In the last few decades the concepts of structure-preserving discretization, geometric
integration and compatible discretizations have emerged as subfields in the numerical …

We show that the generalized Fourier transform can be used for reducing the computational
cost and memory requirements of radial basis function methods for multi-dimensional option …

Electromagnetic devices can be analysed by the coupled BE-FE method, where the
conducting and magnetic parts are discretized by finite elements. In contrast, the …

Abstract When the Boundary Element Method (BEM) is used to analyse electromagnetic
problems one is able to achieve an almost linear complexity by applying matrix compression …

In this paper we review some group theoretic techniques applied to discretizations of PDEs.
Inspired by the recent years active research in Lie group-and exponential-time integrators …

Procedures based on group representation theory, allowing the exploitation of geometrical
symmetry in symmetric Galerkin BEM formulations, are investigated. In particular, this …

Equivariant matrices, commuting with a group of permutation matrices, are considered. Such
matrices typically arise from PDEs and other computational problems where the …

In this paper we survey parts of group theory, with emphasis on structures that are important
in design and analysis of numerical algorithms. and in software design. In particular, we …

A little utilised but fundamental fact is that if one discretises a partial differential equation
using a symmetry-adapted basis corresponding to so-called irreducible representations, the …

Purpose Electrical machines commonly consist of moving and stationary parts. The field
simulation of such devices can be demanding if the underlying numerical scheme is solely …