Form language (differential operators)

Description

Differential operators.

Collaboration diagram for Form language (differential operators):

Functions
template<class B , class TP , std::size_t argIndex>
auto	Dune::Fufem::Forms::jacobian (const FEFunctionOperator< B, TP, argIndex > &op)
	Obtain the jacobian of an operator.
template<class B , class TP , std::size_t argIndex>
auto	Dune::Fufem::Forms::divergence (const FEFunctionOperator< B, TP, argIndex > &op)
	Obtain the divergence of an operator.
template<class B , class TP , std::size_t argIndex>
auto	Dune::Fufem::Forms::curl (const FEFunctionOperator< B, TP, argIndex > &op)
	Obtain the curl of an operator.
template<class... Ops> requires requires(const Ops&... ops) { SumOperator(jacobian(ops)...); }
auto	Dune::Fufem::Forms::jacobian (const SumOperator< Ops... > &op)
	Obtain the jacobian of a sum of operators.
template<class... Ops> requires requires(const Ops&... ops) { SumOperator(jacobian(ops)...); }
auto	Dune::Fufem::Forms::divergence (const SumOperator< Ops... > &op)
	Obtain the divergence of a sum of operators.
template<class... Ops> requires requires(const Ops&... ops) { SumOperator(curl(ops)...); }
auto	Dune::Fufem::Forms::curl (const SumOperator< Ops... > &op)
	Obtain the curl of a sum of operators.
template<class Op > requires requires {Fufem::Forms::transpose(jacobian(op));}
auto	Dune::Fufem::Forms::gradient (const Op &op)
	Obtain the gradient of an operator.
template<class Op > requires requires {Fufem::Forms::transpose(jacobian(op));}
auto	Dune::Fufem::Forms::grad (const Op &op)
	Obtain the gradient of an operator.
template<class Op > requires requires {divergence(op);}
auto	Dune::Fufem::Forms::div (const Op &op)
	Obtain the divergence of an operator.
template<class Op > requires requires {curl(op);}
auto	Dune::Fufem::Forms::rot (const Op &op)
	Obtain the curl of an operator.
template<class Op > requires requires {grad(op);}
auto	Dune::Fufem::Forms::D (const Op &op, std::size_t k)
	Obtain the i-th partial derivative of an operator.

Function Documentation

curl() [1/2]

template<class B , class TP , std::size_t argIndex>

auto Dune::Fufem::Forms::curl

(

const FEFunctionOperator< B, TP, argIndex > &

op

)

Obtain the curl of an operator.

Parameters

op	The operator to differentiate

This is implemented for 2d and 3d vector fields only.

curl() [2/2]

template<class... Ops>
requires requires(const Ops&... ops) { SumOperator(curl(ops)...); }

auto Dune::Fufem::Forms::curl

(

const SumOperator< Ops... > &

op

)

Obtain the curl of a sum of operators.

Parameters

op	The operator to differentiate

This is implemented for 2d and 3d vector fields only.

D()

template<class Op >
requires requires {grad(op);}

auto Dune::Fufem::Forms::D	(	const Op &	op,
		std::size_t	k
	)

Obtain the i-th partial derivative of an operator.

Parameters

op	The operator to differentiate (must support grad(op))
k	Index of the component to extract.

This extracts the k-th component of the gradient, i.e., the k-th partial derivative.

div()

template<class Op >
requires requires {divergence(op);}

auto Dune::Fufem::Forms::div

(

const Op &

op

)

Obtain the divergence of an operator.

Parameters

op	The operator to differentiate

divergence() [1/2]

template<class B , class TP , std::size_t argIndex>

auto Dune::Fufem::Forms::divergence

(

const FEFunctionOperator< B, TP, argIndex > &

op

)

Obtain the divergence of an operator.

Parameters

op	The operator to differentiate

divergence() [2/2]

template<class... Ops>
requires requires(const Ops&... ops) { SumOperator(jacobian(ops)...); }

auto Dune::Fufem::Forms::divergence

(

const SumOperator< Ops... > &

op

)

Obtain the divergence of a sum of operators.

Parameters

op	The operator to differentiate

grad()

template<class Op >
requires requires {Fufem::Forms::transpose(jacobian(op));}

auto Dune::Fufem::Forms::grad

(

const Op &

op

)

Obtain the gradient of an operator.

Parameters

op	The operator to differentiate

This is a shortcut for transpose(jacobian(op)) and gradient(op).

Notice that for a scalar function space, jacobian(op) uses single row matrices (row-vectors) as range type, grad(op) uses single column matrices (column-vectors) as range type.

gradient()

template<class Op >
requires requires {Fufem::Forms::transpose(jacobian(op));}

auto Dune::Fufem::Forms::gradient

(

const Op &

op

)

Obtain the gradient of an operator.

Parameters

op	The operator to differentiate

This is a shortcut for transpose(jacobian(op)).

Notice that for a scalar function space, jacobian(op) uses single row matrices (row-vectors) as range type, gradient(op) uses single column matrices (column-vectors) as range type.

jacobian() [1/2]

template<class B , class TP , std::size_t argIndex>

auto Dune::Fufem::Forms::jacobian

(

const FEFunctionOperator< B, TP, argIndex > &

op

)

Obtain the jacobian of an operator.

Parameters

op	The operator to differentiate

jacobian() [2/2]

template<class... Ops>
requires requires(const Ops&... ops) { SumOperator(jacobian(ops)...); }

auto Dune::Fufem::Forms::jacobian

(

const SumOperator< Ops... > &

op

)

Obtain the jacobian of a sum of operators.

Parameters

op	The operator to differentiate

rot()

template<class Op >
requires requires {curl(op);}

auto Dune::Fufem::Forms::rot

(

const Op &

op

)

Obtain the curl of an operator.

Parameters

op	The operator to differentiate

This is implemented for 2d and 3d vector fields only.