Actual source code: gun.c

slepc-3.8.0 2017-10-20
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2017, 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: */
 10: /*
 11:    This example implements one of the problems found at
 12:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
 13:        The University of Manchester.
 14:    The details of the collection can be found at:
 15:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
 16:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

 18:    The gun problem arises from model of a radio-frequency gun cavity, with
 19:    the complex nonlinear function
 20:    T(lambda) = K-lambda*M+i*lambda^(1/2)*W1+i*(lambda-108.8774^2)^(1/2)*W2

 22:    Data files can be downloaded from http://slepc.upv.es/datafiles
 23: */

 25: static char help[] = "Radio-frequency gun cavity.\n\n"
 26:   "The command line options are:\n"
 27:   "-K <filename1> -M <filename2> -W1 <filename3> -W2 <filename4>, where filename1,..,filename4 are files containing the matrices in PETSc binary form defining the GUN problem.\n\n";

 29: #include <slepcnep.h>

 31: #define NMAT 4
 32: #define SIGMA 108.8774

 34: PetscErrorCode ComputeSingularities(NEP,PetscInt*,PetscScalar*,void*);

 36: int main(int argc,char **argv)
 37: {
 39:   Mat            A[NMAT];         /* problem matrices */
 40:   FN             f[NMAT];         /* functions to define the nonlinear operator */
 41:   FN             ff[2];           /* auxiliary functions to define the nonlinear operator */
 42:   NEP            nep;             /* nonlinear eigensolver context */
 43:   PetscBool      terse,flg;
 44:   const char*    string[NMAT]={"-K","-M","-W1","-W2"};
 45:   char           filename[PETSC_MAX_PATH_LEN];
 46:   PetscScalar    numer[2],sigma;
 47:   PetscInt       i;
 48:   PetscViewer    viewer;

 50:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

 52:   PetscPrintf(PETSC_COMM_WORLD,"GUN problem\n\n");
 53: #if !defined(PETSC_USE_COMPLEX)
 54:   SETERRQ(PETSC_COMM_WORLD,1,"This example requires complex scalars!");
 55: #endif

 57:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 58:                        Load the problem matrices
 59:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 61:   for (i=0;i<NMAT;i++) {
 62:     PetscOptionsGetString(NULL,NULL,string[i],filename,PETSC_MAX_PATH_LEN,&flg);
 63:     if (!flg) SETERRQ1(PETSC_COMM_WORLD,1,"Must indicate a filename with the %s option",string[i]);
 64:     PetscViewerBinaryOpen(PETSC_COMM_WORLD,filename,FILE_MODE_READ,&viewer);
 65:     MatCreate(PETSC_COMM_WORLD,&A[i]);
 66:     MatSetFromOptions(A[i]);
 67:     MatLoad(A[i],viewer);
 68:     PetscViewerDestroy(&viewer);
 69:   }

 71:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 72:                        Create the problem functions
 73:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 75:   /* f1=1 */
 76:   FNCreate(PETSC_COMM_WORLD,&f[0]);
 77:   FNSetType(f[0],FNRATIONAL);
 78:   numer[0] = 1.0;
 79:   FNRationalSetNumerator(f[0],1,numer);

 81:   /* f2=-lambda */
 82:   FNCreate(PETSC_COMM_WORLD,&f[1]);
 83:   FNSetType(f[1],FNRATIONAL);
 84:   numer[0] = -1.0; numer[1] = 0.0;
 85:   FNRationalSetNumerator(f[1],2,numer);

 87:   /* f3=i*sqrt(lambda) */
 88:   FNCreate(PETSC_COMM_WORLD,&f[2]);
 89:   FNSetType(f[2],FNSQRT);
 90:   FNSetScale(f[2],1.0,PETSC_i);

 92:   /* f4=i*sqrt(lambda-sigma^2) */
 93:   sigma = SIGMA*SIGMA;
 94:   FNCreate(PETSC_COMM_WORLD,&ff[0]);
 95:   FNSetType(ff[0],FNSQRT);
 96:   FNCreate(PETSC_COMM_WORLD,&ff[1]);
 97:   FNSetType(ff[1],FNRATIONAL);
 98:   numer[0] = 1.0; numer[1] = -sigma;
 99:   FNRationalSetNumerator(ff[1],2,numer);
100:   FNCreate(PETSC_COMM_WORLD,&f[3]);
101:   FNSetType(f[3],FNCOMBINE);
102:   FNCombineSetChildren(f[3],FN_COMBINE_COMPOSE,ff[1],ff[0]);
103:   FNSetScale(f[3],1.0,PETSC_i);

105:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
106:                 Create the eigensolver and solve the problem
107:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

109:   NEPCreate(PETSC_COMM_WORLD,&nep);
110:   NEPSetSplitOperator(nep,4,A,f,DIFFERENT_NONZERO_PATTERN);
111:   NEPSetFromOptions(nep);

113:   PetscObjectTypeCompare((PetscObject)nep,NEPNLEIGS,&flg);
114:   if (flg) {
115:     NEPNLEIGSSetSingularitiesFunction(nep,ComputeSingularities,NULL);
116:   }

118:   NEPSolve(nep);

120:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
121:                     Display solution and clean up
122:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

124:   /* show detailed info unless -terse option is given by user */
125:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
126:   if (terse) {
127:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
128:   } else {
129:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
130:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
131:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
132:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
133:   }
134:   NEPDestroy(&nep);
135:   for (i=0;i<NMAT;i++) {
136:     MatDestroy(&A[i]);
137:     FNDestroy(&f[i]);
138:   }
139:   for (i=0;i<2;i++) {
140:     FNDestroy(&ff[i]);
141:   }
142:   SlepcFinalize();
143:   return ierr;
144: }

146: /*
147:    ComputeSingularities - Computes maxnp points (at most) in the complex plane where
148:    the function T(.) is not analytic.

150:    In this case, we discretize the singularity region (-inf,108.8774^2)~(-10e+12,-10e-12+108.8774^2)
151: */
152: PetscErrorCode ComputeSingularities(NEP nep,PetscInt *maxnp,PetscScalar *xi,void *pt)
153: {
154:   PetscReal h;
155:   PetscInt  i;
156:   PetscReal   sigma,end;

159:   sigma = SIGMA*SIGMA;
160:   end = PetscLogReal(sigma);
161:   h = (12.0+end)/(*maxnp-1);
162:   xi[0] = sigma;
163:   for (i=1;i<*maxnp;i++) xi[i] = -PetscPowReal(10,h*i)+sigma;
164:   return(0);
165: }