Convergence of collocation methods for time domain boundary integral equations

Davies, P.J. (2004) Convergence of collocation methods for time domain boundary integral equations. Oberwolfach Reports, 1 (1). pp. 579-581. ISSN 1660-8933

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The field of computational electromagnetism is dedicated to the design and analysis of numerical methods for the approximate solution of electromagnetic field problems. Since the exploitation of electromagnetic phenomena is one of the foundations of modern technology, computational electromagnetics is of tremendous industrial relevance: in a sense, it is peer to computational solid and fluid mechanics and huge research efforts are spent on developing and enhancing simulation methods and software for electromagnetic field computations. For a long time, computational electromagnetism remained a realm of engineering research with applied mathematics shunning the area. This was in stark contrast to elasticity and fluid mechanics, where mathematicians have been involved in the development of numerical methods from the very beginning. Maybe, the blame has to be laid on the incorrect belief of mathematicians who thought that the laws governing the behavior of electromagnetic fields basically boil down to well understood second-order elliptic problems. Fortunately, the past fifteen years have seen a real surge of mathematical research activities in the area of computational electromagnetism. This resulted in insights that have begun to have a big impact on the numerical methods used in engineering and industrial environments.