Actual source code: ex11.c


  2: static char help[] = "Solves a linear system in parallel with KSP.\n\n";

  4: /*T
  5:    Concepts: KSP^solving a Helmholtz equation
  6:    Concepts: complex numbers;
  7:    Concepts: Helmholtz equation
  8:    Processors: n
  9: T*/

 11: /*
 12:    Description: Solves a complex linear system in parallel with KSP.

 14:    The model problem:
 15:       Solve Helmholtz equation on the unit square: (0,1) x (0,1)
 16:           -delta u - sigma1*u + i*sigma2*u = f,
 17:            where delta = Laplace operator
 18:       Dirichlet b.c.'s on all sides
 19:       Use the 2-D, five-point finite difference stencil.

 21:    Compiling the code:
 22:       This code uses the complex numbers version of PETSc, so configure
 23:       must be run to enable this
 24: */

 26: /*
 27:   Include "petscksp.h" so that we can use KSP solvers.  Note that this file
 28:   automatically includes:
 29:      petscsys.h       - base PETSc routines   petscvec.h - vectors
 30:      petscmat.h - matrices
 31:      petscis.h     - index sets            petscksp.h - Krylov subspace methods
 32:      petscviewer.h - viewers               petscpc.h  - preconditioners
 33: */
 34: #include <petscksp.h>

 36: int main(int argc,char **args)
 37: {
 38:   Vec            x,b,u;      /* approx solution, RHS, exact solution */
 39:   Mat            A;            /* linear system matrix */
 40:   KSP            ksp;         /* linear solver context */
 41:   PetscReal      norm;         /* norm of solution error */
 42:   PetscInt       dim,i,j,Ii,J,Istart,Iend,n = 6,its,use_random;
 43:   PetscScalar    v,none = -1.0,sigma2,pfive = 0.5,*xa;
 44:   PetscRandom    rctx;
 45:   PetscReal      h2,sigma1 = 100.0;
 46:   PetscBool      flg = PETSC_FALSE;

 48:   PetscInitialize(&argc,&args,(char*)0,help);
 49:   PetscOptionsGetReal(NULL,NULL,"-sigma1",&sigma1,NULL);
 50:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 51:   dim  = n*n;

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:          Compute the matrix and right-hand-side vector that define
 55:          the linear system, Ax = b.
 56:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
 57:   /*
 58:      Create parallel matrix, specifying only its global dimensions.
 59:      When using MatCreate(), the matrix format can be specified at
 60:      runtime. Also, the parallel partitioning of the matrix is
 61:      determined by PETSc at runtime.
 62:   */
 63:   MatCreate(PETSC_COMM_WORLD,&A);
 64:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
 65:   MatSetFromOptions(A);
 66:   MatSetUp(A);

 68:   /*
 69:      Currently, all PETSc parallel matrix formats are partitioned by
 70:      contiguous chunks of rows across the processors.  Determine which
 71:      rows of the matrix are locally owned.
 72:   */
 73:   MatGetOwnershipRange(A,&Istart,&Iend);

 75:   /*
 76:      Set matrix elements in parallel.
 77:       - Each processor needs to insert only elements that it owns
 78:         locally (but any non-local elements will be sent to the
 79:         appropriate processor during matrix assembly).
 80:       - Always specify global rows and columns of matrix entries.
 81:   */

 83:   PetscOptionsGetBool(NULL,NULL,"-norandom",&flg,NULL);
 84:   if (flg) use_random = 0;
 85:   else use_random = 1;
 86:   if (use_random) {
 87:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
 88:     PetscRandomSetFromOptions(rctx);
 89:     PetscRandomSetInterval(rctx,0.0,PETSC_i);
 90:   } else {
 91:     sigma2 = 10.0*PETSC_i;
 92:   }
 93:   h2 = 1.0/((n+1)*(n+1));
 94:   for (Ii=Istart; Ii<Iend; Ii++) {
 95:     v = -1.0; i = Ii/n; j = Ii - i*n;
 96:     if (i>0) {
 97:       J = Ii-n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
 98:     }
 99:     if (i<n-1) {
100:       J = Ii+n; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
101:     }
102:     if (j>0) {
103:       J = Ii-1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
104:     }
105:     if (j<n-1) {
106:       J = Ii+1; MatSetValues(A,1,&Ii,1,&J,&v,ADD_VALUES);
107:     }
108:     if (use_random) PetscRandomGetValue(rctx,&sigma2);
109:     v    = 4.0 - sigma1*h2 + sigma2*h2;
110:     MatSetValues(A,1,&Ii,1,&Ii,&v,ADD_VALUES);
111:   }
112:   if (use_random) PetscRandomDestroy(&rctx);

