template<class TrialFES, class TestFES, class Operator>
Rodin::Variational::BilinearForm class final

Speciallization of BilinearForm for a matrix type.

Template parameters
TrialFES Type of trial finite element space
TestFES Type of test finite element space
Operator

Represents a bilinear form on a trial and test space.

This specialization aids in the construction of a $ m \times n $ matrix $ A $ , which is associated to the bilinear form. Here, $ n $ represents the size (total number of degrees-of-freedom) of the trial space, and $ m $ represents the size of the test space.

An object of type BilinearForm represents a bilinear map:

\[ \begin{aligned} a : U \times V &\rightarrow \mathbb{R}\\ (u, v) &\mapsto a(u, v) \end{aligned} \]

where $ U $ and $ V $ are finite element spaces.

Base classes

template<class Operator>
class BilinearFormBase<Operator>
Abstract base class for objects of type BilinearForm.

Public types

using OperatorType = Operator
Type of operator associated to the bilinear form.
using Parent = BilinearFormBase<OperatorType>
Parent class.

Constructors, destructors, conversion operators

BilinearForm(std::reference_wrapper<const TrialFunction<TrialFES>> u, std::reference_wrapper<const TestFunction<TestFES>> v) constexpr
Constructs a BilinearForm from a TrialFunction and TestFunction.

Public functions

auto operator()(const GridFunction<TrialFES>& u, const GridFunction<TestFES>& v) const -> ScalarType constexpr
Evaluates the linear form at the functions $ u $ and $ v $ .
void assemble() override
Assembles the bilinear form.
auto getTrialFunction() const -> const TrialFunction<TrialFES>& override
Gets the reference to the associated TrialFunction object.
auto getTestFunction() const -> const TestFunction<TestFES>& override
Gets the reference to the associated TestFunction object.
auto operator=(const FormLanguage::List<LocalBilinearFormIntegratorBaseType>& bfis) -> BilinearForm&
auto operator=(const FormLanguage::List<GlobalBilinearFormIntegratorBaseType>& bfis) -> BilinearForm&
auto getOperator() -> OperatorType& override
Gets the reference to sparse matrix.
auto getOperator() const -> const OperatorType& override
Gets the reference to the (local) associated sparse matrix to the bilinear form.
auto from(const LocalBilinearFormIntegratorBaseType& bfi) -> BilinearForm& virtual
Builds the bilinear form the given bilinear integrator.
auto add(const LocalBilinearFormIntegratorBaseType& bfi) -> BilinearForm& virtual
Adds a bilinear integrator to the bilinear form.
auto from(const GlobalBilinearFormIntegratorBaseType& bfi) -> BilinearForm& virtual
Builds the bilinear form the given bilinear integrator.
auto add(const GlobalBilinearFormIntegratorBaseType& bfi) -> BilinearForm& virtual
Adds a bilinear integrator to the bilinear form.
auto copy() const -> BilinearForm* override noexcept
Copies the object and returns a non-owning pointer to the copied object.

Function documentation

template<class TrialFES, class TestFES, class Operator>
Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::BilinearForm(std::reference_wrapper<const TrialFunction<TrialFES>> u, std::reference_wrapper<const TestFunction<TestFES>> v) constexpr

Constructs a BilinearForm from a TrialFunction and TestFunction.

Parameters
u in Trial function argument
v in Test function argument

template<class TrialFES, class TestFES, class Operator>
ScalarType Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::operator()(const GridFunction<TrialFES>& u, const GridFunction<TestFES>& v) const constexpr

Evaluates the linear form at the functions $ u $ and $ v $ .

Returns The action $ a(u, v) $ which the bilinear form takes at $ ( u, v ) $ .

Given grid functions $ u $ and $ v $ , this function will compute the action of the bilinear mapping $ a(u, v) $ .

template<class TrialFES, class TestFES, class Operator>
void Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::assemble() override

Assembles the bilinear form.

This method will assemble the underlying sparse matrix associated the bilinear form.

template<class TrialFES, class TestFES, class Operator>
const TrialFunction<TrialFES>& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::getTrialFunction() const override

Gets the reference to the associated TrialFunction object.

Returns Reference to this (for method chaining)

template<class TrialFES, class TestFES, class Operator>
const TestFunction<TestFES>& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::getTestFunction() const override

Gets the reference to the associated TestFunction object.

Returns Reference to this (for method chaining)

template<class TrialFES, class TestFES, class Operator>
BilinearForm& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::operator=(const FormLanguage::List<LocalBilinearFormIntegratorBaseType>& bfis)

template<class TrialFES, class TestFES, class Operator>
BilinearForm& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::operator=(const FormLanguage::List<GlobalBilinearFormIntegratorBaseType>& bfis)

template<class TrialFES, class TestFES, class Operator>
OperatorType& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::getOperator() override

Gets the reference to sparse matrix.

Returns Reference to the associated sparse matrix.

template<class TrialFES, class TestFES, class Operator>
const OperatorType& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::getOperator() const override

Gets the reference to the (local) associated sparse matrix to the bilinear form.

Returns Constant reference to the associated sparse matrix.

template<class TrialFES, class TestFES, class Operator>
BilinearForm& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::from(const LocalBilinearFormIntegratorBaseType& bfi) virtual

Builds the bilinear form the given bilinear integrator.

Parameters
bfi in Bilinear integrator which will be used to build the bilinear form.
Returns Reference to this (for method chaining)

template<class TrialFES, class TestFES, class Operator>
BilinearForm& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::add(const LocalBilinearFormIntegratorBaseType& bfi) virtual

Adds a bilinear integrator to the bilinear form.

Returns Reference to this (for method chaining)

template<class TrialFES, class TestFES, class Operator>
BilinearForm& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::from(const GlobalBilinearFormIntegratorBaseType& bfi) virtual

Builds the bilinear form the given bilinear integrator.

Parameters
bfi in Bilinear integrator which will be used to build the bilinear form.
Returns Reference to this (for method chaining)

template<class TrialFES, class TestFES, class Operator>
BilinearForm& Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::add(const GlobalBilinearFormIntegratorBaseType& bfi) virtual

Adds a bilinear integrator to the bilinear form.

Returns Reference to this (for method chaining)

template<class TrialFES, class TestFES, class Operator>
BilinearForm* Rodin::Variational::BilinearForm<TrialFES, TestFES, Operator>::copy() const override noexcept

Copies the object and returns a non-owning pointer to the copied object.

Returns Non-owning pointer to the copied object.