Rodin::Variational namespace

Module which provides the necessary tools for constructing variational problems.

The Rodin::Variational module aids in the general construction of variational problems:

\[ \text{Find} \quad u \in U \quad \text{ s.t. } \quad \forall v \in V \quad a(u, v) = b(v) \ , \]

which then can be translated into linear algebra problems of the type:

\[ \mathbf{A} \mathbf{x} = \mathbf{b} \]

where $ \mathbf{A} $ represents the stiffness operator.

Namespaces

namespace F
Contains built-in coordinate functions.

Classes

template<class Operand>
class Abs
Represents the absolute value of a value.
template<class NestedDerived>
class Abs<FunctionBase<NestedDerived>>
Absolute value operation for functions.
template<class LHS, class RHS>
class AND
Represents the logical AND expression.
template<class LHSDerived, class RHSDerived>
class AND<BooleanFunctionBase<LHSDerived>, BooleanFunctionBase<RHSDerived>>
Logical AND operator between two boolean functions.
template<class FunctionDerived>
class Average<FunctionBase<FunctionDerived>>
Average operator for computing interface averages.
template<class Solution, class TrialFES, class TestFES, class OperatorType>
class BilinearForm
Represents a bilinear form on a trial and test space.
template<class Solution, class TrialFES, class TestFES, class Scalar>
class BilinearForm<Solution, TrialFES, TestFES, Math::SparseMatrix<Scalar>>
Speciallization of BilinearForm for a matrix type.
template<class Operator>
class BilinearFormBase
Base class for bilinear form representations.
template<class Number, class Derived>
class BilinearFormIntegratorBase
Abstract base class for bilinear form integrators.
template<class T>
class BooleanFunction
template<class Derived>
class BooleanFunctionBase
Base class for boolean-valued functions.
template<class Integrand>
class BoundaryIntegral
Represents expressions of the integral operator on the boundary of a domain.
template<class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class BoundaryIntegral<Dot<ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>>
Integration of the dot product of a trial and test operators.
template<class NestedDerived, class FES>
class BoundaryIntegral<ShapeFunctionBase<NestedDerived, FES, TestSpace>>
Integration of a test operator.
class BoundaryNormal
Outward unit normal vector on domain boundaries.
template<class ... Values>
class ComplexFunction
template<>
class ComplexFunction<Complex>
Represents a constant scalar function with type Complex.
template<class F>
class ComplexFunction<F>
Represents a scalar function given by an arbitrary scalar function.
template<class Derived>
class ComplexFunctionBase
Base class for complex-valued scalar functions.
template<class OperandDerived>
class Component<FunctionBase<OperandDerived>, size_t>
Extracts a single component from a vector-valued function.
template<class OperandDerived>
class Component<FunctionBase<OperandDerived>, size_t, size_t>
Extracts a single entry from a matrix-valued function.
template<class FES, class Data>
class Component<GridFunction<FES, Data>>
Extracts a component from a vector-valued GridFunction.
template<class OperandDerived, class FES, ShapeFunctionSpaceType Space>
class Component<ShapeFunctionBase<OperandDerived, FES, Space>>
Extracts a component from a vector-valued ShapeFunction.
template<class LHS, class RHS>
class Composition
template<class NestedDerived>
class Conjugate<FunctionBase<NestedDerived>>
Complex conjugate of a function.
template<class NestedDerived, class FES, ShapeFunctionSpaceType Space>
class Conjugate<ShapeFunctionBase<NestedDerived, FES, Space>>
Specialization for shape functions.
template<class Operand>
class Cos
Represents the cosine function.
template<class NestedDerived>
class Cos<FunctionBase<NestedDerived>>
Cosine function operator for real-valued scalar functions.
template<class NestedDerived>
class Cosh<FunctionBase<NestedDerived>>
Hyperbolic cosine function operator for real-valued scalar functions.
class DefaultBoundaryPolicy
Default boundary policy for flow maps.
class DefaultTangentPolicy
Default tangent policy for flow maps.
template<class LinearSystem, class U, class V>
class DenseProblem<LinearSystem, U, V>
General class to assemble linear systems with Math::Matrix and Math::Vector types in a serial context.
template<class Range, class Data, class Mesh>
class Derivative<GridFunction<P1<Range, Mesh>, Data>>
Derivative of a P1 GridFunction.
template<class Operand, class Derived>
class DerivativeBase
Base class for directional derivative operators.
template<class Operand, class Value>
class DirichletBC
template<class Solution, class FES, class ValueDerived>
class DirichletBC<TrialFunction<Solution, FES>, FunctionBase<ValueDerived>>
Represents a Dirichlet boundary condition on a ShapeFunction object.
template<class Scalar>
class DirichletBCBase
Abstract base class for a Dirichlet boundary condition.
