Clenshaw–Curtis and Gauss–Legendre Quadrature for Certain Boundary Element Integrals

Quadrature Rules for Fuzzy Integrals

Extrapolation-based Boundary Element Quadrature

Approximation of Integrals for Boundary Element Methods

A new method for approximating two-dimensional integrals B f (x) µ(dx) over surfaces B ⊂ R 3 is introduced where µ is the standard measure of surface area. Such integrals typically occur in boundary element methods. The algorithm is based on triangulations T := T i approximating B. Under the assumption that the surface B is given implicitly by an equation H(x) = 0, a retraction P : U ⊃ B → B is...

Volume Integrals for Boundary Element Methods

We consider the numerical approximation of volume integrals over bounded domains D := {x ∈ R : H(x) ≤ 0}, where H : R → R is a suitable decidability function. The integrands may be smooth maps or singular maps such as those arising in the volume potentials for boundary element methods. An adaptive integration method is described. It utilizes an automatic simplicial subdivision of the domain. Th...

Quadrature Estimates for Multidimensional Integrals

We prove estimates for the error in the most straightforward discrete approximation to the integral of a compactly supported function of n variables. The methods use Fourier analysis and interpolation theory, and also make contact with classical lattice point estimates. We also prove error estimates for the approximation of the integral over an interval by the trapezoidal rule and the midpoint ...