Volume integrals for boundary element methods

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...

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...

Boundary Element Methods for Eddy

Finite Element-Boundary Element Methods for Accurate Modeling of Excluded Volume Effects in Dielectric Relaxation Spectroscopy

We apply the finite element-boundary element method (FEM-BEM) to accurately model a curvilinear interior interface in a finite domain. This avoids unphysical singularities at the interface due to a piece-wise linear approximation. The investigation of this type of FEM-BEM coupling arises from the need to simulate the biophysical problem of dielectric relaxation spectroscopy of solvated proteins...

Numerical Quadratures for Singular and Hypersingular Integrals in Boundary Element Methods

A method is developed for the computation of the weights and nodes of a numerical quadrature which integrates functions containing singularities up to order 1/x2, without the requirement to know the coefficients of the singularities exactly. The work is motivated by the need to evaluate such integrals on boundary elements in potential problems and is a simplification of a previously published m...