template<class Operand>
class Div
Represents the divergence of a vector valued function.
template<class Scalar, class Data, class Mesh>
class Div<GridFunction<P1<Math::Vector<Scalar>, Mesh>, Data>>
Divergence of a P1 vector GridFunction.
template<class NestedDerived, class Number, class Mesh, ShapeFunctionSpaceType Space>
class Div<ShapeFunction<NestedDerived, P1<Math::Vector<Number>, Mesh>, Space>>
Divergence of a P1 vector ShapeFunction.
template<class Operand, class Derived>
class DivBase
Base class for divergence operator implementations.
template<class FES, class Data, class Derived>
class DivBase<GridFunction<FES, Data>, Derived>
Divergence of a P1 GridFunction.
template<class LHS, class RHS>
class Division
Represents the division operation.
template<class LHSDerived, class RHSDerived>
class Division<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Division of a function by another function.
template<class LHS, class RHS>
class Dot
Represents the dot product between two objects.
template<class LHSDerived, class RHSDerived>
class Dot<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Dot product between two functions.
template<class LHSDerived, class RHSDerived, class FES, ShapeFunctionSpaceType Space>
class Dot<FunctionBase<LHSDerived>, ShapeFunctionBase<RHSDerived, FES, Space>>
Dot product between a function and a shape function.
template<class KernelType, class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class Dot<Potential<KernelType, ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>
Dot product of a potential with a test shape function.
template<class LHSDerived, class RHSDerived, class FES, ShapeFunctionSpaceType Space>
class Dot<ShapeFunctionBase<LHSDerived, FES, Space>, FunctionBase<RHSDerived>>
Dot product between a shape function and a function.
template<class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class Dot<ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>
Dot product of trial and test shape functions for bilinear forms.
template<size_t K>
class DubinerTetrahedron
Dubiner orthogonal modal basis on the reference tetrahedron.
template<size_t K>
class DubinerTriangle
Dubiner orthogonal modal basis on the reference triangle.
template<class LHS, class RHS>
class EQ
template<class LHSDerived, class RHSDerived>
class EQ<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Logical EQ operator between two instances of FunctionBase.
template<class NestedDerived>
class Exp<FunctionBase<NestedDerived>>
Exponential function operation.
template<class Integrand>
class FaceIntegral
Represents expressions of the integral operator on the faces of a mesh.
template<class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class FaceIntegral<Dot<ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>>
Integration of the dot product of a trial and test operators.
template<class NestedDerived, class FES>
class FaceIntegral<ShapeFunctionBase<NestedDerived, FES, TestSpace>>
Integration of a test operator.
class FaceNormal
Unit normal vector on mesh faces.
template<size_t K>
class FeketeTetrahedron
Cached Fekete-type nodes on the reference tetrahedron for degree K.
template<size_t K>
class FeketeTriangle
Cached Fekete-type nodes on the reference triangle for degree K.
template<class Derived>
class FiniteElementBase
Base class for finite elements.
template<class Mesh, class Derived>
class FiniteElementSpace
Represernts a finite element space.
template<class Derived>
class FiniteElementSpace<Geometry::Mesh<Context::MPI>, Derived>
Represernts a finite element space.
class FiniteElementSpaceBase
Base class for finite element spaces.
template<class Derived>
class FiniteElementSpacePullbackBase
Base class for mappings taking functions defined on physical elements to reference elements.
template<class Derived>
class FiniteElementSpacePushforwardBase
Base class for inverse mappings taking functions defined on reference elements to physical elements.
template<class Derived, class VectorField, class Step, class BoundaryPolicy, class TangentPolicy>
class Flow<FunctionBase<Derived>, VectorField, Step, BoundaryPolicy, TangentPolicy>
Flow map operator for functions.
template<class Operand>
class Frobenius
Represents the Frobenius norm.
template<class NestedDerived>
class Frobenius<FunctionBase<NestedDerived>>
Frobenius norm of a function.
template<class Derived>
class FunctionBase
Base class for function objects which can be evaluated over a mesh.
template<class StrictType>
class FunctionBaseCopy
template<class LHS, class RHS>
class GEQ
template<size_t K>
class GLL
Compile-time Gauss–Lobatto–Legendre (GLL) nodes on [-1, 1].
template<size_t K>
class GLL01
Gauss–Lobatto–Legendre nodes mapped from [-1, 1] to [0, 1].
template<class Operand>
class Grad
Represents the gradient $ \nabla u $ of a scalar function $ u $ .
template<class Range, class Data, class Mesh>
class Grad<GridFunction<P0<Range, Mesh>, Data>>
