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

Partial differential equations (PDEs) with random input data, such as random loadings and
coefficients, are reformulated as parametric, deterministic PDEs on parameter spaces of …

A new O (N) fast multipole formulation is proposed for non-oscillatory kernels. This algorithm
is applicable to kernels K (x, y) which are only known numerically, that is their numerical …

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 …

Due to rapid development of boundary element method (BEM), this article explores the
evolution of BEM over the past half century. We here summarize the overall development …

We consider the numerical solution of elliptic boundary value problems in domains with
random boundary perturbations. Assuming normal perturbations with small amplitude and …

Many mathematical assumptions on which classical derivative pricing methods are based
have come under scrutiny in recent years. The present volume offers an introduction to …

We study two nonlinear methods for statistical linear inverse problems when the operator is
not known. The two constructions combine Galerkin regularization and wavelet thresholding …

Abstract The Karhunen–Loève series expansion (KLE) decomposes a stochastic process
into an infinite series of pairwise uncorrelated random variables and pairwise L 2-orthogonal …

In the present paper we consider the fully discrete wavelet Galerkin scheme for the fast
solution of boundary integral equations in three dimensions. It produces approximate …