Actual source code: ex3.c

  1: static char help[] = "Bilinear elements on the unit square for Laplacian.  To test the parallel\n\
  2: matrix assembly, the matrix is intentionally laid out across processors\n\
  3: differently from the way it is assembled.  Input arguments are:\n\
  4:   -m <size> : problem size\n\n";

  6: /*
  7:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
  8:   automatically includes:
  9:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 10:      petscmat.h - matrices
 11:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 12:      petscviewer.h - viewers               petscpc.h  - preconditioners
 13: */
 14: #include <petscksp.h>

 16: /* Declare user-defined routines */
 17: extern PetscErrorCode FormElementStiffness(PetscReal, PetscScalar *);
 18: extern PetscErrorCode FormElementRhs(PetscScalar, PetscScalar, PetscReal, PetscScalar *);

 20: int main(int argc, char **args)
 21: {
 22:   Vec         u, b, ustar; /* approx solution, RHS, exact solution */
 23:   Mat         A;           /* linear system matrix */
 24:   KSP         ksp;         /* Krylov subspace method context */
 25:   PetscInt    N;           /* dimension of system (global) */
 26:   PetscInt    M;           /* number of elements (global) */
 27:   PetscMPIInt rank;        /* processor rank */
 28:   PetscMPIInt size;        /* size of communicator */
 29:   PetscScalar Ke[16];      /* element matrix */
 30:   PetscScalar r[4];        /* element vector */
 31:   PetscReal   h;           /* mesh width */
 32:   PetscReal   norm;        /* norm of solution error */
 33:   PetscScalar x, y;
 34:   PetscInt    idx[4], count, *rows, i, m = 5, start, end, its;

 36:   PetscFunctionBeginUser;
 37:   PetscCall(PetscInitialize(&argc, &args, (char *)0, help));
 38:   PetscCall(PetscOptionsGetInt(NULL, NULL, "-m", &m, NULL));
 39:   N = (m + 1) * (m + 1);
 40:   M = m * m;
 41:   h = 1.0 / m;
 42:   PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
 43:   PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size));

 45:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 46:          Compute the matrix and right-hand-side vector that define
 47:          the linear system, Au = b.
 48:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 50:   /*
 51:      Create stiffness matrix
 52:   */
 53:   PetscCall(MatCreate(PETSC_COMM_WORLD, &A));
 54:   PetscCall(MatSetSizes(A, PETSC_DECIDE, PETSC_DECIDE, N, N));
 55:   PetscCall(MatSetFromOptions(A));
 56:   PetscCall(MatSeqAIJSetPreallocation(A, 9, NULL));
 57:   PetscCall(MatMPIAIJSetPreallocation(A, 9, NULL, 8, NULL));
 58:   start = rank * (M / size) + ((M % size) < rank ? (M % size) : rank);
 59:   end   = start + M / size + ((M % size) > rank);

 61:   /*
 62:      Assemble matrix
 63:   */
 64:   PetscCall(FormElementStiffness(h * h, Ke));
 65:   for (i = start; i < end; i++) {
 66:     /* node numbers for the four corners of element */
 67:     idx[0] = (m + 1) * (i / m) + (i % m);
 68:     idx[1] = idx[0] + 1;
 69:     idx[2] = idx[1] + m + 1;
 70:     idx[3] = idx[2] - 1;
 71:     PetscCall(MatSetValues(A, 4, idx, 4, idx, Ke, ADD_VALUES));
 72:   }
 73:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
 74:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

 76:   /*
 77:      Create right-hand-side and solution vectors
 78:   */
 79:   PetscCall(VecCreate(PETSC_COMM_WORLD, &u));
 80:   PetscCall(VecSetSizes(u, PETSC_DECIDE, N));
 81:   PetscCall(VecSetFromOptions(u));
 82:   PetscCall(PetscObjectSetName((PetscObject)u, "Approx. Solution"));
 83:   PetscCall(VecDuplicate(u, &b));
 84:   PetscCall(PetscObjectSetName((PetscObject)b, "Right hand side"));
 85:   PetscCall(VecDuplicate(b, &ustar));
 86:   PetscCall(VecSet(u, 0.0));
 87:   PetscCall(VecSet(b, 0.0));

 89:   /*
 90:      Assemble right-hand-side vector
 91:   */
 92:   for (i = start; i < end; i++) {
 93:     /* location of lower left corner of element */
 94:     x = h * (i % m);
 95:     y = h * (i / m);
 96:     /* node numbers for the four corners of element */
 97:     idx[0] = (m + 1) * (i / m) + (i % m);
 98:     idx[1] = idx[0] + 1;
 99:     idx[2] = idx[1] + m + 1;
100:     idx[3] = idx[2] - 1;
101:     PetscCall(FormElementRhs(x, y, h * h, r));
102:     PetscCall(VecSetValues(b, 4, idx, r, ADD_VALUES));
103:   }
104:   PetscCall(VecAssemblyBegin(b));
105:   PetscCall(VecAssemblyEnd(b));

