Preface to BIT 55:1

Abstract

This special issue of BIT contains articles related to the Workshop on Computational Electromagnetics andAcoustics, held at theMathematisches Forschungsinstitut Oberwolfach, Germany, in January 2013. This workshop was organized by R. Hiptmair (ETH Zurich, Switzerland), R. H.W. Hoppe (Univ. Augsburg, Germany and Houston, Texas), P. Joly (INRIA, Paris, France), and U. Langer (Univ. Linz, Austria). It was attended by 52 invited researchers in the field and had its focus on recent developments of mathematical theory and algorithms. A total of 26 presentations were given at the workshop, their topics covering major current developments in the field of Computational Electromagnetics and Acoustics. Extended abstracts of all contributions have been collected in the Oberwolfach Report 03/2013 (http://www.ems-ph.org/journals/ show_issue.php?issn=1660-8933&vol=10&iss=1, doi:10.4171/OWR/2013/03). Now, several participants of theworkshop, all leaders in their fields, have heeded the organizers’ call for papers for this special issue of the journal BIT. Their manuscripts provide a glimpse of current progress in the mathematical and numerical analysis of problems arising in acoustics or electromagnetics. The contribution P. Monk and J. Chen is in the very topical area of time-domain boundary integral equation methods, and contains deep numerical analysis of a convolution quadrature based scheme for transient electromagnetics. The article by X. Claeys, E. Spindler and myself proposes and analyses a novel boundary integral formulation for scattering transmission problems, whose Galerkin boundary discretization will always yield well conditioned linear systems In their paper M. Dauge, R. A. Norton, and R. Scheichl study the regularity of Bloch modes in photonic crystals, which arise as solutions of eigenvalue problems. They obtain new results in elliptic regularity theory, which are important for designing good approximation spaces for numerical methods.