Integral

Represents mathematical expressions of the integral operator on a domain.

template <
  class Integrand>
class Integral;

Specializations

SpecializationDescription
Dot<…>
Full specialization
template <
  class Kernel,
  class LHSDerived,
  class TrialFES,
  class RHSDerived,
  class TestFES>
class Integral<
  Dot< Potential< Kernel, ShapeFunctionBase< LHSDerived, TrialFES, TrialSpace > >, ShapeFunctionBase< RHSDerived, TestFES, TestSpace > >> final;
Integral of a potential tested against a shape function.
Dot<…>
Full specialization
template <
  class LHSDerived,
  class TrialFES,
  class RHSDerived,
  class TestFES>
class Integral<
  Dot< ShapeFunctionBase< LHSDerived, TrialFES, TrialSpace >, ShapeFunctionBase< RHSDerived, TestFES, TestSpace > >> final;
Integration of the dot product of a trial and test operators.
GridFunction<FES, Data>
Full specialization
template <
  class FES,
  class Data>
class Integral<
  GridFunction< FES, Data >> final;
Integration of a GridFunction object.
ShapeFunctionBase<NestedDerived, …>
Full specialization
template <
  class NestedDerived,
  class FES>
requires ( std::is_same_v<typename FormLanguage::Traits< ShapeFunctionBase<NestedDerived, FES, TestSpace>>::RangeType, typename FormLanguage::Traits< ShapeFunctionBase<NestedDerived, FES, TestSpace>>::ScalarType>)
class Integral<
  ShapeFunctionBase< NestedDerived, FES, TestSpace >> final;
Integration of a test operator.
Template parameters
Integrand Type of the integrand

Represents the integral operator with a templated integrand type:

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

on the cells $ \mathcal{C}_h $ of a triangulation $ \mathcal{T}_h $ . The domain integral is defined as the sum of all members of the triangulation:

\[ \int_{\mathcal{C}_h} \mathrm{Integrand} := \sum_{T \in \mathcal{C}_h} \int_T \mathrm{Integrand} \ . \]