Gradient of a P0 GridFunction.
template<class NestedDerived, class Scalar, class Mesh, ShapeFunctionSpaceType SpaceType>
class Grad<ShapeFunction<NestedDerived, P0<Scalar, Mesh>, SpaceType>>
Gradient of a P0 ShapeFunction.
template<class NestedDerived, class Scalar, class Mesh, ShapeFunctionSpaceType SpaceType>
class Grad<ShapeFunction<NestedDerived, P1<Scalar, Mesh>, SpaceType>>
Gradient of a ShapeFunction.
template<class Operand, class Derived>
class GradBase
Base class for gradient operator implementations.
template<class FES, class Data, class Derived>
class GradBase<GridFunction<FES, Data>, Derived>
Gradient operator for grid functions.
template<class FES, class Data>
class GridFunction
Represents a grid function belonging to some finite element space.
template<class Derived, class FES = typename FormLanguage::Traits<Derived>::FESType, class Data = typename FormLanguage::Traits<Derived>::DataType>
class GridFunctionBase
Base class for grid function objects.
template<class StrictType>
class GridFunctionBaseReference
Base class for discrete finite element functions.
template<class LHS, class RHS>
class GT
template<size_t K, class Range, class Mesh>
class H1
Degree K H1-conforming Lagrange finite element space.
template<size_t K, class Scalar>
class H1<K, Math::Vector<Scalar>, Geometry::Mesh<Context::Local>>
Vector-valued continuous piecewise polynomial (degree K) Lagrange finite element space.
template<size_t K, class Scalar>
class H1<K, Scalar, Geometry::Mesh<Context::Local>>
Degree K H1-conforming Lagrange finite element space.
template<size_t K, class Scalar>
class H1Element
Degree k H1-conforming Lagrange element.
template<size_t K, class Scalar>
class H1Element<K, Math::Vector<Scalar>>
Continuous H1-conforming piecewise polynomial (degree k) vector Lagrange element.
class IdentityMatrix
Represents the identity matrix function $ I_n $ .
template<class Operand>
class Im
Extracts the imaginary part of a complex-valued function.
template<class NestedDerived>
class Im<FunctionBase<NestedDerived>>
Specialization for FunctionBase operands.
template<class T>
class IntegerFunction
template<class Derived>
class IntegerFunctionBase
Base class for objects representing integer functions.
template<class Integrand>
class Integral
Represents mathematical expressions of the integral operator on a domain.
template<class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class Integral<Dot<ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>>
Integration of the dot product of a trial and test operators.
template<class FES, class Data>
class Integral<GridFunction<FES, Data>>
Integration of a GridFunction object.
template<class NestedDerived, class FES>
class Integral<ShapeFunctionBase<NestedDerived, FES, TestSpace>>
Integration of a test operator.
class Integrator
Abstract base class for integrators in variational formulations.
template<class Integrand>
class InterfaceIntegral
Represents expressions of the integral operator on the interface of a domain.
template<class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class InterfaceIntegral<Dot<ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>>
Integration of the dot product of a trial and test operators.
template<class NestedDerived, class FES>
class InterfaceIntegral<ShapeFunctionBase<NestedDerived, FES, TestSpace>>
Integration of a test operator.
template<class T>
struct IsTestFunction
Type trait to check if a type is a TestFunction.
template<class FES>
struct IsTestFunction<TestFunction<FES>>
Specialization for TestFunction types.
template<class T>
struct IsTrialFunction
Type trait to check if a type is a TrialFunction.
template<class Solution, class FES>
struct IsTrialFunction<TrialFunction<Solution, FES>>
Specialization for TrialFunction types.
template<class Operand>
class Jacobian
Represents the Jacobian matrix of a type.
template<class Range, class Data, class Mesh>
class Jacobian<GridFunction<P1<Range, Mesh>, Data>>
Jacobian of a P1 vector GridFunction.
template<class ShapeFunctionDerived, class Range, class Mesh, ShapeFunctionSpaceType Space>
class Jacobian<ShapeFunction<ShapeFunctionDerived, P1<Range, Mesh>, Space>>
Jacobian of an P1 ShapeFunction object.
template<class Operand, class Derived>
class JacobianBase
Base class for Jacobian matrix operator implementations.
template<class FES, class Data, class Derived>
class JacobianBase<GridFunction<FES, Data>, Derived>
Jacobian of a P1 GridFunction.
template<size_t K>
class JacobiPolynomial
Jacobi polynomial evaluator.
template<class Range, class Context>
class L2
Arbitrary order $ H^1(\mathcal{T}_h)^d \subset L^2 (\Omega) $ broken Sobolev space.
template<size_t K>
class LagrangeBasis1D
Generic 1D Lagrange basis on arbitrary nodes.
template<size_t K>
class LagrangeBasisPoint
Lagrange basis on the reference point (0D element).
template<size_t K>
class LagrangeBasisQuadrilateral
