Actual source code: ex11.c

petsc-master 2017-11-23
Report Typos and Errors

  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;
 44:   PetscScalar    v,none = -1.0,sigma2,pfive = 0.5,*xa;
 45:   PetscRandom    rctx;
 46:   PetscReal      h2,sigma1 = 100.0;
 47:   PetscBool      flg = PETSC_FALSE;

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

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

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

 76:   /*
 77:      Set matrix elements in parallel.
 78:       - Each processor needs to insert only elements that it owns
 79:         locally (but any non-local elements will be sent to the
 80:         appropriate processor during matrix assembly).
 81:       - Always specify global rows and columns of matrix entries.
 82:   */

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

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

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

137:   /*
138:      Set exact solution; then compute right-hand-side vector.
139:   */

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

150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151:                 Create the linear solver and set various options
152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

171:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
172:                       Solve the linear system
173:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

175:   KSPSolve(ksp,b,x);

177:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
178:                       Check solution and clean up
179:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

181:   /*
182:       Print the first 3 entries of x; this demonstrates extraction of the
183:       real and imaginary components of the complex vector, x.
184:   */
185:   flg  = PETSC_FALSE;
186:   PetscOptionsGetBool(NULL,NULL,"-print_x3",&flg,NULL);
187:   if (flg) {
188:     VecGetArray(x,&xa);
189:     PetscPrintf(PETSC_COMM_WORLD,"The first three entries of x are:\n");
190:     for (i=0; i<3; i++) {
191:       PetscPrintf(PETSC_COMM_WORLD,"x[%D] = %g + %g i\n",i,(double)PetscRealPart(xa[i]),(double)PetscImaginaryPart(xa[i]));
192:     }
193:     VecRestoreArray(x,&xa);
194:   }

196:   /*
197:      Check the error
198:   */
199:   VecAXPY(x,none,u);
200:   VecNorm(x,NORM_2,&norm);
201:   KSPGetIterationNumber(ksp,&its);
202:   if (norm < 1.e-12) {
203:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error < 1.e-12 iterations %D\n",its);
204:   } else {
205:     PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);
206:   }

208:   /*
209:      Free work space.  All PETSc objects should be destroyed when they
210:      are no longer needed.
211:   */
212:   KSPDestroy(&ksp);
213:   if (use_random) {PetscRandomDestroy(&rctx);}
214:   VecDestroy(&u); VecDestroy(&x);
215:   VecDestroy(&b); MatDestroy(&A);
216:   PetscFinalize();
217:   return ierr;
218: }