Actual source code: test13.c
slepc-3.12.2 2020-01-13
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[] = "Test the NEPProjectOperator() operator.\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);if (ierr) return ierr;
50: PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
51: PetscOptionsGetReal(NULL,NULL,"-tau",&tau,NULL);
52: PetscPrintf(PETSC_COMM_WORLD,"\n1-D Delay Eigenproblem, n=%D, 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: MatCreate(PETSC_COMM_WORLD,&Id);
63: MatSetSizes(Id,PETSC_DECIDE,PETSC_DECIDE,n,n);
64: MatSetFromOptions(Id);
65: MatSetUp(Id);
66: MatGetOwnershipRange(Id,&Istart,&Iend);
67: for (i=Istart;i<Iend;i++) {
68: MatSetValue(Id,i,i,1.0,INSERT_VALUES);
69: }
70: MatAssemblyBegin(Id,MAT_FINAL_ASSEMBLY);
71: MatAssemblyEnd(Id,MAT_FINAL_ASSEMBLY);
72: MatSetOption(Id,MAT_HERMITIAN,PETSC_TRUE);
74: /* A = 1/h^2*tridiag(1,-2,1) + a*I */
75: MatCreate(PETSC_COMM_WORLD,&A);
76: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,n,n);
77: MatSetFromOptions(A);
78: MatSetUp(A);
79: MatGetOwnershipRange(A,&Istart,&Iend);
80: for (i=Istart;i<Iend;i++) {
81: if (i>0) { MatSetValue(A,i,i-1,1.0/(h*h),INSERT_VALUES); }
82: if (i<n-1) { MatSetValue(A,i,i+1,1.0/(h*h),INSERT_VALUES); }
83: MatSetValue(A,i,i,-2.0/(h*h)+a,INSERT_VALUES);
84: }
85: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
86: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
87: MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
89: /* B = diag(b(xi)) */
90: MatCreate(PETSC_COMM_WORLD,&B);
91: MatSetSizes(B,PETSC_DECIDE,PETSC_DECIDE,n,n);
92: MatSetFromOptions(B);
93: MatSetUp(B);
94: MatGetOwnershipRange(B,&Istart,&Iend);
95: for (i=Istart;i<Iend;i++) {
96: xi = (i+1)*h;
97: b = -4.1+xi*(1.0-PetscExpReal(xi-PETSC_PI));
98: MatSetValues(B,1,&i,1,&i,&b,INSERT_VALUES);
99: }
100: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
101: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
102: MatSetOption(B,MAT_HERMITIAN,PETSC_TRUE);
104: /* Functions: f1=-lambda, f2=1.0, f3=exp(-tau*lambda) */
105: FNCreate(PETSC_COMM_WORLD,&f1);
106: FNSetType(f1,FNRATIONAL);
107: coeffs[0] = -1.0; coeffs[1] = 0.0;
108: FNRationalSetNumerator(f1,2,coeffs);
110: FNCreate(PETSC_COMM_WORLD,&f2);
111: FNSetType(f2,FNRATIONAL);
112: coeffs[0] = 1.0;
113: FNRationalSetNumerator(f2,1,coeffs);
115: FNCreate(PETSC_COMM_WORLD,&f3);
116: FNSetType(f3,FNEXP);
117: FNSetScale(f3,-tau,1.0);
119: /* Set the split operator */
120: mats[0] = A; funs[0] = f2;
121: mats[1] = Id; funs[1] = f1;
122: mats[2] = B; funs[2] = f3;
123: NEPSetSplitOperator(nep,3,mats,funs,SUBSET_NONZERO_PATTERN);
124: NEPSetType(nep,NEPNARNOLDI);
125: NEPSetFromOptions(nep);
127: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
128: Project the NEP
129: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
131: NEPSetUp(nep);
132: NEPGetBV(nep,&V);
133: BVGetSizes(V,NULL,NULL,&nc);
134: for (i=0;i<nc;i++) {
135: BVGetColumn(V,i,&v);
136: VecSetValue(v,i,1.0,INSERT_VALUES);
137: VecAssemblyBegin(v);
138: VecAssemblyEnd(v);
139: BVRestoreColumn(V,i,&v);
140: }
141: NEPGetDS(nep,&ds);
142: DSSetType(ds,DSNEP);
143: DSNEPSetFN(ds,3,funs);
144: DSAllocate(ds,nc);
145: DSSetDimensions(ds,nc,0,0,0);
146: NEPProjectOperator(nep,0,nc);
148: /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
149: Display projected matrices and clean up
150: - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
152: for (k=0;k<3;k++) {
153: DSGetArray(ds,DSMatExtra[k],&M);
154: PetscPrintf(PETSC_COMM_WORLD,"\nMatrix E%d = \n",k);
155: for (i=0;i<nc;i++) {
156: for (j=0;j<nc;j++) {
157: PetscPrintf(PETSC_COMM_WORLD," %.5g",(double)PetscRealPart(M[i+j*nc]));
158: }
159: PetscPrintf(PETSC_COMM_WORLD,"\n");
160: }
161: DSRestoreArray(ds,DSMatExtra[k],&M);
162: }
164: NEPDestroy(&nep);
165: MatDestroy(&Id);
166: MatDestroy(&A);
167: MatDestroy(&B);
168: FNDestroy(&f1);
169: FNDestroy(&f2);
170: FNDestroy(&f3);
171: SlepcFinalize();
172: return ierr;
173: }
175: /*TEST
177: test:
178: suffix: 1
179: args: -nep_ncv 5
180: requires: double
182: TEST*/