FunctionBase

Base class for function objects which can be evaluated over a mesh.

Defined in Rodin/Variational/Function.h

template <
  class Derived>
class FunctionBase;

Template parameters
Derived	Derived class following CRTP (Curiously Recurring Template Pattern)

Base class for functions defined on finite element meshes.

Instances of FunctionBase will always have the getValue() method defined, which enables the evaluation of any function on some mesh element.

FunctionBase provides the foundation for representing mathematical functions defined over geometric domains discretized by finite element meshes. This includes both analytical functions and discrete finite element functions (grid functions) that arise in variational formulations.

Mathematical Foundation

A function maps points in the domain to values in . In finite element analysis, functions serve various roles:

Analytical functions: Exact solutions, boundary conditions, source terms
Discrete functions: Finite element approximations
Test/Trial functions: Basis functions spanning finite element spaces

Key Features

Domain support: Functions can be restricted to subdomains or boundaries
Trace operations: Support for function traces on mesh boundaries
Point evaluation: Evaluation at arbitrary points within the domain
Polymorphic design: CRTP enables compile-time polymorphism for efficiency

Direct inheritance by class family

FormLanguage::Base

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FunctionBase

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Inherits from

Base class	Responsibility
`FormLanguage::Base`public Full type FormLanguage::Base	Base class for all objects in Rodin's FormLanguage system.

Derived classes

Derived class	Description
`BooleanFunctionBase<LHSDerived>`public Full type BooleanFunctionBase< LHSDerived >	Base class for boolean-valued functions.
`MatrixFunctionBase<ScalarType, …>`public Full type MatrixFunctionBase< ScalarType, FittingTensor< GradDerived, Displacement, LocatorType > >	Base class for matrix-valued functions defined on a mesh.
`ScalarFunctionBase<…>`public Full type ScalarFunctionBase< typename FormLanguage::Traits< FunctionBase< OperandDerived > >::ScalarType, Component< FunctionBase< OperandDerived >, size_t, size_t > >	Base class for scalar-valued functions with templated scalar type.

See moreSee less

Derived class	Description
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, FittingForce< PhiDerived, GradDerived, Displacement, LocatorType > >	Base class for vector-valued functions defined on a mesh.
`TraceOperator<FunctionBase>`public Full type TraceOperator< FunctionBase >	Trace (boundary restriction) operator for functions.
`BooleanFunctionBase<RHSDerived>`public Full type BooleanFunctionBase< RHSDerived >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< AND< LHSType, RHSType > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< BooleanFunction< Boolean > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< EQ< LHSType, RHSType > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< GEQ< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< GT< LHSType, RHSType > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< LEQ< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< LT< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< NEQ< LHSType, RHSType > >	Base class for boolean-valued functions.
`BooleanFunctionBase<…>`public Full type BooleanFunctionBase< OR< LHSType, RHSType > >	Base class for boolean-valued functions.
`MatrixFunctionBase<ScalarType, …>`public Full type MatrixFunctionBase< ScalarType, IdentityMatrix >	Base class for matrix-valued functions defined on a mesh.
`MatrixFunctionBase<Scalar, …>`public Full type MatrixFunctionBase< Scalar, MatrixFunction< MatrixType > >	Base class for matrix-valued functions defined on a mesh.
`MatrixFunctionBase<ScalarType, …>`public Full type MatrixFunctionBase< ScalarType, MatrixFunction >	Base class for matrix-valued functions defined on a mesh.
`ScalarFunctionBase<ScalarType, …>`public Full type ScalarFunctionBase< ScalarType, Component >	Base class for scalar-valued functions with templated scalar type.
`ScalarFunctionBase<Scalar, Zero<Scalar>>`public Full type ScalarFunctionBase< Scalar, Zero< Scalar > >	Base class for scalar-valued functions with templated scalar type.
`VectorFunctionBase<Real, GradDerived>`public Full type VectorFunctionBase< Real, GradDerived >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, BoundaryNormal >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, FaceNormal >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, GradBase< OperandType, Derived > >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, VectorFunction< VectorType > >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, VectorFunction< V, Values... > >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<ScalarType, …>`public Full type VectorFunctionBase< ScalarType, VectorFunction< F > >	Base class for vector-valued functions defined on a mesh.
`VectorFunctionBase<Scalar, …>`public Full type VectorFunctionBase< Scalar, Zero< VectorType > >	Base class for vector-valued functions defined on a mesh.

