Rodin›Variational

QuadratureRule

template <
  class Integrand>
class QuadratureRule;

Specializations

SpecializationDescription
Dot<…>
Full specialization
template <
  class Kernel,
  class Range,
  class Mesh,
  class LHSDerived,
  class RHSDerived>
class QuadratureRule<
  Dot< Potential< Kernel, ShapeFunctionBase< LHSDerived, P1< Range, Mesh >, TrialSpace > >, ShapeFunctionBase< RHSDerived, P1< Range, Mesh >, TestSpace > >>;
Specialization for $\int \mathcal{K}(u) \cdot v$ in the case of P1 trial/test shape functions.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class LHSDerived,
  class RHSDerived,
  class TrialRange,
  class TestRange,
  class Mesh>
requires (!FormLanguage::IsMatrixRange<TrialRange>::Value && !FormLanguage::IsMatrixRange<TestRange>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< Div< ShapeFunction< LHSDerived, H1< KTrial, TrialRange, Mesh >, TrialSpace > >, H1< KTrial, TrialRange, Mesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, H1< KTest, TestRange, Mesh >, TestSpace >, H1< KTest, TestRange, Mesh >, TestSpace > >>;
Specialization for $\int \nabla \cdot u \, q \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class RHSDerived,
  class LHSMesh,
  class RHSMesh>
class QuadratureRule<
  Dot< ShapeFunctionBase< Div< ShapeFunction< LHSDerived, P1< Math::SpatialVector< Real >, LHSMesh >, TrialSpace > >, P1< Math::SpatialVector< Real >, LHSMesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, P1< Real, RHSMesh >, TestSpace >, P1< Real, RHSMesh >, TestSpace > >>;
Specialization for $\int (\nabla \cdot u)\, q \ dx$ in the case of P1 shape functions.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class CoeffDerived,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< Dot< FunctionBase< CoeffDerived >, ShapeFunctionBase< Jacobian< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< Dot< FunctionBase< CoeffDerived >, ShapeFunctionBase< Jacobian< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace > >, H1< KTest, Scalar, Mesh >, TestSpace > >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Integration of a rank-one form in the H1 Jacobian of ShapeFunction.
Dot<…>
Full specialization
template <
  class CoeffDerived,
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (FormLanguage::IsVectorRange<LHSRange>::Value && FormLanguage::IsVectorRange<RHSRange>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< Dot< FunctionBase< CoeffDerived >, ShapeFunctionBase< Jacobian< ShapeFunction< LHSDerived, P1< LHSRange, LHSMesh >, TrialSpace > >, P1< LHSRange, LHSMesh >, TrialSpace > >, P1< LHSRange, LHSMesh >, TrialSpace >, ShapeFunctionBase< Dot< FunctionBase< CoeffDerived >, ShapeFunctionBase< Jacobian< ShapeFunction< RHSDerived, P1< RHSRange, RHSMesh >, TestSpace > >, P1< RHSRange, RHSMesh >, TestSpace > >, P1< RHSRange, RHSMesh >, TestSpace > >>;
Integration of a rank-one form in the P1 Jacobian of ShapeFunction.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
class QuadratureRule<
  Dot< ShapeFunctionBase< Grad< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< Grad< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace > >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Specialization for $\int \nabla u \cdot \nabla v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (!FormLanguage::IsMatrixRange<LHSRange>::Value)
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.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
class QuadratureRule<
  Dot< ShapeFunctionBase< Jacobian< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< Jacobian< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace > >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Specialization for $\int J u : J v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (FormLanguage::IsVectorRange<LHSRange>::Value && FormLanguage::IsVectorRange<RHSRange>::Value)
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.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class TrialFES,
  class RHSDerived,
  class TestFES>
class QuadratureRule<
  Dot< ShapeFunctionBase< LHSDerived, TrialFES, TrialSpace >, ShapeFunctionBase< RHSDerived, TestFES, TestSpace > >>;
