Grad.h file

Gradient operator specialization for P1 (piecewise linear) functions.

On affine simplices, the gradient of a P1 function is constant on each element:

where are the P1 basis functions and is the spatial dimension.

Namespaces

namespace Rodin: The Rodin library for finite element methods and shape optimization.
namespace Rodin::Variational: Finite element spaces, fields, and variational problems.
namespace Rodin::FormLanguage: Typed expressions for constructing variational forms.

Classes

template<class Scalar, class Mesh, class Data> class Rodin::Variational::Grad<GridFunction<P1<Scalar, Mesh>, Data>>: Gradient of a P1 grid function.
template<class NestedDerived, class Scalar, class Mesh, ShapeFunctionSpaceType SpaceType> class Rodin::Variational::Grad<ShapeFunction<NestedDerived, P1<Scalar, Mesh>, SpaceType>>: Gradient of a ShapeFunction.
struct Rodin::Variational::Grad<ShapeFunction<NestedDerived, P1<Scalar, Mesh>, SpaceType>>::Cache: Per-cell tabulation cache.
struct Rodin::Variational::Grad<ShapeFunction<NestedDerived, P1<Scalar, Mesh>, SpaceType>>::Cache::CellKey: Key identifying the cell a tabulation was computed for.
struct Rodin::Variational::Grad<ShapeFunction<NestedDerived, P1<Scalar, Mesh>, SpaceType>>::Cache::QuadraturePointKey: Key identifying the quadrature point a tabulation was computed for.
template<class Scalar, class Mesh, class Data> struct Rodin::FormLanguage::Traits<Variational::Grad<Variational::GridFunction<Variational::P1<Math::SpatialMatrix<Scalar>, Mesh>, Data>>>: Rank-three physical gradient range for the matrix P1 solution.
template<class Scalar, class Mesh, class Derived, Variational::ShapeFunctionSpaceType Space> struct Rodin::FormLanguage::Traits<Variational::Grad<Variational::ShapeFunction<Derived, Variational::P1<Math::SpatialMatrix<Scalar>, Mesh>, Space>>>: Rank-three physical gradient range for matrix P1 shape functions.
template<class Scalar, class Mesh, class Data> class Rodin::Variational::Grad<GridFunction<P1<Math::SpatialMatrix<Scalar>, Mesh>, Data>>: Physical gradient of a matrix P1 solution, with derivative axis last. Uses this family's scalar basis and component ordering.
template<class Scalar, class Mesh, class Derived, ShapeFunctionSpaceType Space> class Rodin::Variational::Grad<ShapeFunction<Derived, P1<Math::SpatialMatrix<Scalar>, Mesh>, Space>>: Physical gradients of matrix P1 trial or test bases.