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[] = "Illustrates region filtering in PEP (based on spring).\n"
 12:   "The command line options are:\n"
 13:   "  -n <n> ... number of grid subdivisions.\n"
 14:   "  -mu <value> ... mass (default 1).\n"
 15:   "  -tau <value> ... damping constant of the dampers (default 10).\n"
 16:   "  -kappa <value> ... damping constant of the springs (default 5).\n\n";

 18: #include <slepcpep.h>

 20: int main(int argc,char **argv)
 21: {
 22:   Mat            M,C,K,A[3];      /* problem matrices */
 23:   PEP            pep;             /* polynomial eigenproblem solver context */
 24:   RG             rg;
 25:   PetscInt       n=30,Istart,Iend,i;
 26:   PetscReal      mu=1.0,tau=10.0,kappa=5.0;

 28:   PetscFunctionBeginUser;
 29:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));

 31:   PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL));
 32:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-mu",&mu,NULL));
 33:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL));
 34:   PetscCall(PetscOptionsGetReal(NULL,NULL,"-kappa",&kappa,NULL));
 35:   PetscCall(PetscPrintf(PETSC_COMM_WORLD,"\nDamped mass-spring system, n=%" PetscInt_FMT " mu=%g tau=%g kappa=%g\n\n",n,(double)mu,(double)tau,(double)kappa));

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

 41:   /* K is a tridiagonal */
 42:   PetscCall(MatCreate(PETSC_COMM_WORLD,&K));
 43:   PetscCall(MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,n,n));
 44:   PetscCall(MatSetFromOptions(K));

 46:   PetscCall(MatGetOwnershipRange(K,&Istart,&Iend));
 47:   for (i=Istart;i<Iend;i++) {
 48:     if (i>0) PetscCall(MatSetValue(K,i,i-1,-kappa,INSERT_VALUES));
 49:     PetscCall(MatSetValue(K,i,i,kappa*3.0,INSERT_VALUES));
 50:     if (i<n-1) PetscCall(MatSetValue(K,i,i+1,-kappa,INSERT_VALUES));
 51:   }

 53:   PetscCall(MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY));
 54:   PetscCall(MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY));

 56:   /* C is a tridiagonal */
 57:   PetscCall(MatCreate(PETSC_COMM_WORLD,&C));
 58:   PetscCall(MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,n,n));
 59:   PetscCall(MatSetFromOptions(C));

 61:   PetscCall(MatGetOwnershipRange(C,&Istart,&Iend));
 62:   for (i=Istart;i<Iend;i++) {
 63:     if (i>0) PetscCall(MatSetValue(C,i,i-1,-tau,INSERT_VALUES));
 64:     PetscCall(MatSetValue(C,i,i,tau*3.0,INSERT_VALUES));
 65:     if (i<n-1) PetscCall(MatSetValue(C,i,i+1,-tau,INSERT_VALUES));
 66:   }

 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 (i=Istart;i<Iend;i++) PetscCall(MatSetValue(M,i,i,mu,INSERT_VALUES));
 77:   PetscCall(MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY));
 78:   PetscCall(MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY));

 80:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 81:                     Create a region for filtering
 82:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 84:   PetscCall(RGCreate(PETSC_COMM_WORLD,&rg));
 85:   PetscCall(RGSetType(rg,RGINTERVAL));
 86: #if defined(PETSC_USE_COMPLEX)
 87:   PetscCall(RGIntervalSetEndpoints(rg,-47.0,-35.0,-0.001,0.001));
 88: #else
 89:   PetscCall(RGIntervalSetEndpoints(rg,-47.0,-35.0,-0.0,0.0));
 90: #endif

 92:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 93:                 Create the eigensolver and solve the problem
 94:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 96:   PetscCall(PEPCreate(PETSC_COMM_WORLD,&pep));
 97:   PetscCall(PEPSetRG(pep,rg));
 98:   A[0] = K; A[1] = C; A[2] = M;
 99:   PetscCall(PEPSetOperators(pep,3,A));
100:   PetscCall(PEPSetTolerances(pep,PETSC_SMALL,PETSC_DEFAULT));
101:   PetscCall(PEPSetFromOptions(pep));
102:   PetscCall(PEPSolve(pep));

104:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
105:                     Display solution and clean up
106:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

108:   PetscCall(PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL));
109:   PetscCall(PEPDestroy(&pep));
110:   PetscCall(MatDestroy(&M));
111:   PetscCall(MatDestroy(&C));
112:   PetscCall(MatDestroy(&K));
113:   PetscCall(RGDestroy(&rg));
114:   PetscCall(SlepcFinalize());
115:   return 0;
116: }

118: /*TEST

120:    test:
121:       args: -pep_nev 8 -pep_type {{toar linear qarnoldi}}
122:       suffix: 1
123:       requires: !single
124:       output_file: output/test12_1.out

126: TEST*/