Actual source code: pdde_stability.c

slepc-3.5.2 2014-10-10
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2014, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.

  8:    SLEPc is free software: you can redistribute it and/or modify it under  the
  9:    terms of version 3 of the GNU Lesser General Public License as published by
 10:    the Free Software Foundation.

 12:    SLEPc  is  distributed in the hope that it will be useful, but WITHOUT  ANY
 13:    WARRANTY;  without even the implied warranty of MERCHANTABILITY or  FITNESS
 14:    FOR  A  PARTICULAR PURPOSE. See the GNU Lesser General Public  License  for
 15:    more details.

 17:    You  should have received a copy of the GNU Lesser General  Public  License
 18:    along with SLEPc. If not, see <http://www.gnu.org/licenses/>.
 19:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 20: */
 21: /*
 22:    This example implements one of the problems found at
 23:        NLEVP: A Collection of Nonlinear Eigenvalue Problems,
 24:        The University of Manchester.
 25:    The details of the collection can be found at:
 26:        [1] T. Betcke et al., "NLEVP: A Collection of Nonlinear Eigenvalue
 27:            Problems", ACM Trans. Math. Software 39(2), Article 7, 2013.

 29:    The pdde_stability problem is a complex-symmetric QEP from the stability
 30:    analysis of a discretized partial delay-differential equation. It requires
 31:    complex scalars.
 32: */

 34: static char help[] = "NLEVP problem: pdde_stability.\n\n"
 35:   "The command line options are:\n"
 36:   "  -m <m>, grid size, the matrices have dimension n=m*m.\n"
 37:   "  -c <a0,b0,a1,b1,a2,b2,phi1>, comma-separated list of 7 real parameters.\n\n";

 39: #include <slepcpep.h>

 41: #define NMAT 3

 45: int main(int argc,char **argv)
 46: {
 47:   Mat            A[NMAT];         /* problem matrices */
 48:   PEP            pep;             /* polynomial eigenproblem solver context */
 49:   PetscInt       m=15,n,II,Istart,Iend,i,j,k;
 50:   PetscReal      h,xi,xj,c[7] = { 2, .3, -2, .2, -2, -.3, -PETSC_PI/2 };
 51:   PetscScalar    alpha,beta,gamma;
 52:   PetscBool      flg;

 55:   SlepcInitialize(&argc,&argv,(char*)0,help);
 56: #if !defined(PETSC_USE_COMPLEX)
 57:   SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP, "This example requires complex scalars");
 58: #endif

 60:   PetscOptionsGetInt(NULL,"-m",&m,NULL);
 61:   n = m*m;
 62:   h = PETSC_PI/(m+1);
 63:   gamma = PetscExpScalar(PETSC_i*c[6]);
 64:   gamma = gamma/PetscAbsScalar(gamma);
 65:   k = 7;
 66:   PetscOptionsGetRealArray(NULL,"-c",c,&k,&flg);
 67:   if (flg && k!=7) SETERRQ1(PETSC_COMM_WORLD,1,"The number of parameters -c should be 7, you provided %D",k); 
 68:   PetscPrintf(PETSC_COMM_WORLD,"\nPDDE stability, n=%D (m=%D)\n\n",n,m);

 70:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
 71:                      Compute the polynomial matrices 
 72:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 74:   /* initialize matrices */
 75:   for (i=0;i<NMAT;i++) {
 76:     MatCreate(PETSC_COMM_WORLD,&A[i]);
 77:     MatSetSizes(A[i],PETSC_DECIDE,PETSC_DECIDE,n,n);
 78:     MatSetFromOptions(A[i]);
 79:     MatSetUp(A[i]);
 80:   }
 81:   MatGetOwnershipRange(A[0],&Istart,&Iend);

 83:   /* A[1] has a pattern similar to the 2D Laplacian */
 84:   for (II=Istart;II<Iend;II++) {
 85:     i = II/m; j = II-i*m;
 86:     xi = (i+1)*h; xj = (j+1)*h;
 87:     alpha = c[0]+c[1]*PetscSinReal(xi)+gamma*(c[2]+c[3]*xi*(1.0-PetscExpReal(xi-PETSC_PI)));
 88:     beta = c[0]+c[1]*PetscSinReal(xj)-gamma*(c[2]+c[3]*xj*(1.0-PetscExpReal(xj-PETSC_PI)));
 89:     MatSetValue(A[1],II,II,alpha+beta-4.0/(h*h),INSERT_VALUES);
 90:     if (j>0) { MatSetValue(A[1],II,II-1,1.0/(h*h),INSERT_VALUES); }
 91:     if (j<m-1) { MatSetValue(A[1],II,II+1,1.0/(h*h),INSERT_VALUES); }
 92:     if (i>0) { MatSetValue(A[1],II,II-m,1.0/(h*h),INSERT_VALUES); }
 93:     if (i<m-1) { MatSetValue(A[1],II,II+m,1.0/(h*h),INSERT_VALUES); }
 94:   }

 96:   /* A[0] and A[2] are diagonal */
 97:   for (II=Istart;II<Iend;II++) {
 98:     i = II/m; j = II-i*m;
 99:     xi = (i+1)*h; xj = (j+1)*h;
100:     alpha = c[4]+c[5]*xi*(PETSC_PI-xi);
101:     beta = c[4]+c[5]*xj*(PETSC_PI-xj);
102:     MatSetValue(A[0],II,II,alpha,INSERT_VALUES);
103:     MatSetValue(A[2],II,II,beta,INSERT_VALUES);
104:   }
105:   
106:   /* assemble matrices */
107:   for (i=0;i<NMAT;i++) {
108:     MatAssemblyBegin(A[i],MAT_FINAL_ASSEMBLY);
109:   }
110:   for (i=0;i<NMAT;i++) {
111:     MatAssemblyEnd(A[i],MAT_FINAL_ASSEMBLY);
112:   }

114:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
115:                 Create the eigensolver and solve the problem
116:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

118:   PEPCreate(PETSC_COMM_WORLD,&pep);
119:   PEPSetOperators(pep,NMAT,A);
120:   PEPSetFromOptions(pep);
121:   PEPSolve(pep);

123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
124:                     Display solution and clean up
125:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
126:   
127:   PEPPrintSolution(pep,NULL);
128:   PEPDestroy(&pep);
129:   for (i=0;i<NMAT;i++) {
130:     MatDestroy(&A[i]);
131:   }
132:   SlepcFinalize();
133:   return 0;
134: }