Actual source code: test10.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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[] = "Tests multiple calls to NEPSolve(). Based on ex22.c.\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,Istart,Iend,i;
 44:   PetscReal      tau=0.001,h,a=20,xi;

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

 53:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 54:              Create functions that define the split operator
 55:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

 57:   /* f1=-lambda */
 58:   FNCreate(PETSC_COMM_WORLD,&f1);
 59:   FNSetType(f1,FNRATIONAL);
 60:   coeffs[0] = -1.0; coeffs[1] = 0.0;
 61:   FNRationalSetNumerator(f1,2,coeffs);

 63:   /* f2=1.0 */
 64:   FNCreate(PETSC_COMM_WORLD,&f2);
 65:   FNSetType(f2,FNRATIONAL);
 66:   coeffs[0] = 1.0;
 67:   FNRationalSetNumerator(f2,1,coeffs);

 69:   /* f3=exp(-tau*lambda) */
 70:   FNCreate(PETSC_COMM_WORLD,&f3);
 71:   FNSetType(f3,FNEXP);
 72:   FNSetScale(f3,-tau,1.0);

 74:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 75:                          Create problem matrices
 76:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

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

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

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

121:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
122:               Create nonlinear eigensolver and set options
123:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

125:   NEPCreate(PETSC_COMM_WORLD,&nep);
126:   mats[0] = A;  funs[0] = f2;
127:   mats[1] = Id; funs[1] = f1;
128:   mats[2] = B;  funs[2] = f3;
129:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
130:   NEPSetTolerances(nep,1e-9,PETSC_DEFAULT);
131:   NEPSetFromOptions(nep);

133:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
134:                       Solve the eigensystem
135:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

137:   NEPSolve(nep);
138:   NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);

140:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
141:                    Create problem matrices of size 2*n
142:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

144:   MatDestroy(&Id);
145:   MatDestroy(&A);
146:   MatDestroy(&B);
147:   n *= 2;
148:   PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, tau=%g\n\n",n,(double)tau);
149:   h = PETSC_PI/(PetscReal)(n+1);

151:   /* Identity matrix */
152:   MatCreate(PETSC_COMM_WORLD,&Id);
153:   MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
154:   MatSetFromOptions(Id);
155:   MatSetUp(Id);
156:   MatGetOwnershipRange(Id,&Istart,&Iend);
157:   for (i=Istart;i<Iend;i++) {
158:     MatSetValue(Id,i,i,1.0,INSERT_VALUES);
159:   }
160:   MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
161:   MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
162:   MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);

164:   /* A = 1/h^2*tridiag(1,-2,1) + a*I */
165:   MatCreate(PETSC_COMM_WORLD,&A);
166:   MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
167:   MatSetFromOptions(A);
168:   MatSetUp(A);
169:   MatGetOwnershipRange(A,&Istart,&Iend);
170:   for (i=Istart;i<Iend;i++) {
171:     if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
172:     if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
173:     MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
174:   }
175:   MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
176:   MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
177:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);

179:   /* B = diag(b(xi)) */
180:   MatCreate(PETSC_COMM_WORLD,&B);
181:   MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
182:   MatSetFromOptions(B);
183:   MatSetUp(B);
184:   MatGetOwnershipRange(B,&Istart,&Iend);
185:   for (i=Istart;i<Iend;i++) {
186:     xi = (i+1)*h;
187:     b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
188:     MatSetValue(B,i,i,b,INSERT_VALUES);
189:   }
190:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
191:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
192:   MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);

194:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
195:        Solve again, calling NEPReset() since matrix size has changed
196:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

198:   NEPReset(nep);  /* if this is omitted, it will be called in NEPSetSplitOperators() */
199:   mats[0] = A;  funs[0] = f2;
200:   mats[1] = Id; funs[1] = f1;
201:   mats[2] = B;  funs[2] = f3;
202:   NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
203:   NEPSolve(nep);
204:   NEPErrorView(nep,NEP_ERROR_RELATIVE,NULL);

206:   NEPDestroy(&nep);
207:   MatDestroy(&Id);
208:   MatDestroy(&A);
209:   MatDestroy(&B);
210:   FNDestroy(&f1);
211:   FNDestroy(&f2);
212:   FNDestroy(&f3);
213:   SlepcFinalize();
214:   return ierr;
215: }

217: /*TEST

219:    testset:
220:       nsize: 2
221:       requires: !single
222:       output_file: output/test10_1.out
223:       test:
224:          suffix: 1
225:          args: -nep_type {{rii narnoldi}} -nep_target 0.55
226:       test:
227:          suffix: 1_slp
228:          args: -nep_type slp -nep_slp_st_pc_type redundant
229:       test:
230:          suffix: 1_interpol
231:          args: -nep_type interpol -rg_type interval -rg_interval_endpoints .5,1,-.1,.1 -nep_target .7 -nep_interpol_st_pc_type redundant
232:       test:
233:          suffix: 1_narnoldi_sync
234:          args: -nep_type narnoldi -ds_parallel synchronized

236:    test:
237:       suffix: 2
238:       args: -nep_nev 2 -nep_type interpol -rg_type interval -rg_interval_endpoints .5,15,-.1,.1 -nep_target .7 -nep_interpol_pep_type jd -nep_interpol_st_pc_type sor
239:       requires: !single

241: TEST*/