Overrides

Member	Base declaration
`copy()`	Base::copy

Inherited interface

Declared in	Members
`FormLanguage::Base`	3 members `getName()` `operator=()` `operator=()`
`Identifiable`	2 members `getUUID()` `UUID`

Public types

class Cache: Function value retained for the current quadrature binding.
using Parent = FormLanguage::Base: Parent class type.
using TraceDomain = FlatSet<Geometry::Attribute>: Domain type for trace operations (set of mesh attributes).

Constructors, destructors, conversion operators

FunctionBase() defaulted: Default constructor.
FunctionBase(const FunctionBase& other): Copy constructor.
FunctionBase(FunctionBase&& other): Move constructor.
~FunctionBase() defaulted virtual: Virtual destructor.

Public functions

auto operator=(FunctionBase&& other) -> FunctionBase&: Move assignment operator.
auto operator()(const Geometry::Point& p) const -> auto constexpr: Evaluates the function on a Point belonging to the mesh.
auto operator()(const IntegrationPoint& ip) const -> auto constexpr: Evaluates the function at an integration point.
auto operator()(size_t i) const -> auto: Extracts the i-th component of the function.
auto operator()(size_t i, size_t j) const -> auto: Extracts the (i,j)-th component of a matrix function.
auto x() const -> auto constexpr: Convenience accessor for the first component (x-component).
auto y() const -> auto constexpr: Convenience accessor for the second component (y-component).
auto z() const -> auto constexpr: Convenience accessor for the third component (z-component).
auto T() const -> auto constexpr: Returns the transpose of the function.
auto traceOf(const Geometry::Attribute& attr) -> Derived& constexpr: Sets a single attribute as the trace domain.
traceOf: Sets multiple attributes as the trace domain.
See declaration

template<class A1, class A2, class... As>
auto traceOf(const A1& a1, const A2& a2, const As&... as) -> Derived& constexpr
auto traceOf(const FlatSet<Geometry::Attribute>& attr) -> Derived& constexpr: Sets a set of attributes as the trace domain.
auto getTraceDomain() const -> const TraceDomain& constexpr: Gets the set of attributes which will be interpreted as the domains to "trace".
auto getValue(const Geometry::Point& p) const -> auto constexpr: Evaluates the function on a Point belonging to the mesh.
auto getValue(const IntegrationPoint& ip) const -> auto constexpr: Evaluates the function at an integration point.
auto getOrder(const Geometry::Polytope& geom) const -> Optional<size_t> constexpr noexcept: Recommends an automatic integration order on a mesh entity.
auto getDerived() -> Derived& noexcept: Returns this object as the CRTP-derived type.
auto getDerived() const -> const Derived& noexcept: Returns this object as the CRTP-derived type.
auto copy() const -> FunctionBase* override noexcept: Polymorphically copies the derived function.

Function documentation

FunctionBase(const FunctionBase& other)

Copy constructor.

Parameters
other	Object to copy from.

FunctionBase(FunctionBase&& other)

Move constructor.

Parameters
other	Object to move from.

FunctionBase& operator=(FunctionBase&& other)

Move assignment operator.

Parameters
other	Object to move from.
Returns	Reference to this object after the operation.

auto operator()(const Geometry::Point& p) const constexpr

Evaluates the function on a Point belonging to the mesh.

Parameters
p in	Point at which to evaluate the function
Returns	Function value at the given point

This operator provides convenient function call syntax for evaluation. Delegates to the derived class's getValue() method via CRTP.

auto operator()(const IntegrationPoint& ip) const constexpr

Evaluates the function at an integration point.

Parameters
ip	Integration point at which the expression is evaluated.
Returns	Value of the expression at the supplied evaluation point.

auto operator()(size_t i) const

Extracts the i-th component of the function.

Parameters
i in	Component index
Returns	Component function object

For vector or matrix-valued functions, this returns a scalar function representing the specified component.

auto operator()(size_t i, size_t j) const

Extracts the (i,j)-th component of a matrix function.

Parameters
i in	Row index
j in	Column index
Returns	Component function object

auto x() const constexpr

Convenience accessor for the first component (x-component).

Returns	Component function for index 0

auto y() const constexpr

Convenience accessor for the second component (y-component).

Returns	Component function for index 1

auto z() const constexpr

Convenience accessor for the third component (z-component).

