Integral equation formulations are a competitive strategy in computational electromagnetics
but, lamentably, are often plagued by ill-conditioning and by related numerical instabilities …

Hierarchical matrices present an efficient way of treating dense matrices that arise in the
context of integral equations, elliptic partial differential equations, and control theory. While a …

We present a high-order boundary integral equation solver for 3D elliptic boundary value
problems on domains with smooth boundaries. We use Nyström's method for discretization …

We employ a data-sparse, recursive matrix representation, so-called-matrices, for the
efficient treatment of discretized integral operators. We obtain this format using local tensor …

Wavelets for the discretization of boundary integral operators usually have fixed order and
are constructed in some parameter space of the surface. Here a new approach is presented …

The advantages of the multiresolution finite wavelet domain method in terms of convergence
speed and solution localization capabilities have been demonstrated in dynamic simulations …

An explicitly-sparse representation for oscillatory kernels is presented in this work by
developing a wave atom based method. Multilevel wave atom-like functions are constructed …

We discuss the variable order Fast Multipole Method (FMM) applied to piecewise constant
Galerkin discretizations of boundary integral equations. In this version of the FMM low-order …

When the Fast Multipole Method is implemented with Taylor instead of multipole expansions
a large class of Green's functions can be treated in a unified manner. If in addition the order …

The success of the wavelet boundary element method (BEM) depends on its matrix
compression capability. The wavelet Galerkin BEM (WGBEM) based on non-standard form …