A MeshFunction which combines two other mesh functions using a binary operator (advanced use). More...

#include <lf/uscalfe/uscalfe.h>

Public Member Functions
	MeshFunctionBinary (OP op, A a, B b)
	Create a new MeshFunctionBinary.

auto	operator() (const lf::mesh::Entity &e, const Eigen::MatrixXd &local) const

Private Attributes
OP	op_

A	a_

B	b_

Related Symbols
(Note that these are not member symbols.)
template<MeshFunction A, MeshFunction B>
auto	operator+ (const A &a, const B &b) -> MeshFunctionBinary< internal::OperatorAddition, A, B >
	Add's two mesh functions.

template<MeshFunction A, MeshFunction B>
auto	operator- (const A &a, const B &b) -> MeshFunctionBinary< internal::OperatorSubtraction, A, B >
	Subtracts two mesh functions.

template<MeshFunction A, MeshFunction B>
auto	operator* (const A &a, const B &b) -> MeshFunctionBinary< internal::OperatorMultiplication, A, B >
	Multiply two mesh functions with each other.

Detailed Description

template<class OP, class A, class B>
class lf::mesh::utils::MeshFunctionBinary< OP, A, B >

A MeshFunction which combines two other mesh functions using a binary operator (advanced use).

Template Parameters

OP	The type of operator that combines the mesh functions.
A	The type of the lhs mesh function.
B	The type of the rhs mesh function.

Requirements for OP

The Operator OP must fulfill the following requirements:

It must be moveable
It should overload operator() as follows:
template <class U, class V>

std::vector<Z> operator()(const std::vector<U>& u, const std::vector<V>& v,

int)

lf::mesh::utils::MeshFunctionBinary::operator()
auto operator()(const lf::mesh::Entity &e, const Eigen::MatrixXd &local) const
Definition mesh_function_binary.h:65

where U is the MeshFunctionReturnType of the lhs MeshFunction, V is the MeshFunctionReturnType of the rhs MeshFunction and Z is the type of the mesh function A OP B.

Note: Usually there is no need to use MeshFunctionBinary directly. There are a number of operator overloads which use MeshFunctionBinary internally.; The last int argument of operator() can be used to prefer certain overloads over others, e.g. operator()(const std::vector<U>& u, const std::vector<V>& int) takes higher precedence than operator()(const std::vector<U>& u, const std::vector<V>& long)

Definition at line 51 of file mesh_function_binary.h.

Constructor & Destructor Documentation

◆ MeshFunctionBinary()

template<class OP, class A, class B>

lf::mesh::utils::MeshFunctionBinary< OP, A, B >::MeshFunctionBinary	(	OP	op,
		A	a,
		B	b )

inline

Create a new MeshFunctionBinary.

Parameters

op	The operator to apply
a	The lhs mesh function
b	The rhs mesh function.

Definition at line 59 of file mesh_function_binary.h.

References a_, b_, and op_.

Referenced by operator*(), operator+(), and operator-().

Member Function Documentation

◆ operator()()

template<class OP, class A, class B>

auto lf::mesh::utils::MeshFunctionBinary< OP, A, B >::operator()	(	const lf::mesh::Entity &	e,
		const Eigen::MatrixXd &	local ) const

inline

see MeshFunction for details.

Definition at line 65 of file mesh_function_binary.h.

References a_, b_, and op_.

Friends And Related Symbol Documentation

◆ operator*()

template<MeshFunction A, MeshFunction B>

auto operator*	(	const A &	a,
		const B &	b ) -> MeshFunctionBinary<internal::OperatorMultiplication, A, B>

Multiply two mesh functions with each other.

Template Parameters

A	The type of the lhs MeshFunction
B	The type of the rhs MeshFunction

Parameters

a	the lhs MeshFunction
b	the rhs MeshFunction

Returns: Return a*b, i.e. a new mesh function which represents the pointwise product of a and b.

