Rodin›Variational

FeketeTetrahedron

Cached Fekete-type nodes on the reference tetrahedron for degree K.

Defined in Rodin/Variational/H1/Fekete.h

template <
  size_t K>
class FeketeTetrahedron;
Template parameters
K Polynomial degree on the tetrahedron.

Reference tetrahedron: (0,0,0), (1,0,0), (0,1,0), (0,0,1).

Construction:

  • start from equispaced barycentric nodes (integer lattice with i + j + k <= K, normalized by K),
  • apply warp–blend algorithm (WarpBlendTetrahedron<K>) to move them towards Fekete-type positions.

For a given polynomial degree K, the number of nodes is $ (K + 1)(K + 2)(K + 3) / 6 $ .

Nodes are computed once per template instantiation and cached.

Public static variables

static size_t Count constexpr
Total number of nodes: (K+1)(K+2)(K+3)/6.

Public static functions

static auto getNodes() -> const std::array<Math::SpatialPoint, Count>&

Function documentation

static const std::array<Math::SpatialPoint, Count>& getNodes()

Returns The nodes.

Return cached nodes as a std::array.