pbat::fem::CElement Concept Reference

Reference finite element. More...

#include <Concepts.h>

Concept definition

template<class T>
concept pbat::fem::CElement =  requires(T t)
{
    typename T::AffineBaseType;
    {T::bHasConstantJacobian}->std::convertible_to<bool>;
    
    typename T::template QuadratureType<1, Scalar>;
    {T::kOrder}->std::convertible_to<int>;
    {T::kDims}->std::convertible_to<int>;
    {T::kNodes}->std::convertible_to<int>;
    requires common::CContiguousIndexRange<decltype(T::Coordinates)>;
    requires common::CContiguousIndexRange<decltype(T::Vertices)>;
    {t.N(Vector<T::kDims>{})}->std::convertible_to<Vector<T::kNodes>>;
    {t.GradN(Vector<T::kDims>{})}->std::convertible_to<Matrix<T::kNodes, T::kDims>>;
}

Detailed Description

Reference finite element.

Example type TElement satisfying concept CElement

template <int Order>
struct TElement
{
    using AffineBaseType = TElement<1>;
 
    static int constexpr kOrder;
    static int constexpr kDims;
    static int constexpr kNodes;
    static std::array<int, kNodes * kDims> constexpr Coordinates;
    static std::array<int, AffineBaseType::kNodes> constexpr Vertices;
 
    static bool constexpr bHasConstantJacobian;
 
    template <int PolynomialOrder>
    using QuadratureType = math::SymmetricSimplexPolynomialQuadratureRule<kDims,
PolynomialOrder>;
 
    template <class TDerived, class TScalar = typename TDerived::Scalar>
    static Eigen::Vector<TScalar, kNodes>
    N(Eigen::DenseBase<TDerived> const& X);
 
    static Matrix<kNodes, kDims> GradN(Vector<kDims> const& X);
};

Note

• Divide Coordinates by kOrder to obtain actual coordinates in the reference element
• Vertices are indices into nodes [0,kNodes-1] revealing vertices of the element
• bHasConstantJacobian is true if the Jacobian is constant over the element
• QuadratureType proposes a quadrature rule suitable for integrating over the element
• N computes the nodal shape functions evaluated at the given reference point X
• GradN computes the gradient of the nodal shape functions evaluated at the given reference point X

Template Parameters

T	Element type