Lagrange basis on the reference quadrilateral [0,1]².
template<size_t K>
class LagrangeBasisSegment
Lagrange basis on the reference segment [0,1] using GLL nodes.
template<size_t K>
class LagrangeBasisTetrahedron
Lagrange basis on the reference tetrahedron.
template<size_t K>
class LagrangeBasisTriangle
Lagrange basis on the reference triangle.
template<size_t K>
class LagrangeBasisWedge
Lagrange basis on the reference wedge (triangular prism).
template<size_t K>
class LegendrePolynomial
Compile-time degree Legendre polynomial evaluator.
template<class LHS, class RHS>
class LEQ
template<class Solution, class FES>
class LinearElasticityIntegral
Helper class to construct linear elasticity integrators.
template<class Solution, class FES, class LambdaDerived, class MuDerived>
class LinearElasticityIntegrator
Bilinear form integrator for linear elasticity.
template<class Solution, class MuDerived, class LambdaDerived, class Range, class Mesh>
class LinearElasticityIntegrator<Solution, P1<Range, Mesh>, MuDerived, LambdaDerived>
P1 linear elasticity bilinear form integrator.
template<class FES, class VectorType>
class LinearForm
Represents a linear form on some finite element space.
template<class FES>
class LinearForm<FES, Math::Vector<typename FormLanguage::Traits<FES>::ScalarType>>
Represents a linear form defined over some finite element space.
template<class Vector>
class LinearFormBase
Base class for linear form objects.
template<class Number>
class LinearFormIntegratorBase
Base class for linear form integrators.
template<class LHS, class RHS>
class LT
template<class T>
class MatrixFunction
template<class Scalar, class Derived>
class MatrixFunctionBase
Base class for matrix-valued functions defined on a mesh.
template<class LHSDerived, class RHSDerived>
class Max<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Represents the maximum operation between two functions.
template<class LHSDerived, class RHSDerived>
class Min<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Represents the minimum operation between two functions.
template<class LHS, class RHS>
class Mult
Represents the multiplication operation.
template<class LHSDerived, class RHSDerived>
class Mult<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Multiplication of two FunctionBase instances.
template<class LHSDerived, class RHSDerived, class FES, ShapeFunctionSpaceType Space>
class Mult<FunctionBase<LHSDerived>, ShapeFunctionBase<RHSDerived, FES, Space>>
Left Multiplication of a ShapeFunctionBase by a FunctionBase.
template<class LHSDerived, class RHSDerived, class FES, ShapeFunctionSpaceType Space>
class Mult<ShapeFunctionBase<LHSDerived, FES, Space>, FunctionBase<RHSDerived>>
Right multiplication of a ShapeFunctionBase by a FunctionBase.
template<class LHS, class RHS>
class NEQ
template<class LHS, class RHS>
class OR
template<class LHSDerived, class RHSDerived>
class OR<BooleanFunctionBase<LHSDerived>, BooleanFunctionBase<RHSDerived>>
Logical OR operator between two instances of BooleanFunctionBase.
template<class Range, class Mesh>
class P0
Degree 0 Lagrange finite element space.
template<>
class P0<Real, Geometry::Mesh<Context::Local>>
Scalar-valued piecewise constant (P0) Lagrange finite element space.
template<class Scalar>
class P0Element
Degree 0 Lagrange element.
template<class Scalar>
class P0Element<Math::Vector<Scalar>>
Piecewise constant (degree 0) vector Lagrange element.
template<class Range, class Mesh>
class P1
Degree 1 Lagrange finite element space.
template<class Scalar>
class P1<Math::Vector<Scalar>, Geometry::Mesh<Context::Local>>
Vector-valued continuous piecewise linear Lagrange finite element space.
template<class Scalar>
class P1<Scalar, Geometry::Mesh<Context::Local>>
Real valued Lagrange finite element space.
template<class Scalar>
class P1Element
Degree 1 Lagrange element.
template<class Scalar>
class P1Element<Math::Vector<Scalar>>
Continuous piecewise linear (degree 1) vector Lagrange element.
template<class Solution, class FES>
class PeriodicBC<TrialFunction<Solution, FES>, IndexMap<IndexSet>>
Represents a Peridodic boundary condition on a ShapeFunction object.
template<class Scalar>
class PeriodicBCBase
Abstract base class for a periodic boundary condition.
template<class LHS, class RHSDerived, class FES, ShapeFunctionSpaceType SpaceType>
class Potential<LHS, ShapeFunctionBase<ShapeFunction<RHSDerived, FES, SpaceType>, FES, SpaceType>>
template<class Base, class Exponent>
class Pow
Represents the power function.
template<class BaseDerived, class Number>
class Pow<FunctionBase<BaseDerived>, Number>
Represents the power function.
template<class ... Parameters>
class Problem
Represents a variational problem.
template<class LinearSystem>
class ProblemBase
Base class for variational problem objects.
template<class Scalar>
class ProblemBodyBase
Base class representing the body of a variational problem.