Local bilinear-form quadrature for the dot product of a trial and a test shape function.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
requires (((!FormLanguage::IsMatrixRange<Scalar>::Value)) && (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value))
class QuadratureRule<
  Dot< ShapeFunctionBase< Mult< FunctionBase< CoefficientDerived >, ShapeFunctionBase< Grad< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< Grad< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace > >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Specialization for $\int (A \nabla u) \cdot \nabla v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (((!FormLanguage::IsMatrixRange<LHSRange>::Value)) && (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value))
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.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
requires (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value && !FormLanguage::IsMatrixRange<Scalar>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< Mult< FunctionBase< CoefficientDerived >, ShapeFunctionBase< Jacobian< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< Jacobian< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace > >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Specialization for $\int (A J u) : J v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value && !FormLanguage::IsMatrixRange<LHSRange>::Value && !FormLanguage::IsMatrixRange<RHSRange>::Value)
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.
Dot<…>
Full specialization
template <
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value)
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.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class LeftOperand,
  class RightOperand,
  class RHSDerived,
  class Scalar,
  class Mesh>
requires (H1MassOperands<Mult<LeftOperand, RightOperand>>::Value && std::is_same_v<typename H1MassOperands< Mult<LeftOperand, RightOperand>>::MultiplicandType::FESType, H1<KTrial, Scalar, Mesh>>)
class QuadratureRule<
  Dot< ShapeFunctionBase< Mult< LeftOperand, RightOperand >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Weighted mass quadrature for plain H1 trial and test leaves.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
requires (!FormLanguage::IsMatrixRange<Scalar>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< Mult< ShapeFunctionBase< Jacobian< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, FunctionBase< CoefficientDerived > >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Specialization for $\int (\mathbf{J}\,u \cdot f) \cdot v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value && !FormLanguage::IsMatrixRange<LHSRange>::Value && !FormLanguage::IsMatrixRange<RHSRange>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< Mult< ShapeFunctionBase< Jacobian< ShapeFunction< LHSDerived, P1< LHSRange, LHSMesh >, TrialSpace > >, P1< LHSRange, LHSMesh >, TrialSpace >, FunctionBase< CoefficientDerived > >, P1< LHSRange, LHSMesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, P1< RHSRange, RHSMesh >, TestSpace >, P1< RHSRange, RHSMesh >, TestSpace > >>;
Specialization for $ \int (\nabla u \cdot f) \cdot v $ in the case of P1 shape functions.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
class QuadratureRule<
  Dot< ShapeFunctionBase< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace >, H1< KTest, Scalar, Mesh >, TestSpace > >>;
Specialization for $\int u \cdot v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class LHSDerived,
  class RHSDerived,
  class TrialRange,
  class TestRange,
  class Mesh>
requires (!FormLanguage::IsMatrixRange<TrialRange>::Value && !FormLanguage::IsMatrixRange<TestRange>::Value)
class QuadratureRule<
  Dot< ShapeFunctionBase< ShapeFunction< LHSDerived, H1< KTrial, TrialRange, Mesh >, TrialSpace >, H1< KTrial, TrialRange, Mesh >, TrialSpace >, ShapeFunctionBase< Div< ShapeFunction< RHSDerived, H1< KTest, TestRange, Mesh >, TestSpace > >, H1< KTest, TestRange, Mesh >, TestSpace > >>;
