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Als ub ] erragende Gestalt ...tritt unsHelmholtz entgegen ...Seine ausserordentliche Stellung in der Geschichte der Naturwissensch- ten beruht auf einer ungew] ohnlich vielseitigen, eindringenden Be- bung, innerhalb deren die mathematische Seite eine wichtige, fur ] uns naturlic ] h in erster Linie in Betracht kommende Rolle spielt. (Felix 1 Klein, 84, p. 223]) Waves are interesting physical phenomena with important practical app- cations. Physicists and engineers are interested in the reliable simulation of processes in which waves are scattered from obstacles (scattering pr- lems). This...

A cognitive journey towards the reliable simulation of scattering problems using finite element methods, with the pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forming the core of this book. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations, while the main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. In the final chapter, three dimensional computational simulations are...