Returns	Component function for index 2

auto T() const constexpr

Returns the transpose of the function.

Returns	Transposed function object

For matrix-valued functions , returns .

Derived& traceOf(const Geometry::Attribute& attr) constexpr

Sets a single attribute as the trace domain.

Parameters
attr in	Mesh attribute defining the trace domain
Returns	Reference to self (for method chaining)

Convenience function to call traceOf(FlatSet<int>) with only one attribute. The trace operation restricts function evaluation to the specified boundary or interface regions.

template<class Derived> template<class A1, class A2, class... As>
Derived& traceOf(const A1& a1, const A2& a2, const As&... as) constexpr

Sets multiple attributes as the trace domain.

Parameters
a1	Mesh attributes selecting the region.
a2	Mesh attributes selecting the region.
as	Mesh attributes selecting the region.
Returns	Reference to self (for method chaining)

The attributes are collected into the trace domain of the function.

Derived& traceOf(const FlatSet<Geometry::Attribute>& attr) constexpr

Sets a set of attributes as the trace domain.

Parameters
attr in	Set of mesh attributes defining the trace domain
Returns	Reference to self (for method chaining)

The trace domain specifies regions (typically boundaries or interfaces) where the function should be evaluated via continuous extension from adjacent elements.

const TraceDomain& getTraceDomain() const constexpr

Gets the set of attributes which will be interpreted as the domains to "trace".

Returns	The set of attributes which will be interpreted as the domains to "trace".

The domains to trace are interpreted as the domains where there shall be a continuous extension from values to the interior boundaries. If the trace domain is empty, then this has the semantic value that it has not been specified yet.

auto getValue(const Geometry::Point& p) const constexpr

Evaluates the function on a Point belonging to the mesh.

Parameters
p	Point at which the operation is evaluated.
Returns	Value of the expression at the supplied evaluation point.

auto getValue(const IntegrationPoint& ip) const constexpr

Evaluates the function at an integration point.

Parameters
ip	Integration point at which the expression is evaluated.
Returns	Value of the expression at the supplied evaluation point.

Optional<size_t> getOrder(const Geometry::Polytope& geom) const constexpr noexcept

Recommends an automatic integration order on a mesh entity.

Parameters
geom	Entity supplying reference geometry and coordinate mapping.
Returns	An integration recommendation, or no established estimate.

Known polynomial structure supplies a degree-based recommendation. Rational expressions may use a documented accuracy estimate instead; no polynomial exactness is implied in that case. An empty result means that no recommendation is established. A result of zero must certify an elementwise constant expression, since constant-value optimizations also consume this information. Integrators retain explicit overrides and account for the geometric measure in their selection policies.

Derived& getDerived() noexcept

Returns this object as the CRTP-derived type.

Returns	This object as the CRTP-derived type.

const Derived& getDerived() const noexcept

Returns this object as the CRTP-derived type.

Returns	This object as the CRTP-derived type.

FunctionBase* copy() const override noexcept

Polymorphically copies the derived function.

Returns	Pointer to a newly allocated copy; the caller owns the returned object.

FunctionBase

Function documentation

FunctionBase(const FunctionBase& other)

FunctionBase(FunctionBase&& other)

FunctionBase& operator=(FunctionBase&& other)

auto operator()(const Geometry::Point& p) const constexpr

auto operator()(const IntegrationPoint& ip) const constexpr

auto operator()(size_t i) const

auto operator()(size_t i, size_t j) const

auto x() const constexpr

auto y() const constexpr

auto z() const constexpr

auto T() const constexpr

Derived& traceOf(const Geometry::Attribute& attr) constexpr

template<class Derived> template<class A1, class A2, class... As> Derived& traceOf(const A1& a1, const A2& a2, const As&... as) constexpr

Derived& traceOf(const FlatSet<Geometry::Attribute>& attr) constexpr

const TraceDomain& getTraceDomain() const constexpr

auto getValue(const Geometry::Point& p) const constexpr

auto getValue(const IntegrationPoint& ip) const constexpr

Optional<size_t> getOrder(const Geometry::Polytope& geom) const constexpr noexcept

Derived& getDerived() noexcept

const Derived& getDerived() const noexcept

FunctionBase* copy() const override noexcept

template<class Derived> template<class A1, class A2, class... As>
Derived& traceOf(const A1& a1, const A2& a2, const As&... as) constexpr