Actual source code: ex22.c

  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2013, 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:   PetscScalar    lambda;          /* eigenvalue */
 52:   Mat            Id,A,B;          /* problem matrices */
 53:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
 54:   Mat            mats[3];
 55:   FN             funs[3];
 56:   NEPType        type;
 57:   PetscScalar    value[3],coeffs[2],b;
 58:   PetscInt       n=128,nev,Istart,Iend,col[3],i,its,nconv;
 59:   PetscReal      tau=0.001,h,a=20,xi,re,im,norm;
 60:   PetscBool      FirstBlock=PETSC_FALSE,LastBlock=PETSC_FALSE;

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

 69:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 70:      Create nonlinear eigensolver context
 71:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 73:   NEPCreate(PETSC_COMM_WORLD,&nep);

 75:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 76:      Create problem matrices and coefficient functions. Pass them to NEP
 77:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 79:   /*
 80:      Identity matrix
 81:   */
 82:   MatCreate(PETSC_COMM_WORLD,&Id);
 83:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
 84:   MatSetFromOptions(Id);
 85:   MatSetUp(Id);
 86:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
 87:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
 88:   MatShift(Id,1.0);
 89:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

 91:   /*
 92:      A = 1/h^2*tridiag(1,-2,1) + a*I
 93:   */
 94:   MatCreate(PETSC_COMM_WORLD,&A);
 95:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 96:   MatSetFromOptions(A);
 97:   MatSetUp(A);
 98:   MatGetOwnershipRange(A,&Istart,&Iend);
 99:   if (Istart==0) FirstBlock=PETSC_TRUE;
100:   if (Iend==n) LastBlock=PETSC_TRUE;
101:   value[0]=1.0/(h*h); value[1]=-2.0/(h*h)+a; value[2]=1.0/(h*h);
102:   for (i=(FirstBlock? Istart+1: Istart); i<(LastBlock? Iend-1: Iend); i++) {
103:     col[0]=i-1; col[1]=i; col[2]=i+1;
104:     MatSetValues(A,1,&i,3,col,value,INSERT_VALUES);
105:   }
106:   if (LastBlock) {
107:     i=n-1; col[0]=n-2; col[1]=n-1;
108:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
109:   }
110:   if (FirstBlock) {
111:     i=0; col[0]=0; col[1]=1; value[0]=-2.0/(h*h)+a; value[1]=1.0/(h*h);
112:     MatSetValues(A,1,&i,2,col,value,INSERT_VALUES);
113:   }
114:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
115:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
116:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

118:   /*
119:      B = diag(b(xi))
120:   */
121:   MatCreate(PETSC_COMM_WORLD,&B);
122:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
123:   MatSetFromOptions(B);
124:   MatSetUp(B);
125:   MatGetOwnershipRange(B,&Istart,&Iend);
126:   for (i=Istart;i<Iend;i++) {
127:     xi = (i+1)*h;
128:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
129:     MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
130:   }
131:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
132:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
133:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

135:   /*
136:      Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
137:   */
138:   FNCreate(PETSC_COMM_WORLD,&f1);
139:   FNSetType(f1,FNRATIONAL);
140:   coeffs[0] = -1.0; coeffs[1] = 0.0;
141:   FNSetParameters(f1,2,coeffs,0,NULL);

143:   FNCreate(PETSC_COMM_WORLD,&f2);
144:   FNSetType(f2,FNRATIONAL);
145:   coeffs[0] = 1.0;
146:   FNSetParameters(f2,1,coeffs,0,NULL);

148:   FNCreate(PETSC_COMM_WORLD,&f3);
149:   FNSetType(f3,FNEXP);
150:   coeffs[0] = -tau;
151:   FNSetParameters(f3,1,coeffs,0,NULL);

153:   /*
154:      Set the split operator. Note that A is passed first so that
155:      SUBSET_NONZERO_PATTERN can be used
156:   */
157:   mats[0] = A;  funs[0] = f2;
158:   mats[1] = Id; funs[1] = f1;
159:   mats[2] = B;  funs[2] = f3;
160:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

162:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
163:              Customize nonlinear solver; set runtime options
164:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

166:   NEPSetTolerances(nep,0,1e-9,0,0,0);
167:   NEPSetDimensions(nep,1,0,0);
168:   NEPSetLagPreconditioner(nep,0);

170:   /*
171:      Set solver parameters at runtime
172:   */
173:   NEPSetFromOptions(nep);

175:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
176:                       Solve the eigensystem
177:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

179:   NEPSolve(nep);
180:   NEPGetIterationNumber(nep,&its);
181:   PetscPrintf(PETSC_COMM_WORLD," Number of NEP iterations = %D\n\n",its);

183:   /*
184:      Optional: Get some information from the solver and display it
185:   */
186:   NEPGetType(nep,&type);
187:   PetscPrintf(PETSC_COMM_WORLD," Solution method: %s\n",type);
188:   NEPGetDimensions(nep,&nev,NULL,NULL);
189:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %D\n",nev);

191:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
192:                     Display solution and clean up
193:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

195:   /*
196:      Get number of converged approximate eigenpairs
197:   */
198:   NEPGetConverged(nep,&nconv);
199:   PetscPrintf(PETSC_COMM_WORLD," Number of converged approximate eigenpairs: %D\n\n",nconv);

201:   if (nconv>0) {
202:     /*
203:        Display eigenvalues and relative errors
204:     */
205:     PetscPrintf(PETSC_COMM_WORLD,
206:          "           k              ||T(k)x||\n"
207:          "   ----------------- ------------------\n");
208:     for (i=0;i<nconv;i++) {
209:       NEPGetEigenpair(nep,i,&lambda,NULL);
210:       NEPComputeRelativeError(nep,i,&norm);
211: #if defined(PETSC_USE_COMPLEX)
212:       re = PetscRealPart(lambda);
213:       im = PetscImaginaryPart(lambda);
214: #else
215:       re = lambda;
216:       im = 0.0;
217: #endif
218:       if (im!=0.0) {
219:         PetscPrintf(PETSC_COMM_WORLD," %9F%+9F j %12G\n",re,im,norm);
220:       } else {
221:         PetscPrintf(PETSC_COMM_WORLD,"   %12F         %12G\n",re,norm);
222:       }
223:     }
224:     PetscPrintf(PETSC_COMM_WORLD,"\n");
225:   }

227:   NEPDestroy(&nep);
228:   MatDestroy(&Id);
229:   MatDestroy(&A);
230:   MatDestroy(&B);
231:   FNDestroy(&f1);
232:   FNDestroy(&f2);
233:   FNDestroy(&f3);
234:   SlepcFinalize();
235:   return 0;
236: }