107:   /*
108:      Modify matrix and right-hand-side for Dirichlet boundary conditions
109:   */
110:   PetscCall(PetscMalloc1(4 * m, &rows));
111:   for (i = 0; i < m + 1; i++) {
112:     rows[i]             = i;               /* bottom */
113:     rows[3 * m - 1 + i] = m * (m + 1) + i; /* top */
114:   }
115:   count = m + 1; /* left side */
116:   for (i = m + 1; i < m * (m + 1); i += m + 1) rows[count++] = i;
117:   count = 2 * m; /* left side */
118:   for (i = 2 * m + 1; i < m * (m + 1); i += m + 1) rows[count++] = i;
119:   for (i = 0; i < 4 * m; i++) {
120:     y = h * (rows[i] / (m + 1));
121:     PetscCall(VecSetValues(u, 1, &rows[i], &y, INSERT_VALUES));
122:     PetscCall(VecSetValues(b, 1, &rows[i], &y, INSERT_VALUES));
123:   }
124:   PetscCall(MatZeroRows(A, 4 * m, rows, 1.0, 0, 0));
125:   PetscCall(PetscFree(rows));

127:   PetscCall(VecAssemblyBegin(u));
128:   PetscCall(VecAssemblyEnd(u));
129:   PetscCall(VecAssemblyBegin(b));
130:   PetscCall(VecAssemblyEnd(b));

132:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
133:                 Create the linear solver and set various options
134:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

136:   PetscCall(KSPCreate(PETSC_COMM_WORLD, &ksp));
137:   PetscCall(KSPSetOperators(ksp, A, A));
138:   PetscCall(KSPSetInitialGuessNonzero(ksp, PETSC_TRUE));
139:   PetscCall(KSPSetFromOptions(ksp));

141:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
142:                       Solve the linear system
143:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

145:   PetscCall(KSPSolve(ksp, b, u));

147:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
148:                       Check solution and clean up
149:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

151:   /* Check error */
152:   PetscCall(VecGetOwnershipRange(ustar, &start, &end));
153:   for (i = start; i < end; i++) {
154:     y = h * (i / (m + 1));
155:     PetscCall(VecSetValues(ustar, 1, &i, &y, INSERT_VALUES));
156:   }
157:   PetscCall(VecAssemblyBegin(ustar));
158:   PetscCall(VecAssemblyEnd(ustar));
159:   PetscCall(VecAXPY(u, -1.0, ustar));
160:   PetscCall(VecNorm(u, NORM_2, &norm));
161:   PetscCall(KSPGetIterationNumber(ksp, &its));
162:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Norm of error %g Iterations %" PetscInt_FMT "\n", (double)(norm * h), its));

164:   /*
165:      Free work space.  All PETSc objects should be destroyed when they
166:      are no longer needed.
167:   */
168:   PetscCall(KSPDestroy(&ksp));
169:   PetscCall(VecDestroy(&u));
170:   PetscCall(VecDestroy(&ustar));
171:   PetscCall(VecDestroy(&b));
172:   PetscCall(MatDestroy(&A));

174:   /*
175:      Always call PetscFinalize() before exiting a program.  This routine
176:        - finalizes the PETSc libraries as well as MPI
177:        - provides summary and diagnostic information if certain runtime
178:          options are chosen (e.g., -log_view).
179:   */
180:   PetscCall(PetscFinalize());
181:   return 0;
182: }

184: /* --------------------------------------------------------------------- */
185: /* element stiffness for Laplacian */
186: PetscErrorCode FormElementStiffness(PetscReal H, PetscScalar *Ke)
187: {
188:   PetscFunctionBeginUser;
189:   Ke[0]  = H / 6.0;
190:   Ke[1]  = -.125 * H;
191:   Ke[2]  = H / 12.0;
192:   Ke[3]  = -.125 * H;
193:   Ke[4]  = -.125 * H;
194:   Ke[5]  = H / 6.0;
195:   Ke[6]  = -.125 * H;
196:   Ke[7]  = H / 12.0;
197:   Ke[8]  = H / 12.0;
198:   Ke[9]  = -.125 * H;
199:   Ke[10] = H / 6.0;
200:   Ke[11] = -.125 * H;
201:   Ke[12] = -.125 * H;
202:   Ke[13] = H / 12.0;
203:   Ke[14] = -.125 * H;
204:   Ke[15] = H / 6.0;
205:   PetscFunctionReturn(PETSC_SUCCESS);
206: }
207: /* --------------------------------------------------------------------- */
208: PetscErrorCode FormElementRhs(PetscScalar x, PetscScalar y, PetscReal H, PetscScalar *r)
209: {
210:   PetscFunctionBeginUser;
211:   r[0] = 0.;
212:   r[1] = 0.;
213:   r[2] = 0.;
214:   r[3] = 0.0;
215:   PetscFunctionReturn(PETSC_SUCCESS);
216: }

218: /*TEST

220:    test:
221:       suffix: 1
222:       nsize: 2
223:       args: -ksp_monitor_short

225: TEST*/