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

Publisher Summary This chapter explains basic examples of wavelet methods in numerical
analysis. It introduces the approximations and shows show the way they are related to …

This book presents a unified theory of the Finite Element Method and the Boundary Element
Method for a numerical solution of second order elliptic boundary value problems. This …

The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

The paper presents a new scheme for the representation of tensors which is well-suited for
high-order tensors. The construction is based on a hierarchy of tensor product subspaces …

The rapid development of parallel computing systems made it possible to recreate and
predict physical processes on computers. Nowadays, computer simulations complement …

The preceding Part I of this paper has introduced a class of matrices (ℋ-matrices) which are
data-sparse and allow an approximate matrix arithmetic of almost linear complexity. The …

More than anything else, the increase of computing power seems to stimulate the greed for
tackling ever larger problems involving large-scale numerical simulation. As a consequence …

The authors have been beguiled and entranced by mathematics all of their lives, and both
believe it is the highest expression of pure thought and an essential component-one might …

Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …