Class xlifepp::NedelecEdgeFirstHexahedronPk

class NedelecEdgeFirstHexahedronPk : public xlifepp::NedelecEdgeHexahedron

Nedelec edge first family of any order k on tetrahedron t (NCE1k) space Vk: Q_(k-1,k,k) x Q_(k,k-1,k)x Q_(k,k,k-1), Q_(k,l,m) monomials of degree at most k in x1, of degree at most l in x2, of degree at most m in x3, 3k(k+1)^2 dofs edge dofs: v-> int_e v.t q, q in P_(k-1)[e] k dofs by edge e face dofs (k>1) : v-> int_f (v x n).q, q in Q_(k-2,k-1) x Q_(k-1,k-2) 2k(k-1) dofs by face hexahedron dofs (k>1) : v-> int_t v.q, q in Q_(k-1,k-2,k-2) x Q_(k-2,k-1,k-2)x Q_(k-2,k-2,k-1) 3k(k-1)^2 dofs.

Public Functions

NedelecEdgeFirstHexahedronPk(const Interpolation *int_p)

Nedelec edge first family of order k on hexahedron (NE1k) Degrees Of Freedom of reference element, defined as moment D.o.Fs space Vk: Q_(k-1,k,k) x Q_(k,k-1,k)x Q_(k,k,k-1), Q_(k,l,m) monomials of degree at most k in x1, at most l in x2, at most m in x3, 3k(k+1)^2 dofs edge dofs: u-> int_e u.t q, q in P_(k-1)[e] k dofs by edge e face dofs (k>1) : u-> int_f (u x n).q, q in Q_(k-2,k-1) x Q_(k-1,k-2) 2k(k-1) dofs by face tetrahedron dofs (k>1): u-> int_t u.q, q in Q_(k-1,k-2,k-2) x Q_(k-2,k-1,k-2)x Q_(k-2,k-2,k-1) 3k(k-1)^2 dofs numbering of D.oFs are given by the basis functions order of dual spaces defining D.o.Fs beginning by edges, then faces and hexahedron.

NOTE: moment D.o.Fs can be reinterpreted as punctual D.o.Fs using a well adapted quadrature formulae we do not use this representation here

virtual void computeShapeFunctions()

compute shape functions as polynomials

compute shape functions as polynomials using general algorithm edge dofs: u-> int_e u.t q, q in P_(k-1)[e] k dofs by edge e face dofs (k>1) : u-> int_f (u x n).q, q in Q_(k-2,k-1) x Q_(k-1,k-2) 2k(k-1) dofs by face hexahedron dofs (k>1) : u-> int_t u.q, q in Q_(k-1,k-2,k-2) x Q_(k-2,k-1,k-2)x Q_(k-2,k-2,k-1) 3k(k-1)^2 dofs

virtual void computeShapeValues(std::vector<real_t>::const_iterator it_pt, ShapeValues &shv, const bool der1 = true, const bool der2 = false) const

compute shape values at a point

virtual Value evalEltDof(const FeDof &dof, const Function &f, const Function &gradf, const Function &grad2f) const

specific eval elt dof

virtual Value evalFaceDof(const FeDof &dof, const GeomElement &selt, const Function &f, const Function &gradf, const Function &grad2f) const

specific eval face dof function

virtual void interpolationData()

defines reference element interpolation data

interp defines Reference Element interpolation data

void pointCoordinates()

builds virtual coordinates of moment dofs

virtual void rotateDofs(const std::vector<number_t>&, ShapeValues &shv, const bool der1 = true, const bool der2 = false) const

rotation of face dofs to ensure matching of dofs on shared face

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

face dofs mapping

virtual void sideNumbering()

local numbering on faces (side)

virtual number_t sideofsideDofsMap(const number_t &n, const number_t &i, const number_t &j) const

edge dof mapping

void sideOfSideNumbering()

local numbering on edges (side of side)