Rodin›Variational

BoundaryIntegral

Represents expressions of the integral operator on the boundary of a domain.

template <
  class Integrand>
class BoundaryIntegral;

Specializations

SpecializationDescription
Dot<…>
Full specialization
template <
  class LHSDerived,
  class TrialFES,
  class RHSDerived,
  class TestFES>
class BoundaryIntegral<
  Dot< ShapeFunctionBase< LHSDerived, TrialFES, TrialSpace >, ShapeFunctionBase< RHSDerived, TestFES, TestSpace > >> final;
Integration of the dot product of a trial and test operators.
ShapeFunctionBase<NestedDerived, …>
Full specialization
template <
  class NestedDerived,
  class FES>
class BoundaryIntegral<
  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:

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

on the boundary $ \mathcal{B}_h $ of a triangulation $\mathcal{T}_h $ a domain $ \Omega $ with boundary $ \partial \Omega $ . The boundary $ \mathcal{B}_h $ is defined as the union of the boundary faces:

\[ \mathcal{B}_h := \left\{ \partial T \cap \partial \Omega : T \in \mathcal{T}_h \right\} \ . \]

Then the boundary integral is just the sum of integrals over each member of the boundary:

\[ \int_{\mathcal{B}_h} \mathrm{Integrand} := \sum_{F \in \mathcal{B}_h} \int_F \mathrm{Integrand} \ . \]