template<class LinearSystem, class U, class V>
class ProblemUVBase
General class to assemble linear systems with Operator and Vector generic types in a sequential context.
template<class Integrand>
class QuadratureRule
template<class LHSDerived, class RHSDerived, class LHSRange, class RHSRange, class LHSMesh, class RHSMesh>
class QuadratureRule<Dot<ShapeFunctionBase<Grad<ShapeFunction<LHSDerived, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>, ShapeFunctionBase<Grad<ShapeFunction<RHSDerived, P1<RHSRange, RHSMesh>, TestSpace>>, P1<RHSRange, RHSMesh>, TestSpace>>>
Integration of the isotropic Dot product of two instances of the P1 Grad of ShapeFunction.
template<class LHSDerived, class RHSDerived, class LHSRange, class RHSRange, class LHSMesh, class RHSMesh>
class QuadratureRule<Dot<ShapeFunctionBase<Jacobian<ShapeFunction<LHSDerived, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>, ShapeFunctionBase<Jacobian<ShapeFunction<RHSDerived, P1<RHSRange, RHSMesh>, TestSpace>>, P1<RHSRange, RHSMesh>, TestSpace>>>
Integration of the isotropic Frobenius inner product two instances of the P1 Jacobian of ShapeFunction.
template<class LHSDerived, class TrialFES, class RHSDerived, class TestFES>
class QuadratureRule<Dot<ShapeFunctionBase<LHSDerived, TrialFES, TrialSpace>, ShapeFunctionBase<RHSDerived, TestFES, TestSpace>>>
Approximation of the integral of the the dot product between a trial shape function and a test shape function.
template<class CoefficientDerived, class LHSDerived, class RHSDerived, class LHSRange, class RHSRange, class LHSMesh, class RHSMesh>
class QuadratureRule<Dot<ShapeFunctionBase<Mult<FunctionBase<CoefficientDerived>, ShapeFunctionBase<Grad<ShapeFunction<LHSDerived, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>, ShapeFunctionBase<Grad<ShapeFunction<RHSDerived, P1<RHSRange, RHSMesh>, TestSpace>>, P1<RHSRange, RHSMesh>, TestSpace>>>
Integration of the anisotropic Dot product of two instances of the P1 Grad of ShapeFunction.
template<class CoefficientDerived, class LHSDerived, class RHSDerived, class LHSRange, class RHSRange, class LHSMesh, class RHSMesh>
class QuadratureRule<Dot<ShapeFunctionBase<Mult<FunctionBase<CoefficientDerived>, ShapeFunctionBase<Jacobian<ShapeFunction<LHSDerived, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>, ShapeFunctionBase<Jacobian<ShapeFunction<RHSDerived, P1<RHSRange, RHSMesh>, TestSpace>>, P1<RHSRange, RHSMesh>, TestSpace>>>
Integration of the anisotropic Frobenius inner product two instances of the P1 Jacobian of ShapeFunction.
template<class CoefficientDerived, class LHSDerived, class RHSDerived, class LHSRange, class RHSRange, class LHSMesh, class RHSMesh>
class QuadratureRule<Dot<ShapeFunctionBase<Mult<FunctionBase<CoefficientDerived>, ShapeFunctionBase<ShapeFunction<LHSDerived, P1<LHSRange, LHSMesh>, TrialSpace>, P1<LHSRange, LHSMesh>, TrialSpace>>, P1<LHSRange, LHSMesh>, TrialSpace>, ShapeFunctionBase<ShapeFunction<RHSDerived, P1<RHSRange, RHSMesh>, TestSpace>, P1<RHSRange, RHSMesh>, TestSpace>>>
Integration of the anisotropic Dot product of two instances of the P1 ShapeFunction.
template<class FunctionDerived>
class QuadratureRule<FunctionBase<FunctionDerived>>
Quadrature rule for integrating functions on mesh polytopes.
template<class FES, class Data>
class QuadratureRule<GridFunction<FES, Data>>
Integration of a GridFunction object.
template<class LHSDerived, class RHSDerived, class Range, class Mesh>
class QuadratureRule<ShapeFunctionBase<Dot<FunctionBase<LHSDerived>, ShapeFunctionBase<ShapeFunction<RHSDerived, P1<Range, Mesh>, TestSpace>, P1<Range, Mesh>, TestSpace>>, P1<Range, Mesh>, TestSpace>>
Integration of the Dot product of some coefficient function and a P1 ShapeFunction.
template<class NestedDerived, class FES>
class QuadratureRule<ShapeFunctionBase<NestedDerived, FES, TestSpace>>
Approximation of the integral of a test shape function.
template<class NestedDerived, class Range, class Mesh>
class QuadratureRule<ShapeFunctionBase<ShapeFunction<NestedDerived, P1<Range, Mesh>, TestSpace>, P1<Range, Mesh>, TestSpace>>
Integration of a P1 ShapeFunction.
template<class Operand>
class Re
Extracts the real part of a complex-valued function.
template<class NestedDerived>
class Re<FunctionBase<NestedDerived>>
Specialization for FunctionBase operands.
template<class ... Values>
class RealFunction
template<class F>
class RealFunction<F>
Represents a scalar function given by an arbitrary scalar function.
template<>
class RealFunction<Real>
Represents a constant scalar function with type Real.
template<class Derived>
class RealFunctionBase
Base class for real-valued functions defined on a mesh.
class RelativeError
Utility class for computing relative errors.
template<class Scalar, class Derived>
class ScalarFunctionBase
Base class for scalar-valued functions with templated scalar type.
template<class Derived, class FES, ShapeFunctionSpaceType Space>
