Frank Ihlenburg - Böcker

This book is a report of a cognitive journey towards the reliable simulation of scattering problems using finite element methods. The pre-asymptotic analysis of Galerkin FEM for the Helmholtz equation with moderate and large wave number forms the core of the book. The topics include a priori and a posteriori error estimation as well as the stabilized methods. The mathematical investigation of model problems is given in close connection with the physical problem of acoustic scattering and fluid-solid interaction. Starting from the basic physical assumptions, the author methodically develops both the strong and weak forms of the governing equations. The main chapter on finite element analysis is preceded by a systematic treatment of Galerkin methods for indefinite sesquilinear forms. The book also contains broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. In the final chapter, three dimensional computational simulations are presented and compared with experimental data.Students and researchers in mathematics, physics and engineering, as well as scientists and computational engineers working on scattering problems will find this book of interest. The author has produced a self-contained and easily readable work containing numerous illustrations of the theory with numerical examples and computational results.

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 presented and compared with experimental data. The author also includes broad reference material on numerical methods for the Helmholtz equation in unbounded domains, including Dirichlet-to-Neumann methods, absorbing boundary conditions, infinite elements and the perfectly matched layer. A self-contained and easily readable work.

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Das Lehr- und Übungsbuch ist im Stil der Standardliteratur zur Technischen/Höheren Mechanik geschrieben und schließt inhaltlich an diese an. Theoretische Zusammenhänge werden mit Beispielen und Grafiken illustriert, dazu Übungsaufgaben mit durchgerechneten Lösungen im Anhang. Zielgruppe sind Studierende des Ingenieurwesens und praktisch tätige Ingenieure werden bei nichtlinearen Finite-Elemente-Simulationen unterstützt.  In der Verknüpfung FEM-CAD setzt sich die kontinuumsmechanische Modellierung mit Volumenelementen durch, zudem wird Stahl oft durch nichtmetallische Werkstoffe ersetzt. Die Kapitel zur Materialtheorie tragen diesen Trends Rechnung.  Weitere Themen sind Kinematik und Kinetik großer Deformationen sowie mathematische und thermodynamische Grundlagen. Für Elastizität und Plastizität wird jeweils auch das viskose Verhalten diskutiert. Das Materialverhalten bei großen Deformationen wird im Kontext mit der linearen Theorie und einfachen FE-Simulationen erläutert.