1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Solve a quadratic problem with CISS.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
 14:   "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

 16: #include <slepcpep.h>

 18: int main(int argc,char **argv)
 19: {
 20:   Mat               M,C,K,A[3];
 21:   PEP               pep;
 22:   RG                rg;
 23:   KSP               *ksp;
 24:   PC                pc;
 25:   PEPCISSExtraction ext;
 26:   PetscInt          N,n=10,m,Istart,Iend,II,i,j,nsolve;
 27:   PetscBool         flg;

 29:   PetscFunctionBeginUser;
 30:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
 31:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 32:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-m",&m,&flg));
 33:   if (!flg) m=n;
 34:   N = n*m;
 35:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m));

 37:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 38:      Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
 39:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 41:   /* K is the 2-D Laplacian */
 42:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
 43:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N));
 44:   PetscCall(MatSetFromOptions(K));
 45:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
 46:   for (II=Istart;II<Iend;II++) {
 47:     i = II/n; j = II-i*n;
 48:     if (i>0) PetscCall(MatSetValue(K,II,II-n,-1.0,INSERT_VALUES));
 49:     if (i<m-1) PetscCall(MatSetValue(K,II,II+n,-1.0,INSERT_VALUES));
 50:     if (j>0) PetscCall(MatSetValue(K,II,II-1,-1.0,INSERT_VALUES));
 51:     if (j<n-1) PetscCall(MatSetValue(K,II,II+1,-1.0,INSERT_VALUES));
 52:     PetscCall(MatSetValue(K,II,II,4.0,INSERT_VALUES));
 53:   }
 54:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
 55:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

 57:   /* C is the 1-D Laplacian on horizontal lines */
 58:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
 59:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N));
 60:   PetscCall(MatSetFromOptions(C));
 61:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
 62:   for (II=Istart;II<Iend;II++) {
 63:     i = II/n; j = II-i*n;
 64:     if (j>0) PetscCall(MatSetValue(C,II,II-1,-1.0,INSERT_VALUES));
 65:     if (j<n-1) PetscCall(MatSetValue(C,II,II+1,-1.0,INSERT_VALUES));
 66:     PetscCall(MatSetValue(C,II,II,2.0,INSERT_VALUES));
 67:   }
 68:   PetscCall(MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY));
 69:   PetscCall(MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY));

 71:   /* M is a diagonal matrix */
 72:   PetscCall(MatCreate(PETSC_COMM_WORLD,&M));
 73:   PetscCall(MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N));
 74:   PetscCall(MatSetFromOptions(M));
 75:   PetscCall(MatGetOwnershipRange(M,&Istart,&Iend));
 76:   for (II=Istart;II<Iend;II++) PetscCall(MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES));
 77:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
 78:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

 80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 81:              Create the eigensolver and solve the eigensystem
 82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 84:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
 85:   A[0] = K; A[1] = C; A[2] = M;
 86:   PetscCall(PEPSetOperators(pep,3,A));
 87:   PetscCall(PEPSetProblemType(pep,PEP_GENERAL));

 89:   /* customize polynomial eigensolver; set runtime options */
 90:   PetscCall(PEPSetType(pep,PEPCISS));
 91:   PetscCall(PEPGetRG(pep,&rg));
 92:   PetscCall(RGSetType(rg,RGELLIPSE));
 93:   PetscCall(RGEllipseSetParameters(rg,PetscCMPLX(-0.1,0.3),0.1,0.25));
 94:   PetscCall(PEPCISSSetSizes(pep,24,PETSC_DEFAULT,PETSC_DEFAULT,1,PETSC_DEFAULT,PETSC_TRUE));
 95:   PetscCall(PEPCISSGetKSPs(pep,&nsolve,&ksp));
 96:   for (i=0;i<nsolve;i++) {
 97:     PetscCall(KSPSetTolerances(ksp[i],1e-12,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT));
 98:     PetscCall(KSPSetType(ksp[i],KSPPREONLY));
 99:     PetscCall(KSPGetPC(ksp[i],&pc));
100:     PetscCall(PCSetType(pc,PCLU));
101:   }
102:   PetscCall(PEPSetFromOptions(pep));

104:   /* solve */
105:   PetscCall(PetscObjectTypeCompare((PetscObject)pep,PEPCISS,&flg));
106:   if (flg) {
107:     PetscCall(PEPCISSGetExtraction(pep,&ext));
108:     PetscCall(PetscPrintf(PETSC_COMM_WORLD," Running CISS with %" PetscInt_FMT " KSP solvers (%s extraction)\n",nsolve,PEPCISSExtractions[ext]));
109:   }
110:   PetscCall(PEPSolve(pep));

112:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
113:                     Display solution and clean up
114:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

116:   PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
117:   PetscCall(PEPDestroy(&pep));
118:   PetscCall(MatDestroy(&M));
119:   PetscCall(MatDestroy(&C));
120:   PetscCall(MatDestroy(&K));
121:   PetscCall(SlepcFinalize());
122:   return 0;
123: }

125: /*TEST

127:    build:
128:       requires: complex

130:    test:
131:       suffix: 1
132:       requires: complex

134: TEST*/