class ShapeFunction
Intermediate shape function class for CRTP derivation.
template<class Derived, class FES = typename FormLanguage::Traits<Derived>::FESType, ShapeFunctionSpaceType SpaceType = FormLanguage::Traits<Derived>::SpaceType>
class ShapeFunctionBase
Base class for shape function objects.
template<class NestedDerived>
class Sin<FunctionBase<NestedDerived>>
Sine function operator for real-valued scalar functions.
template<class NestedDerived>
class Sinh<FunctionBase<NestedDerived>>
Hyperbolic sine function operator for real-valued scalar functions.
template<class TrialFES, class TestFES>
class SparseProblem<TrialFES, TestFES, Math::Matrix<typename FormLanguage::Mult<typename FormLanguage::Traits<TrialFES>::ScalarType, typename FormLanguage::Traits<TestFES>::ScalarType>::Type>, Math::Vector<typename FormLanguage::Traits<TestFES>::ScalarType>>
General class to assemble linear systems with Math::SparseMatrix and Math::Vector types in a serial context.
template<class NestedDerived>
class Sqrt<FunctionBase<NestedDerived>>
Square root operation for functions.
template<class LHS, class RHS>
class Sum
Represents the sum operation.
template<class LHSDerived, class RHSDerived>
class Sum<FunctionBase<LHSDerived>, FunctionBase<RHSDerived>>
Addition of two functions.
template<class LHSDerived, class RHSDerived, class FES, ShapeFunctionSpaceType Space>
class Sum<ShapeFunctionBase<LHSDerived, FES, Space>, ShapeFunctionBase<RHSDerived, FES, Space>>
Addition of two shape functions.
template<class Operand>
class Tan
Represents the tangent function.
template<class NestedDerived>
class Tan<FunctionBase<NestedDerived>>
Tangent function operator for real-valued scalar functions.
template<class FES>
class TestFunction
Represents a function which belongs to a test space.
template<size_t K>
class TetrahedronBlend
Optimized blending parameter α for tetrahedral warp-blend.
template<class Operand>
class Trace
Represents the trace of a matrix function.
template<class NestedDerived>
class Trace<FunctionBase<NestedDerived>>
Trace of a FunctionBase instance.
template<>
class TraceOperator<FunctionBase>
Trace (boundary restriction) operator for functions.
template<class Operand>
class Transpose
Represents the transpose matrix $ A^T $ of some matrix $ A $ .
template<class NestedDerived>
class Transpose<FunctionBase<NestedDerived>>
Transpose of a matrix-valued function.
template<class NestedDerived, class FES, ShapeFunctionSpaceType Space>
class Transpose<ShapeFunctionBase<NestedDerived, FES, Space>>
Transpose of a matrix-valued ShapeFunction.
template<class Solution, class FES>
class TrialFunction
Represents a function which belongs to a trial space.
template<class Solution, class FES>
class TrialFunctionReference
Reference wrapper for trial functions.
template<size_t K>
class TriangleBlend
Optimized blending parameter α for triangular warp-blend.
template<class Operand>
class UnaryMinus
Represent the negation of an operand.
template<class Number>
class UnaryMinus<FormLanguage::List<LinearFormIntegratorBase<Number>>>
Negation of a list of linear form integrators.
template<class Number>
class UnaryMinus<FormLanguage::List<LocalBilinearFormIntegratorBase<Number>>>
Negation of a list of bilinear form integrators.
template<class NestedDerived>
class UnaryMinus<FunctionBase<NestedDerived>>
Negation of a function.
template<class Number>
class UnaryMinus<LinearFormIntegratorBase<Number>>
Negation of a linear form integrator.
template<class Number>
class UnaryMinus<LocalBilinearFormIntegratorBase<Number>>
Negation of a bilinear form integrator.
template<class NestedDerived, class FES, ShapeFunctionSpaceType Space>
class UnaryMinus<ShapeFunctionBase<NestedDerived, FES, Space>>
Negation of a shape function.
template<size_t K>
class VandermondeTriangle
Vandermonde matrix for nodal-to-modal transformation on triangles.
template<class ... Values>
class VectorFunction
template<class V, class ... Values>
class VectorFunction<V, Values...>
Represents a vector function which may be constructed from values which can be converted to objects of type RealFunction.
template<class Scalar, class Derived>
class VectorFunctionBase
Base class for vector-valued functions defined on a mesh.
template<size_t K>
class WarpBlendTetrahedron
Applies warp-blend algorithm to move tetrahedron nodes toward Fekete positions.
template<size_t K>
class WarpBlendTriangle
Applies warp-blend algorithm to move triangle nodes toward Fekete positions.
template<size_t K>
class WarpFactor1D
Computes the 1D warp factor for moving equispaced nodes to GLL positions.
template<size_t K>
class WarpShiftFace2D
Computes 2D warp-blend shift for a triangular face.
template<size_t K>
class WarpShiftFace3D
Computes 3D warp-blend shift for a tetrahedral face.
template<class Scalar>
class Zero<Math::Vector<Scalar>>
Vector zero function.
template<class Scalar>
class Zero<Scalar>
Scalar zero function.

