Jacobian

Represents the Jacobian matrix of a type.

template <
  class Operand>
class Jacobian;

Specializations

SpecializationDescription
GridFunction<FES, Data>
Full specialization
template <
  class FES,
  class Data>
requires FormLanguage::IsMatrixRange< typename FormLanguage::Traits<FES>::RangeType>::Value
class Jacobian<
  GridFunction< FES, Data >> final;
Matrix-field jacobian, $ J_{ijk}=\partial_k A_{ij} $.
GridFunction<…>
Full specialization
template <
  size_t K,
  class Scalar,
  class Data,
  class Mesh>
class Jacobian<
  GridFunction< H1< K, Math::SpatialVector< Scalar >, Mesh >, Data >> final;
Jacobian of an H1 vector GridFunction.
GridFunction<…>
Full specialization
template <
  class Data,
  class Mesh,
  class Scalar>
class Jacobian<
  GridFunction< P0g< Math::SpatialVector< Scalar >, Mesh >, Data >> final;
Jacobian of a P0g vector GridFunction (identically zero).
GridFunction<…>
Full specialization
template <
  class Data,
  class Mesh,
  class Scalar>
class Jacobian<
  GridFunction< P1< Math::SpatialVector< Scalar >, Mesh >, Data >> final;
Jacobian of a P1 vector GridFunction.
ShapeFunction<Derived, FES, Space>
Full specialization
template <
  class Derived,
  class FES,
  ShapeFunctionSpaceType Space>
requires FormLanguage::IsMatrixRange< typename FormLanguage::Traits<FES>::RangeType>::Value
class Jacobian<
  ShapeFunction< Derived, FES, Space >> final;
Matrix-basis jacobian, $ J_{ijk}=\partial_k A_{ij} $.
ShapeFunction<NestedDerived, …>
Full specialization
template <
  size_t K,
  class NestedDerived,
  class Scalar,
  class Mesh,
  ShapeFunctionSpaceType Space>
class Jacobian<
  ShapeFunction< NestedDerived, H1< K, Math::SpatialVector< Scalar >, Mesh >, Space >> final;
Jacobian of an H1 ShapeFunction object.
ShapeFunction<…>
Full specialization
template <
  class ShapeFunctionDerived,
  class Scalar,
  class Mesh,
  ShapeFunctionSpaceType Space>
class Jacobian<
  ShapeFunction< ShapeFunctionDerived, P0g< Math::SpatialVector< Scalar >, Mesh >, Space >> final;
Jacobian of a P0g vector ShapeFunction (identically zero).
ShapeFunction<…>
Full specialization
template <
  class ShapeFunctionDerived,
  class Range,
  class Mesh,
  ShapeFunctionSpaceType Space>
requires (!FormLanguage::IsMatrixRange<Range>::Value)
class Jacobian<
  ShapeFunction< ShapeFunctionDerived, P1< Range, Mesh >, Space >> final;
Jacobian of a P1 ShapeFunction object.
Template parameters
Operand Type of operand

Represents the following mathematical expression:

\[ \mathbf{J}_\mathrm{Operand} \]

where Operand is a type representing a function $ u : \mathbb{R}^s \rightarrow \mathbb{R}^d $ whose Jacobian matrix $ \mathbf{J}_u(x) $ at any point $ x = (x_1, \ldots, x_s) $ is defined by the $ d \times s $ matrix:

\[\mathbf{J}_u = \begin{bmatrix} \dfrac{\partial u_1}{\partial x_1} & \ldots & \dfrac{\partial u_s}{\partial x_1}\\ \vdots & \ddots & \vdots\\ \dfrac{\partial u_1}{\partial x_d} & \ldots & \dfrac{\partial u_s}{\partial x_d} \end{bmatrix} . \]