Rodin›Variational

Grad

Represents the gradient $ \nabla u $ of a scalar function $ u $ .

template <
  class Operand>
class Grad;

Specializations

SpecializationDescription
GridFunction<…>
Full specialization
template <
  size_t K,
  class Scalar,
  class Mesh,
  class Data>
class Grad<
  GridFunction< H1< K, Math::SpatialMatrix< Scalar >, Mesh >, Data >> final;
Physical gradient of a matrix H1 solution, with derivative axis last. Uses this family's scalar basis and component ordering.
GridFunction<H1<K, Scalar, Mesh>, Data>
Full specialization
template <
  size_t K,
  class Scalar,
  class Mesh,
  class Data>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  GridFunction< H1< K, Scalar, Mesh >, Data >> final;
Gradient of a GridFunction on H1<K> space.
GridFunction<…>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Data>
class Grad<
  GridFunction< P0< Math::SpatialMatrix< Scalar >, Mesh >, Data >> final;
Physical gradient of a matrix P0 solution, with derivative axis last. Uses this family's scalar basis and component ordering.
GridFunction<P0<Range, Mesh>, Data>
Full specialization
template <
  class Range,
  class Data,
  class Mesh>
requires (!FormLanguage::IsMatrixRange<Range>::Value)
class Grad<
  GridFunction< P0< Range, Mesh >, Data >> final;
Gradient of a P0 GridFunction.
GridFunction<…>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Data>
class Grad<
  GridFunction< P0g< Math::SpatialMatrix< Scalar >, Mesh >, Data >> final;
Physical gradient of a matrix P0g solution, with derivative axis last. Uses this family's scalar basis and component ordering.
GridFunction<P0g<Scalar, Mesh>, Data>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Data>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  GridFunction< P0g< Scalar, Mesh >, Data >> final;
Gradient of a P0g grid function.
GridFunction<…>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Data>
class Grad<
  GridFunction< P1< Math::SpatialMatrix< Scalar >, Mesh >, Data >> final;
Physical gradient of a matrix P1 solution, with derivative axis last. Uses this family's scalar basis and component ordering.
GridFunction<P1<Scalar, Mesh>, Data>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Data>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  GridFunction< P1< Scalar, Mesh >, Data >> final;
Gradient of a P1 grid function.
ShapeFunction<Derived, …>
Full specialization
template <
  size_t K,
  class Scalar,
  class Mesh,
  class Derived,
  ShapeFunctionSpaceType Space>
class Grad<
  ShapeFunction< Derived, H1< K, Math::SpatialMatrix< Scalar >, Mesh >, Space >> final;
Physical gradients of matrix H1 trial or test bases.
ShapeFunction<Derived, …>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Derived,
  ShapeFunctionSpaceType Space>
class Grad<
  ShapeFunction< Derived, P0< Math::SpatialMatrix< Scalar >, Mesh >, Space >> final;
Physical gradients of matrix P0 trial or test bases.
ShapeFunction<Derived, …>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Derived,
  ShapeFunctionSpaceType Space>
class Grad<
  ShapeFunction< Derived, P0g< Math::SpatialMatrix< Scalar >, Mesh >, Space >> final;
Physical gradients of matrix P0g trial or test bases.
ShapeFunction<Derived, …>
Full specialization
template <
  class Scalar,
  class Mesh,
  class Derived,
  ShapeFunctionSpaceType Space>
class Grad<
  ShapeFunction< Derived, P1< Math::SpatialMatrix< Scalar >, Mesh >, Space >> final;
Physical gradients of matrix P1 trial or test bases.
ShapeFunction<NestedDerived, …>
Full specialization
template <
  size_t K,
  class NestedDerived,
  class Scalar,
  class Mesh,
  ShapeFunctionSpaceType SpaceType>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  ShapeFunction< NestedDerived, H1< K, Scalar, Mesh >, SpaceType >> final;
Gradient of a ShapeFunction on H1<K> space.
ShapeFunction<NestedDerived, …>
Full specialization
template <
  class NestedDerived,
  class Scalar,
  class Mesh,
  ShapeFunctionSpaceType SpaceType>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  ShapeFunction< NestedDerived, P0< Scalar, Mesh >, SpaceType >> final;
Gradient of a P0 ShapeFunction.
ShapeFunction<NestedDerived, …>
Full specialization
template <
  class NestedDerived,
  class Scalar,
  class Mesh,
  ShapeFunctionSpaceType SpaceType>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  ShapeFunction< NestedDerived, P0g< Scalar, Mesh >, SpaceType >> final;
Gradient of a P0g shape function.
ShapeFunction<NestedDerived, …>
Full specialization
template <
  class NestedDerived,
  class Scalar,
  class Mesh,
  ShapeFunctionSpaceType SpaceType>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class Grad<
  ShapeFunction< NestedDerived, P1< Scalar, Mesh >, SpaceType >> final;
Gradient of a ShapeFunction.
Template parameters
Operand Type of operand

Represents the mathematical expression:

\[ \nabla \text{Operand} \]

where Operand is a type representing a scalar function $ u : \mathbb{R}^n \rightarrow \mathbb{R} $ and the gradient $ \nabla u : \mathbb{R}^n \rightarrow \mathbb{R}^n $ at the point $ x = (x_1, \ldots, x_n) $ is defined by:

\[ \nabla u (x) = \left[ \dfrac{\partial u}{\partial x_1}(x), \ldots, \dfrac{\partial u}{\partial x_n}(x) \right]^T \]