Typedefs

template<class Scalar>
using EssentialBoundary = FormLanguage::List<DirichletBCBase<Scalar>>
Alias for a list of Dirichlet boundary conditions.
template<size_t K>
using RealH1Element = H1Element<K, Real>
Convenience alias for real-valued H1 element.
template<size_t K>
using ComplexH1Element = H1Element<K, Complex>
Convenience alias for complex-valued H1 element.
template<size_t K>
using VectorH1Element = H1Element<K, Math::Vector<Real>>
Convenience alias for real vector-valued H1 element.
template<size_t K>
using ComplexVectorH1Element = H1Element<K, Math::Vector<Complex>>
Convenience alias for complex vector-valued H1 element.
template<size_t K, class Mesh>
using RealH1 = H1<K, Real, Mesh>
Alias for a scalar real-valued H1 finite element space.
template<size_t K, class Mesh>
using ComplexH1 = H1<K, Complex, Mesh>
Alias for a scalar complex-valued H1 finite element space.
template<size_t K, class Mesh>
using VectorH1 = H1<K, Math::Vector<Real>, Mesh>
Alias for a vector-valued real H1 finite element space.
using RealP0Element = P0Element<Real>
Alias for P0Element<Real>
using ComplexP0Element = P0Element<Complex>
Alias for P0Element<Complex>
template<class Scalar>
using VectorP0Element = P0Element<Math::Vector<Scalar>>
Alias for P0Element<Math::Vector<Real>>
using RealVectorP0Element = VectorP0Element<Real>
Alias for real vector P0Element.
using ComplexVectorP0Element = VectorP0Element<Complex>
Alias for complex vector P0Element.
template<class Mesh>
using RealP0 = P0<Real, Mesh>
Alias for a scalar real-valued P0 finite element space.
template<class Mesh>
using ComplexP0 = P0<Complex, Mesh>
Alias for a scalar complex-valued P0 finite element space.
using RealP1Element = P1Element<Real>
Alias for P1Element<Real>
using ComplexP1Element = P1Element<Complex>
Alias for P1Element<Complex>
template<class Scalar>
using VectorP1Element = P1Element<Math::Vector<Scalar>>
Alias for P1Element<Math::Vector<Scalar>>
using RealVectorP1Element = P1Element<Math::Vector<Real>>
Alias for real vector P1Element.
template<class Mesh>
using RealP1 = P1<Real, Mesh>
Alias for a scalar real-valued P1 finite element space.
template<class Mesh>
using ComplexP1 = P1<Complex, Mesh>
Alias for a scalar complex-valued P1 finite element space.
template<class Mesh>
using VectorP1 = P1<Math::Vector<Real>, Mesh>
Alias for a vector-valued real P1 finite element space.
template<class Scalar>
using PeriodicBoundary = FormLanguage::List<PeriodicBCBase<Scalar>>
Alias for a list of peridodic boundary conditions.
template<class Scalar>
using VectorZero = Zero<Math::Vector<Scalar>>
Convenience typedef for vector zero function.

