Class xlifepp::LagrangeTetrahedron#

class LagrangeTetrahedron : public xlifepp::RefTetrahedron #

defines Lagrange Reference Element interpolation data on tetrahedra

Subclassed by xlifepp::LagrangeStdTetrahedron< Pk >, xlifepp::LagrangeStdTetrahedronPk

Public Functions

LagrangeTetrahedron(const Interpolation *interp_p)#

constructor by interpolation

LagrangeTetrahedron constructor for Lagrange reference elements.

virtual ~LagrangeTetrahedron()#: destructor

void buildBarycentricSideDof()#: build barycentricSideDofMap

virtual number_t sideDofsMap(const number_t &n, const number_t &i, const number_t &j, const number_t &k = 0) const#

internal side dofs mapping when vertices of side are permuted

internal side dofs mapping when vertices of side are permuted this function returns the number of the n-th internal dof of a face where vertices are permuted if no permutation, it returns n

Numbering of internal side dofs of Pk tetrahedron, p= k-3

1      2      2          2              2                  2                      2
p=0    | \    | \        | \            | \                | \                    | \
       3---1  5   4      5   7          5  10              5  13                  5  16
        p=1   |     \    |     \        |     \            |     \                |     \
              3---6---1  8  10   4      8  14   7          8  17  10              8  20  13
                 p=2     |         \    |  |  \   \        |  | \    \            |  | \    \
                         3---6---9---1 11  15--13   4     11  20  19   7         11  23  25  10
                               p=3      |             \    |  |     \    \        |  |     \    \
                                        3---6---9--12---1 14  18--21--16   4     14  26  28  22   7
                                                 p=4       |                 \    |  |         \    \
                                                           3---6---9--12--15---1 17  21--24--27--19   4
                                                                    p=5           |                     \
                                                                                  3---6---9--12--15--18---1
                                                                                             p=6

Map exemple for P4 tetrahedron

2 1 | \ | \ | \ | \ | \ | \ sideDofsMap(1,3,1,2)=2 | 2 \ | 1 \ sideDofsMap(2,3,1,2)=3 | | \ \ | | \ \ sideDofsMap(3,3,1,2)=1 | 3—1 \ | 2—3 \ | \ | \ 3—————1 2———–—3

standard face permuted face

inline virtual number_t sideofsideDofsMap(const number_t &n, const number_t &i, const number_t &j = 0) const#: internal side dofs mapping when vertices of side are permuted

Public Members

std::map<Triplet<number_t>, number_t> barycentricSideDofMap#: internal dof on side (face) ordered by barycentric coordinates

std::vector<Triplet<number_t>> barycentricSideDofs#: dof barycentric coordinates