Actual source code: ex22.c

slepc-3.6.1 2015-09-03
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2015, 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: */

 22: static char help[] = "Delay differential equation.\n\n"
 23:   "The command line options are:\n"
 24:   "  -n <n>, where <n> = number of grid subdivisions.\n"
 25:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

 27: /*
 28:    Solve parabolic partial differential equation with time delay tau

 30:             u_t = u_xx + a*u(t) + b*u(t-tau)
 31:             u(0,t) = u(pi,t) = 0

 33:    with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).

 35:    Discretization leads to a DDE of dimension n

 37:             -u' = A*u(t) + B*u(t-tau)

 39:    which results in the nonlinear eigenproblem

 41:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
 42: */

 44: #include <slepcnep.h>

 48: int main(int argc,char **argv)
 49: {
 50:   NEP            nep;             /* nonlinear eigensolver context */
 51:   Mat            Id,A,B;          /* problem matrices */
 52:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
 53:   Mat            mats[3];
 54:   FN             funs[3];
 55:   NEPType        type;
 56:   PetscScalar    coeffs[2],b;
 57:   PetscInt       n=128,nev,Istart,Iend,i,its;
 58:   PetscReal      tau=0.001,h,a=20,xi;
 59:   PetscBool      terse;

 62:   SlepcInitialize(&argc,&argv,(char*)0,help);
 63:   PetscOptionsGetInt(NULL,"-n",&n,NULL);
 64:   PetscOptionsGetReal(NULL,"-tau",&tau,NULL);
 65:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
 66:   h = PETSC_PI/(PetscReal)(n+1);

 68:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 69:      Create nonlinear eigensolver context
 70:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 72:   NEPCreate(PETSC_COMM_WORLD,&nep);

 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75:      Create problem matrices and coefficient functions. Pass them to NEP
 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 78:   /*
 79:      Identity matrix
 80:   */
 81:   MatCreate(PETSC_COMM_WORLD,&Id);
 82:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
 83:   MatSetFromOptions(Id);
 84:   MatSetUp(Id);
 85:   MatGetOwnershipRange(Id,&Istart,&Iend);
 86:   for (i=Istart;i<Iend;i++) {
 87:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
 88:   }
 89:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
 90:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
 91:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

 93:   /*
 94:      A = 1/h^2*tridiag(1,-2,1) + a*I
 95:   */
 96:   MatCreate(PETSC_COMM_WORLD,&A);
 97:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 98:   MatSetFromOptions(A);
 99:   MatSetUp(A);
100:   MatGetOwnershipRange(A,&Istart,&Iend);
101:   for (i=Istart;i<Iend;i++) {
102:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
103:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
104:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
105:   }
106:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
107:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
108:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

110:   /*
111:      B = diag(b(xi))
112:   */
113:   MatCreate(PETSC_COMM_WORLD,&B);
114:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
115:   MatSetFromOptions(B);
116:   MatSetUp(B);
117:   MatGetOwnershipRange(B,&Istart,&Iend);
118:   for (i=Istart;i<Iend;i++) {
119:     xi = (i+1)*h;
120:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
121:     MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
122:   }
123:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
124:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
125:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

127:   /*
128:      Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
129:   */
130:   FNCreate(PETSC_COMM_WORLD,&f1);
131:   FNSetType(f1,FNRATIONAL);
132:   coeffs[0] = -1.0; coeffs[1] = 0.0;
133:   FNRationalSetNumerator(f1,2,coeffs);

135:   FNCreate(PETSC_COMM_WORLD,&f2);
136:   FNSetType(f2,FNRATIONAL);
137:   coeffs[0] = 1.0;
138:   FNRationalSetNumerator(f2,1,coeffs);

140:   FNCreate(PETSC_COMM_WORLD,&f3);
141:   FNSetType(f3,FNEXP);
142:   FNSetScale(f3,-tau,1.0);

144:   /*
145:      Set the split operator. Note that A is passed first so that
146:      SUBSET_NONZERO_PATTERN can be used
147:   */
148:   mats[0] = A;  funs[0] = f2;
149:   mats[1] = Id; funs[1] = f1;
150:   mats[2] = B;  funs[2] = f3;
151:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

153:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
154:              Customize nonlinear solver; set runtime options
155:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

157:   NEPSetTolerances(nep,PETSC_DEFAULT,1e-9,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT);
158:   NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);
159:   NEPSetLagPreconditioner(nep,0);

161:   /*
162:      Set solver parameters at runtime
163:   */
164:   NEPSetFromOptions(nep);

166:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
167:                       Solve the eigensystem
168:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

170:   NEPSolve(nep);
171:   NEPGetIterationNumber(nep,&its);
172:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

174:   /*
175:      Optional: Get some information from the solver and display it
176:   */
177:   NEPGetType(nep,&type);
178:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
179:   NEPGetDimensions(nep,&nev,NULL,NULL);
180:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

182:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
183:                     Display solution and clean up
184:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

186:   /* show detailed info unless -terse option is given by user */
187:   PetscOptionsHasName(NULL,"-terse",&terse);
188:   if (terse) {
189:     NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
190:   } else {
191:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
192:     NEPReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
193:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
194:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
195:   }
196:   NEPDestroy(&nep);
197:   MatDestroy(&Id);
198:   MatDestroy(&A);
199:   MatDestroy(&B);
200:   FNDestroy(&f1);
201:   FNDestroy(&f2);
202:   FNDestroy(&f3);
203:   SlepcFinalize();
204:   return 0;
205: }