Specialization for $\int p \, \nabla \cdot v \ dx$ with H1 trial and test shape functions.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
class QuadratureRule<
  Dot< ShapeFunctionBase< ShapeFunction< LHSDerived, P1< LHSRange, LHSMesh >, TrialSpace >, P1< LHSRange, LHSMesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, P1< RHSRange, RHSMesh >, TestSpace >, P1< RHSRange, RHSMesh >, TestSpace > >>;
Integration of the isotropic Dot product of two instances of the P1 ShapeFunction.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class RHSDerived,
  class LHSMesh,
  class RHSMesh>
class QuadratureRule<
  Dot< ShapeFunctionBase< ShapeFunction< LHSDerived, P1< Real, LHSMesh >, TrialSpace >, P1< Real, LHSMesh >, TrialSpace >, ShapeFunctionBase< Div< ShapeFunction< RHSDerived, P1< Math::SpatialVector< Real >, RHSMesh >, TestSpace > >, P1< Math::SpatialVector< Real >, RHSMesh >, TestSpace > >>;
Specialization for $\int p \, (\nabla \cdot v)\, dx$ in the case of P1 shape functions.
FunctionBase<FunctionDerived>
Full specialization
template <
  class FunctionDerived>
class QuadratureRule<
  FunctionBase< FunctionDerived >> final;
Quadrature rule for integrating general functions on mesh polytopes.
GridFunction<FES, Data>
Full specialization
template <
  class FES,
  class Data>
class QuadratureRule<
  GridFunction< FES, Data >>;
Integration of a scalar grid function over a mesh region.
Mult<…>
Full specialization
template <
  size_t KTrial,
  size_t KTest,
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
requires (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value)
class QuadratureRule<
  Mult< FunctionBase< CoefficientDerived >, Dot< ShapeFunctionBase< ShapeFunction< LHSDerived, H1< KTrial, Scalar, Mesh >, TrialSpace >, H1< KTrial, Scalar, Mesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, H1< KTest, Scalar, Mesh >, TestSpace >, H1< KTest, Scalar, Mesh >, TestSpace > > >>;
Specialization for $\int c \, (u \cdot v) \ dx$ with H1 trial and test shape functions.
Mult<…>
Full specialization
template <
  class CoefficientDerived,
  class LHSDerived,
  class RHSDerived,
  class LHSRange,
  class RHSRange,
  class LHSMesh,
  class RHSMesh>
requires (!FormLanguage::IsTensorRange<typename FormLanguage::Traits< FunctionBase<CoefficientDerived>>::RangeType>::Value)
class QuadratureRule<
  Mult< FunctionBase< CoefficientDerived >, Dot< ShapeFunctionBase< ShapeFunction< LHSDerived, P1< LHSRange, LHSMesh >, TrialSpace >, P1< LHSRange, LHSMesh >, TrialSpace >, ShapeFunctionBase< ShapeFunction< RHSDerived, P1< RHSRange, RHSMesh >, TestSpace >, P1< RHSRange, RHSMesh >, TestSpace > > >>;
Specialization for $\int c \, (u \cdot v) \ dx$ in the case of P1 shape functions.
ShapeFunctionBase<…>
Full specialization
template <
  size_t K,
  class LHSDerived,
  class RHSDerived,
  class Scalar,
  class Mesh>
class QuadratureRule<
  ShapeFunctionBase< Dot< FunctionBase< LHSDerived >, ShapeFunctionBase< ShapeFunction< RHSDerived, H1< K, Scalar, Mesh >, TestSpace >, H1< K, Scalar, Mesh >, TestSpace > >, H1< K, Scalar, Mesh >, TestSpace >>;
Specialization for $\int f \cdot v \ dx$ with an H1 test shape function.
ShapeFunctionBase<…>
Full specialization
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.
ShapeFunctionBase<NestedDerived, …>
Full specialization
template <
  class NestedDerived,
  class FES>
class QuadratureRule<
  ShapeFunctionBase< NestedDerived, FES, TestSpace >>;
Local linear-form quadrature for a test shape function expression.
ShapeFunctionBase<…>
Full specialization
template <
  size_t K,
  class NestedDerived,
  class Scalar,
  class Mesh>
class QuadratureRule<
  ShapeFunctionBase< ShapeFunction< NestedDerived, H1< K, Scalar, Mesh >, TestSpace >, H1< K, Scalar, Mesh >, TestSpace >>;
Specialization for $\int v \ dx$ with an H1 test shape function.
ShapeFunctionBase<…>
Full specialization
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 parameters
Integrand Type of the integrand

Represents the quadrature rule approximation of an integral:

\[ \int_{\mathcal{R}_h} \mathrm{Integrand} \]

where $ \mathcal{R}_h $ is some region of the mesh $ \mathcal{T}_h $ .