114:   /*
115:      Assemble matrix, using the 2-step process:
116:        MatAssemblyBegin(), MatAssemblyEnd()
117:      Computations can be done while messages are in transition
118:      by placing code between these two statements.
119:   */
120:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
121:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

123:   /*
124:      Create parallel vectors.
125:       - When using VecCreate(), VecSetSizes() and VecSetFromOptions(),
126:       we specify only the vector's global
127:         dimension; the parallel partitioning is determined at runtime.
128:       - Note: We form 1 vector from scratch and then duplicate as needed.
129:   */
130:   VecCreate(PETSC_COMM_WORLD,&u);
131:   VecSetSizes(u,PETSC_DECIDE,dim);
132:   VecSetFromOptions(u);
133:   VecDuplicate(u,&b);
134:   VecDuplicate(b,&x);

136:   /*
137:      Set exact solution; then compute right-hand-side vector.
138:   */

140:   if (use_random) {
141:     PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
142:     PetscRandomSetFromOptions(rctx);
143:     VecSetRandom(u,rctx);
144:   } else {
145:     VecSet(u,pfive);
146:   }
147:   MatMult(A,u,b);

149:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
150:                 Create the linear solver and set various options
151:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

153:   /*
154:      Create linear solver context
155:   */
156:   KSPCreate(PETSC_COMM_WORLD,&ksp);

158:   /*
159:      Set operators. Here the matrix that defines the linear system
160:      also serves as the preconditioning matrix.
161:   */
162:   KSPSetOperators(ksp,A,A);

164:   /*
165:     Set runtime options, e.g.,
166:         -ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
167:   */
168:   KSPSetFromOptions(ksp);

170:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
171:                       Solve the linear system
172:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

174:   KSPSolve(ksp,b,x);

176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
177:                       Check solution and clean up
178:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

180:   /*
181:       Print the first 3 entries of x; this demonstrates extraction of the
182:       real and imaginary components of the complex vector, x.
183:   */
184:   flg  = PETSC_FALSE;
185:   PetscOptionsGetBool(NULL,NULL,"-print_x3",&flg,NULL);
186:   if (flg) {
187:     VecGetArray(x,&xa);
188:     PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
189:     for (i=0; i<3; i++) {
190:       PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));
191:     }
192:     VecRestoreArray(x,&xa);
193:   }

195:   /*
196:      Check the error
197:   */
198:   VecAXPY(x,none,u);
199:   VecNorm(x,NORM_2,&norm);
200:   KSPGetIterationNumber(ksp,&its);
201:   if (norm < 1.e-12) {
202:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",its);
203:   } else {
204:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
205:   }

207:   /*
208:      Free work space.  All PETSc objects should be destroyed when they
209:      are no longer needed.
210:   */
211:   KSPDestroy(&ksp);
212:   if (use_random) PetscRandomDestroy(&rctx);
213:   VecDestroy(&u)); PetscCall(VecDestroy(&x);
214:   VecDestroy(&b)); PetscCall(MatDestroy(&A);
215:   PetscFinalize();
216:   return 0;
217: }

219: /*TEST

221:    build:
222:       requires: complex

224:    test:
225:       args: -n 6 -norandom -pc_type none -ksp_monitor_short -ksp_gmres_cgs_refinement_type refine_always

227:    testset:
228:       suffix: deflation
229:       args: -norandom -pc_type deflation -ksp_monitor_short
230:       requires: superlu_dist

232:       test:
233:         nsize: 6

235:       test:
236:         nsize: 3
237:         args: -pc_deflation_compute_space {{db2 aggregation}}

239:       test:
240:         suffix: pc_deflation_init_only-0
241:         nsize: 4
242:         args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
243:         #TODO remove suffix and next test when this works
244:         #args: -pc_deflation_init_only {{0 1}separate output}
245:         args: -pc_deflation_init_only 0

247:       test:
248:         suffix: pc_deflation_init_only-1
249:         nsize: 4
250:         args: -ksp_type fgmres -pc_deflation_compute_space db4 -pc_deflation_compute_space_size 2 -pc_deflation_levels 2 -deflation_ksp_max_it 10
251:         args: -pc_deflation_init_only 1

253: TEST*/