Actual source code: ex22.c

slepc-3.17.0 2022-03-31
Report Typos and Errors
  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[] = "Delay differential equation.\n\n"
 12:   "The command line options are:\n"
 13:   "  -n <n>, where <n> = number of grid subdivisions.\n"
 14:   "  -tau <tau>, where <tau> is the delay parameter.\n\n";

 16: /*
 17:    Solve parabolic partial differential equation with time delay tau

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

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

 24:    Discretization leads to a DDE of dimension n

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

 28:    which results in the nonlinear eigenproblem

 30:             (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
 31: */

 33: #include <slepcnep.h>

 35: int main(int argc,char **argv)
 36: {
 37:   NEP            nep;             /* nonlinear eigensolver context */
 38:   Mat            Id,A,B;          /* problem matrices */
 39:   FN             f1,f2,f3;        /* functions to define the nonlinear operator */
 40:   Mat            mats[3];
 41:   FN             funs[3];
 42:   PetscScalar    coeffs[2],b;
 43:   PetscInt       n=128,nev,Istart,Iend,i;
 44:   PetscReal      tau=0.001,h,a=20,xi;
 45:   PetscBool      terse;

 47:   SlepcInitialize(&argc,&argv,(char*)0,help);
 48:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 49:   PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
 50:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n\n",n,(double)tau);
 51:   h = PETSC_PI/(PetscReal)(n+1);

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:      Create nonlinear eigensolver context
 55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 57:   NEPCreate(PETSC_COMM_WORLD,&nep);

 59:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 60:      Create problem matrices and coefficient functions. Pass them to NEP
 61:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 63:   /*
 64:      Identity matrix
 65:   */
 66:   MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
 67:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

 69:   /*
 70:      A = 1/h^2*tridiag(1,-2,1) + a*I
 71:   */
 72:   MatCreate(PETSC_COMM_WORLD,&A);
 73:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
 74:   MatSetFromOptions(A);
 75:   MatSetUp(A);
 76:   MatGetOwnershipRange(A,&Istart,&Iend);
 77:   for (i=Istart;i<Iend;i++) {
 78:     if (i>0) MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);
 79:     if (i<n-1) MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);
 80:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
 81:   }
 82:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
 83:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
 84:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

 86:   /*
 87:      B = diag(b(xi))
 88:   */
 89:   MatCreate(PETSC_COMM_WORLD,&B);
 90:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
 91:   MatSetFromOptions(B);
 92:   MatSetUp(B);
 93:   MatGetOwnershipRange(B,&Istart,&Iend);
 94:   for (i=Istart;i<Iend;i++) {
 95:     xi = (i+1)*h;
 96:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
 97:     MatSetValue(B,i,i,b,INSERT_VALUES);
 98:   }
 99:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
100:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
101:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

103:   /*
104:      Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda)
105:   */
106:   FNCreate(PETSC_COMM_WORLD,&f1);
107:   FNSetType(f1,FNRATIONAL);
108:   coeffs[0] = -1.0; coeffs[1] = 0.0;
109:   FNRationalSetNumerator(f1,2,coeffs);

111:   FNCreate(PETSC_COMM_WORLD,&f2);
112:   FNSetType(f2,FNRATIONAL);
113:   coeffs[0] = 1.0;
114:   FNRationalSetNumerator(f2,1,coeffs);

116:   FNCreate(PETSC_COMM_WORLD,&f3);
117:   FNSetType(f3,FNEXP);
118:   FNSetScale(f3,-tau,1.0);

120:   /*
121:      Set the split operator. Note that A is passed first so that
122:      SUBSET_NONZERO_PATTERN can be used
123:   */
124:   mats[0] = A;  funs[0] = f2;
125:   mats[1] = Id; funs[1] = f1;
126:   mats[2] = B;  funs[2] = f3;
127:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);

129:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
130:              Customize nonlinear solver; set runtime options
131:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

133:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
134:   NEPSetDimensions(nep,1,PETSC_DEFAULT,PETSC_DEFAULT);
135:   NEPRIISetLagPreconditioner(nep,0);

137:   /*
138:      Set solver parameters at runtime
139:   */
140:   NEPSetFromOptions(nep);

142:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
143:                       Solve the eigensystem
144:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

146:   NEPSolve(nep);
147:   NEPGetDimensions(nep,&nev,NULL,NULL);
148:   PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);

150:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
151:                     Display solution and clean up
152:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

154:   /* show detailed info unless -terse option is given by user */
155:   PetscOptionsHasName(NULL,NULL,"-terse",&terse);
156:   if (terse) NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);
157:   else {
158:     PetscViewerPushFormat(PETSC_VIEWER_STDOUT_WORLD,PETSC_VIEWER_ASCII_INFO_DETAIL);
159:     NEPConvergedReasonView(nep,PETSC_VIEWER_STDOUT_WORLD);
160:     NEPErrorView(nep,NEP_ERROR_RELATIVE,PETSC_VIEWER_STDOUT_WORLD);
161:     PetscViewerPopFormat(PETSC_VIEWER_STDOUT_WORLD);
162:   }
163:   NEPDestroy(&nep);
164:   MatDestroy(&Id);
165:   MatDestroy(&A);
166:   MatDestroy(&B);
167:   FNDestroy(&f1);
168:   FNDestroy(&f2);
169:   FNDestroy(&f3);
170:   SlepcFinalize();
171:   return 0;
172: }

174: /*TEST

176:    testset:
177:       suffix: 1
178:       args: -nep_type {{rii slp narnoldi}} -terse
179:       filter: sed -e "s/[+-]0\.0*i//g"
180:       requires: !single

182:    test:
183:       suffix: 1_ciss
184:       args: -nep_type ciss -nep_ciss_extraction {{ritz hankel caa}} -rg_type ellipse -rg_ellipse_center 10 -rg_ellipse_radius 9.5 -nep_ncv 24 -terse
185:       requires: complex !single

187:    test:
188:       suffix: 2
189:       args: -nep_type interpol -nep_interpol_pep_extract {{none norm residual}} -rg_type interval -rg_interval_endpoints 5,20,-.1,.1 -nep_nev 3 -nep_target 5 -terse
190:       filter: sed -e "s/[+-]0\.0*i//g"
191:       requires: !single

193:    testset:
194:       args: -n 512 -nep_target 10 -nep_nev 3 -terse
195:       filter: sed -e "s/[+-]0\.0*i//g"
196:       requires: !single
197:       output_file: output/ex22_3.out
198:       test:
199:          suffix: 3
200:          args: -nep_type {{rii slp narnoldi}}
201:       test:
202:          suffix: 3_simpleu
203:          args: -nep_type {{rii slp narnoldi}} -nep_deflation_simpleu
204:       test:
205:          suffix: 3_slp_thres
206:          args: -nep_type slp -nep_slp_deflation_threshold 1e-8
207:       test:
208:          suffix: 3_rii_thres
209:          args: -nep_type rii -nep_rii_deflation_threshold 1e-8

211:    test:
212:       suffix: 4
213:       args: -nep_type interpol -rg_type interval -rg_interval_endpoints 5,20,-.1,.1 -nep_nev 3 -nep_target 5 -terse -nep_monitor draw::draw_lg
214:       filter: sed -e "s/[+-]0\.0*i//g"
215:       requires: x !single
216:       output_file: output/ex22_2.out

218: TEST*/