Variables

template<class LHSDerived, class RHSDerived>
AND< BooleanFunctionBase< LHSDerived >, BooleanFunctionBase< RHSDerived > >
Deduction guide for AND.
static const ShapeFunctionSpaceType TrialSpace constexpr
Shorthand variable for ShapeFunctionSpaceType::Trial.
static const ShapeFunctionSpaceType TestSpace constexpr
Shorthand variable for ShapeFunctionSpaceType::Test.
template<class LHSDerived, class RHSDerived>
GEQ< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > >
CTAD for GEQ.
template<class LHSDerived, class RHSDerived>
GT< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > >
CTAD for GT.
template<class LHSDerived, class RHSDerived>
LT< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > >
CTAD for LT.

Typedef documentation

#include <Rodin/Variational/DirichletBC.h>
template<class Scalar>
using Rodin::Variational::EssentialBoundary = FormLanguage::List<DirichletBCBase<Scalar>>

Alias for a list of Dirichlet boundary conditions.

#include <Rodin/Variational/H1/ForwardDecls.h>
template<size_t K>
using Rodin::Variational::RealH1Element = H1Element<K, Real>

Convenience alias for real-valued H1 element.

Template parameters
K Polynomial degree

Equivalent to H1Element<K, Real>. Used for scalar-valued problems such as the Poisson equation or heat conduction.

#include <Rodin/Variational/H1/ForwardDecls.h>
template<size_t K>
using Rodin::Variational::ComplexH1Element = H1Element<K, Complex>

Convenience alias for complex-valued H1 element.

Template parameters
K Polynomial degree

Equivalent to H1Element<K, Complex>. Used for complex-valued problems such as wave equations in frequency domain.

#include <Rodin/Variational/H1/ForwardDecls.h>
template<size_t K>
using Rodin::Variational::VectorH1Element = H1Element<K, Math::Vector<Real>>

Convenience alias for real vector-valued H1 element.

Template parameters
K Polynomial degree

Equivalent to H1Element<K, Math::Vector<Real>>. Used for vector-valued problems such as linear elasticity or fluid mechanics.

#include <Rodin/Variational/H1/ForwardDecls.h>
template<size_t K>
using Rodin::Variational::ComplexVectorH1Element = H1Element<K, Math::Vector<Complex>>

Convenience alias for complex vector-valued H1 element.

Template parameters
K Polynomial degree

Equivalent to H1Element<K, Math::Vector<Complex>>. Used for complex vector-valued problems such as electromagnetic wave propagation.

template<class Scalar>
using Rodin::Variational::VectorP1Element = P1Element<Math::Vector<Scalar>>

Alias for P1Element<Math::Vector<Scalar>>

Template parameters
Scalar Scalar type for vector components

#include <Rodin/Variational/PeriodicBC.h>
template<class Scalar>
using Rodin::Variational::PeriodicBoundary = FormLanguage::List<PeriodicBCBase<Scalar>>

Alias for a list of peridodic boundary conditions.

#include <Rodin/Variational/Zero.h>
template<class Scalar>
using Rodin::Variational::VectorZero = Zero<Math::Vector<Scalar>>

Convenience typedef for vector zero function.

Template parameters
Scalar Scalar type for vector components

Variable documentation

#include <Rodin/Variational/AND.h>
template<class LHSDerived, class RHSDerived>
Rodin::Variational::AND< BooleanFunctionBase< LHSDerived >, BooleanFunctionBase< RHSDerived > >

Deduction guide for AND.

static const ShapeFunctionSpaceType Rodin::Variational::TrialSpace constexpr
#include <Rodin/Variational/ForwardDecls.h>

Shorthand variable for ShapeFunctionSpaceType::Trial.

static const ShapeFunctionSpaceType Rodin::Variational::TestSpace constexpr
#include <Rodin/Variational/ForwardDecls.h>

Shorthand variable for ShapeFunctionSpaceType::Test.

#include <Rodin/Variational/GEQ.h>
template<class LHSDerived, class RHSDerived>
Rodin::Variational::GEQ< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > >

CTAD for GEQ.

#include <Rodin/Variational/GT.h>
template<class LHSDerived, class RHSDerived>
Rodin::Variational::GT< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > >

CTAD for GT.

#include <Rodin/Variational/LT.h>
template<class LHSDerived, class RHSDerived>
Rodin::Variational::LT< FunctionBase< LHSDerived >, FunctionBase< RHSDerived > >

CTAD for LT.