Conformal and Multi-scale Time-Domain Methods: From Unstructured Meshes to Meshless Discretisations

Christophe Fumeaux, Dirk Baumann, Thomas Kaufmann, Zahra Shaterian, Maciej Klemm

Research output: Chapter in Book/Report/Conference proceedingChapter in a book


This chapter reviews recent advances in numerical time-domain techniques for solving Maxwell’s equations in non-Cartesian discretisations. This class of techniques, which can be denoted as conformal time-domain methods, provides an approach particularly advantageous for geometries comprising curved surfaces and multi-scale features. The first part of the chapter reviews the developments of a particular time-domain method applied in tetrahedral meshes, namely the Finite-Volume Time-Domain (FVTD) method. Different associated techniques aiming at enhancing the capability of the method are described, and the potential of the FVTD method for solving multi-scale problems is illustrated with the example of a 31-antenna breast cancer imaging system. The successful solution of this particular example demonstrates
the benefits of the approach for problems which might challenge time-domain methods applied in Cartesian grids, even when coupled to sub-cell models and sub-gridding schemes. The second part of the chapter points out to a novel class of methods which are amenable to conformal time-domain implementation on clouds of points. These so-called “meshless methods” do not require an explicit mesh definition, and open new perspectives towards future applications involving multi-scale multi-physics problems.
Original languageEnglish
Title of host publicationComputational Electromagnetics- Retrospective and Outlook
PublisherSpringer Verlag
ISBN (Print)978-981-287-094-0
Publication statusPublished - 14 Sept 2014


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