dune-pdelab  2.7-git
geneobasis.hh
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1 #ifndef DUNE_PDELAB_BACKEND_ISTL_GENEO_GENEOBASIS_HH
2 #define DUNE_PDELAB_BACKEND_ISTL_GENEO_GENEOBASIS_HH
3 
4 #include <algorithm>
5 #include <functional>
6 
9 
10 #if HAVE_ARPACKPP
11 
12 namespace Dune {
13  namespace PDELab {
14 
21  template<class GFS, class M, class X, int dim>
22  class GenEOBasis : public SubdomainBasis<X>
23  {
26 
27  public:
28 
42  GenEOBasis(const GFS& gfs, const M& AF_exterior, const M& AF_ovlp, const double eigenvalue_threshold, X& part_unity,
43  int& nev, int nev_arpack = -1, double shift = 0.001, bool add_part_unity = false, int verbose = 0) {
45 
46  if (nev_arpack == -1)
47  nev_arpack = std::max(nev, 2);
48  if (nev_arpack < nev)
49  DUNE_THROW(Dune::Exception,"nev_arpack is less then nev!");
50 
51  // X * A_0 * X
52  M ovlp_mat(AF_ovlp);
53  for (auto row_iter = native(ovlp_mat).begin(); row_iter != native(ovlp_mat).end(); row_iter++) {
54  for (auto col_iter = row_iter->begin(); col_iter != row_iter->end(); col_iter++) {
55  *col_iter *= native(part_unity)[row_iter.index()] * native(part_unity)[col_iter.index()];
56  }
57  }
58 
59  // Setup Arpack for solving generalized eigenproblem
60  ArpackGeneo::ArPackPlusPlus_Algorithms<ISTLM, X> arpack(native(AF_exterior));
61  double eps = 0.0;
62 
63  std::vector<double> eigenvalues(nev_arpack,0.0);
64  std::vector<X> eigenvectors(nev_arpack,X(gfs,0.0));
65 
66  arpack.computeGenNonSymMinMagnitude(native(ovlp_mat), eps, eigenvectors, eigenvalues, shift);
67 
68  // Count eigenvectors below threshold
69  int cnt = -1;
70  if (eigenvalue_threshold >= 0) {
71  for (int i = 0; i < nev; i++) {
72  if (eigenvalues[i] > eigenvalue_threshold) {
73  cnt = i;
74  break;
75  }
76  }
77  if (verbose > 0)
78  std::cout << "Process " << gfs.gridView().comm().rank() << " picked " << cnt << " eigenvectors" << std::endl;
79  if (cnt == -1)
80  DUNE_THROW(Dune::Exception,"No eigenvalue above threshold - not enough eigenvalues computed!");
81  } else {
82  cnt = nev;
83  }
84 
85  // Write results to basis
86  this->local_basis.resize(cnt);
87  for (int base_id = 0; base_id < cnt; base_id++) {
88  this->local_basis[base_id] = std::make_shared<X>(part_unity);
89  // scale partition of unity with eigenvector
90  std::transform(
91  this->local_basis[base_id]->begin(),this->local_basis[base_id]->end(),
92  eigenvectors[base_id].begin(),
93  this->local_basis[base_id]->begin(),
94  std::multiplies<>()
95  );
96  }
97 
98  // Normalize basis vectors
99  for (auto& v : this->local_basis) {
100  *v *= 1.0 / v->two_norm2();
101  }
102 
103  // Optionally add partition of unity to eigenvectors
104  // Only if there is no near-zero eigenvalue (that usually already corresponds to a partition of unity!)
105  if (add_part_unity && eigenvalues[0] > 1E-10) {
106  this->local_basis.insert (this->local_basis.begin(), std::make_shared<X>(part_unity));
107  this->local_basis.pop_back();
108  }
109  }
110  };
111 
112 
113  }
114 }
115 
116 #endif
117 
118 #endif //DUNE_PDELAB_BACKEND_ISTL_GENEO_GENEOBASIS_HH
For backward compatibility – Do not use this!
Definition: adaptivity.hh:28
std::enable_if< std::is_base_of< impl::WrapperBase, T >::value, Native< T > & >::type native(T &t)
Definition: backend/interface.hh:192
typename native_type< T >::type Native
Alias of the native container type associated with T or T itself if it is not a backend wrapper.
Definition: backend/interface.hh:176