAssemblyEnd(b);
140: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141: Create the linear solver and set various options
142: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
144: KSPCreate(PETSC_COMM_WORLD,&ksp);
145: KSPSetOperators(ksp,A,A);
146: KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);
147: KSPSetFromOptions(ksp);
149: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150: Solve the linear system
151: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
153: KSPSolve(ksp,b,u);
155: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
156: Check solution and clean up
157: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
159: /* Check error */
160: VecGetOwnershipRange(ustar,&start,&end);
161: for (i=start; i<end; i++) {
162: x = h*(i % (m+1)); y = h*(i/(m+1));
163: val = y;
164: VecSetValues(ustar,1,&i,&val,INSERT_VALUES);
165: }
166: VecAssemblyBegin(ustar);
167: VecAssemblyEnd(ustar);
168: VecAXPY(u,-1.0,ustar);
169: VecNorm(u,NORM_2,&norm);
170: KSPGetIterationNumber(ksp,&its);
171: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Iterations %D\n",(double)(norm*h),its);
173: /*
174: Free work space. All PETSc objects should be destroyed when they
175: are no longer needed.
176: */
177: KSPDestroy(&ksp); VecDestroy(&u);
178: VecDestroy(&ustar); VecDestroy(&b);
179: MatDestroy(&A);
181: /*
182: Always call PetscFinalize() before exiting a program. This routine
183: - finalizes the PETSc libraries as well as MPI
184: - provides summary and diagnostic information if certain runtime
185: options are chosen (e.g., -log_summary).
186: */
187: PetscFinalize();
188: return 0;
189: }
191: /* --------------------------------------------------------------------- */
194: /* element stiffness for Laplacian */
195: PetscErrorCode FormElementStiffness(PetscReal H,PetscScalar *Ke)
196: {
198: Ke[0] = H/6.0; Ke[1] = -.125*H; Ke[2] = H/12.0; Ke[3] = -.125*H;
199: Ke[4] = -.125*H; Ke[5] = H/6.0; Ke[6] = -.125*H; Ke[7] = H/12.0;
200: Ke[8] = H/12.0; Ke[9] = -.125*H; Ke[10] = H/6.0; Ke[11] = -.125*H;
201: Ke[12] = -.125*H; Ke[13] = H/12.0; Ke[14] = -.125*H; Ke[15] = H/6.0;
202: return(0);
203: }
204: /* --------------------------------------------------------------------- */
207: PetscErrorCode FormElementRhs(PetscReal x,PetscReal y,PetscReal H,PetscScalar *r)
208: {
210: r[0] = 0.; r[1] = 0.; r[2] = 0.; r[3] = 0.0;
211: return(0);
212: }