API Reference

(::CommonEdge)(f, η1, η2, η3, ξ)

Regularizing coordinate transform for parametrization on the unit triangle.

Common edge case.

(::CommonEdgeQuad)(f, η1, η2, η3, ξ)

Regularizing coordinate transform for parametrization on the unit square: [0,1]² ↦ Γ.

Common edge case.

(::CommonFace)(f, η1, η2, η3, ξ)

Regularizing coordinate transform for parametrization on the unit triangle.

Common face case.

(::CommonFaceQuad)(f, η1, η2, η3, ξ)

Regularizing coordinate transform for parametrization on the unit square: [0,1]² ↦ Γ.

Common face case.

(::CommonVertex)(f, η1, η2, η3, ξ)

Regularizing coordinate transform for parametrization on the unit triangle.

Common vertex case.

(::CommonVertexQuad)(f, η1, η2, η3, ξ)

Regularizing coordinate transform for parametrization on the unit square: [0,1]² ↦ Γ.

Common vertex case.

sauterschwab_parameterized(integrand, method::SauterSchwabStrategy)

Compute interaction integrals using the quadrature introduced in [1].

Here, integrand is the pull-back of the integrand into the parametric domain of the two triangles that define the integration domain.

The second argument 'strategy' is an object whose type is for triangles one of

- `CommonFace`
- `CommonEdge`
- `CommonVertex`
- `PositiveDistance`

and for quadrilaterals one of

- `CommonFaceQuad`
- `CommonEdgeQuad`
- `CommonVertexQuad`

according to the configuration of the two patches defining the domain of integration. The constructors of these classes take a single argument acc that defines the number of quadrature points along each of the four axes of the final rectangular (ξ,η) integration domain (see [1], Ch 5).

Note that here we use for a planar triangle the representation:

x = x[3] + u*(x[1]-x[3]) + v*(x[2]-x[3])

with u ranging from 0 to 1 and v ranging from 0 to 1-u. This parameter domain and representation is different from the one used in [1].

[1] Sauter. Schwwab, 'Boundary Element Methods', Springer Berlin Heidelberg, 2011