Actual source code: test13.c
slepc-3.18.1 2022-11-02
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[] = "Test the NEPProjectOperator() function.\n\n"
12: "This is based on ex22.\n"
13: "The command line options are:\n"
14: " -n <n>, where <n> = number of grid subdivisions.\n"
15: " -tau <tau>, where <tau> is the delay parameter.\n";
17: /*
18: Solve parabolic partial differential equation with time delay tau
20: u_t = u_xx + a*u(t) + b*u(t-tau)
21: u(0,t) = u(pi,t) = 0
23: with a = 20 and b(x) = -4.1+x*(1-exp(x-pi)).
25: Discretization leads to a DDE of dimension n
27: -u' = A*u(t) + B*u(t-tau)
29: which results in the nonlinear eigenproblem
31: (-lambda*I + A + exp(-tau*lambda)*B)*u = 0
32: */
34: #include <slepcnep.h>
36: int main(int argc,char **argv)
37: {
38: NEP nep;
39: Mat Id,A,B,mats[3];
40: FN f1,f2,f3,funs[3];
41: BV V;
42: DS ds;
43: Vec v;
44: PetscScalar coeffs[2],b,*M;
45: PetscInt n=32,Istart,Iend,i,j,k,nc;
46: PetscReal tau=0.001,h,a=20,xi;
49: SlepcInitialize(&argc,&argv,(char*)0,help);
50: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
51: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
52: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%" PetscInt_FMT ", tau=%g\n",n,(double)tau);
53: h = PETSC_PI/(PetscReal)(n+1);
55: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
56: Create nonlinear eigensolver context
57: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
59: NEPCreate(PETSC_COMM_WORLD,&nep);
61: /* Identity matrix */
62: MatCreateConstantDiagonal(PETSC_COMM_WORLD,PETSC_DECIDE,PETSC_DECIDE,n,n,1.0,&Id);
63: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
65: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
66: MatCreate(PETSC_COMM_WORLD,&A);
67: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
68: MatSetFromOptions(A);
69: MatSetUp(A);
70: MatGetOwnershipRange(A,&Istart,&Iend);
71: for (i=Istart;i<Iend;i++) {
72: if (i>0) MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES);
73: if (i<n-1) MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES);
74: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
75: }
76: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
77: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
78: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
80: /* B = diag(b(xi)) */
81: MatCreate(PETSC_COMM_WORLD,&B);
82: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
83: MatSetFromOptions(B);
84: MatSetUp(B);
85: MatGetOwnershipRange(B,&Istart,&Iend);
86: for (i=Istart;i<Iend;i++) {
87: xi = (i+1)*h;
88: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
89: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
90: }
91: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
92: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
93: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
95: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
96: FNCreate(PETSC_COMM_WORLD,&f1);
97: FNSetType(f1,FNRATIONAL);
98: coeffs[0] = -1.0; coeffs[1] = 0.0;
99: FNRationalSetNumerator(f1,2,coeffs);
101: FNCreate(PETSC_COMM_WORLD,&f2);
102: FNSetType(f2,FNRATIONAL);
103: coeffs[0] = 1.0;
104: FNRationalSetNumerator(f2,1,coeffs);
106: FNCreate(PETSC_COMM_WORLD,&f3);
107: FNSetType(f3,FNEXP);
108: FNSetScale(f3,-tau,1.0);
110: /* Set the split operator */
111: mats[0] = A; funs[0] = f2;
112: mats[1] = Id; funs[1] = f1;
113: mats[2] = B; funs[2] = f3;
114: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
115: NEPSetType(nep,NEPNARNOLDI);
116: NEPSetFromOptions(nep);
118: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
119: Project the NEP
120: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
122: NEPSetUp(nep);
123: NEPGetBV(nep,&V);
124: BVGetSizes(V,NULL,NULL,&nc);
125: for (i=0;i<nc;i++) {
126: BVGetColumn(V,i,&v);
127: VecSetValue(v,i,1.0,INSERT_VALUES);
128: VecAssemblyBegin(v);
129: VecAssemblyEnd(v);
130: BVRestoreColumn(V,i,&v);
131: }
132: NEPGetDS(nep,&ds);
133: DSSetType(ds,DSNEP);
134: DSNEPSetFN(ds,3,funs);
135: DSAllocate(ds,nc);
136: DSSetDimensions(ds,nc,0,0);
137: NEPProjectOperator(nep,0,nc);
139: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
140: Display projected matrices and clean up
141: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
143: for (k=0;k<3;k++) {
144: DSGetArray(ds,DSMatExtra[k],&M);
145: PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%" PetscInt_FMT " = \n",k);
146: for (i=0;i<nc;i++) {
147: for (j=0;j<nc;j++) PetscPrintf(PETSC_COMM_WORLD," %.5g",(double)PetscRealPart(M[i+j*nc]));
148: PetscPrintf(PETSC_COMM_WORLD,"\n");
149: }
150: DSRestoreArray(ds,DSMatExtra[k],&M);
151: }
153: NEPDestroy(&nep);
154: MatDestroy(&Id);
155: MatDestroy(&A);
156: MatDestroy(&B);
157: FNDestroy(&f1);
158: FNDestroy(&f2);
159: FNDestroy(&f3);
160: SlepcFinalize();
161: return 0;
162: }
164: /*TEST
166: test:
167: suffix: 1
168: args: -nep_ncv 5
170: TEST*/