Note: if A and B are Eigen::Matrix valued, the resulting MeshFunction will also be Matrix/Vector valued and will represent the Matrix product of a and b.; If you want to apply this operator overload to meshfunctions" which do not reside in the lf::uscalfe namespace, it will not be found by Argument Dependent Lookup (ADL). You can get around this by explicitly importing the operator overload: using lf::uscalfe::operator*;

Example

  auto mesh_factory = std::make_unique<mesh::hybrid2d::MeshFactory>(2);
  auto gmsh_reader = io::GmshReader(std::move(mesh_factory), "mesh.msh");
 
  // a mesh function which takes the value 1 everywhere
  auto mf_one = mesh::utils::MeshFunctionConstant(1.);
 
  // a mesh function which represents the radial vector field (x,y)
  auto mf_radial = mesh::utils::MeshFunctionGlobal(
      [](const Eigen::Vector2d& x) { return x; });
 
  // a matrix valued mesh function ((x,y),(x^2,y^2))
  auto mf_matrix =
      mesh::utils::MeshFunctionGlobal([](const Eigen::Vector2d& x) {
        return (Eigen::Matrix2d() << x[0], x[1], x[0] * x[0], x[1] * x[1])
            .finished();
      });
 
  // product of two scalar valued mesh functions:
  auto p0 = mf_one * mesh::utils::MeshFunctionConstant(3.);
 
  // product of a scalar valued mesh function with a matrix valued one:
  auto p1 = mf_one * mf_matrix;
 
  // product of matrix valued with a vector valued mesh function:
  auto p2 = mf_matrix * mf_radial;  // will be vector valued
 
  // product of a matrix valued mesh function with itself:
  auto p3 = mf_matrix * mf_matrix;

Definition at line 722 of file mesh_function_binary.h.

References MeshFunctionBinary().

◆ operator+()

template<MeshFunction A, MeshFunction B>

auto operator+	(	const A &	a,
		const B &	b ) -> MeshFunctionBinary<internal::OperatorAddition, A, B>

Add's two mesh functions.

Template Parameters

A	Type of the lhs MeshFunction
B	Type of the rhs MeshFunction

Parameters

a	the lhs MeshFunction
b	the rhs MeshFunction

Returns: a + b, i.e. a new mesh function which represents the pointwise addition of a and b

Note: the two mesh functions a and b should produce the same type of values, e.g. both should be scalar valued or both matrix/vector/array valued.; If you want to apply this operator overload to meshfunctions" which do not reside in the lf::uscalfe namespace, it will not be found by Argument Dependent Lookup. You can get around this by explictly importing the operator overload: using lf::uscalfe::operator+;

Example

  auto mesh_factory = std::make_unique<mesh::hybrid2d::MeshFactory>(2);
  auto gmsh_reader = io::GmshReader(std::move(mesh_factory), "mesh.msh");
 
  // a mesh function that takes the value 1 everywhere
  auto mf_one = mesh::utils::MeshFunctionConstant(1.);
 
  // a mesh function which represents the function `sin(x)*cos(y)` (x,y are
  // global coordinates)
  auto mf_trig = mesh::utils::MeshFunctionGlobal(
      [](const Eigen::Vector2d& x) { return std::sin(x[0]) * std::cos(x[1]); });
 
  // mesh function `1+sin(x)*cos(y)`
  auto mf_one_trig = mf_one + mf_trig;

Definition at line 664 of file mesh_function_binary.h.

References MeshFunctionBinary().

◆ operator-()

template<MeshFunction A, MeshFunction B>

auto operator-	(	const A &	a,
		const B &	b ) -> MeshFunctionBinary<internal::OperatorSubtraction, A, B>

Subtracts two mesh functions.

Template Parameters

A	Type of the lhs MeshFunction
B	Type of the rhs MeshFunction

Parameters

a	the lhs MeshFunction
b	the rhs MeshFunction

Returns: a - b, i.e. a new mesh function which represents the pointwise difference of a minus b

Note: the two mesh functions a and b should produce the same type of values, e.g. both should be scalar valued or both matrix/vector valued.; If you want to apply this operator overload to meshfunctions" which do not reside in the lf::uscalfe namespace, it will not be found by Argument Dependent Lookup (ADL). You can get around this by explicitly importing the operator overload: using lf::uscalfe::operator-;

Example

  auto mesh_factory = std::make_unique<mesh::hybrid2d::MeshFactory>(2);
  auto gmsh_reader = io::GmshReader(std::move(mesh_factory), "mesh.msh");
 
  // a mesh function that takes the value 1 everywhere
  auto mf_one = mesh::utils::MeshFunctionConstant(1.);
 
  // a mesh function which represents the function `sin(x)*cos(y)` (x,y are
  // global coordinates)
  auto mf_trig = mesh::utils::MeshFunctionGlobal(
      [](const Eigen::Vector2d& x) { return std::sin(x[0]) * std::cos(x[1]); });
 
  // mesh function `1-sin(x)*cos(y)`
  auto mf_one_minus_trig = mf_one - mf_trig;