Gary Cohen - Böcker

These proceedings include articles of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2003), held in Jyviiskylii, Finland, from June 30 to July 4, 2003. As in the previous five conferences in this series, its program covered a broad range of topics related to the mathematical modeling and numerical simulation of wave phenomena. Topics of specific interest included various areas of acoustics, electromagnetics, elasticity, and related optimization and inverse problems. In addition to the nine invited presentations, we selected for this confer- ence 152 high-level papers from over 20 countries, especially from Europe. Most of them are contained in this book. They provide an extensive overview on the recent developments in the theoretical and applied wave propagation. The conference was organized by the University of Jyviiskylii and the Institut National de Recherche en Informatique et en Automatique (INRIA) in cooperation with Jyviiskylii Congresses. The editors would like to thank the organizing institutions and the in- ternational scientific committee for their efforts in the preparation of this conference.We are also grateful to all the authors of the papers for their contributions to these proceedings. Special acknowledgment is due to Ms. Dominique Potherat, to Ms. Helene Chanut and to Ms. Marja-Leena Ranta- lainen for their valuable assistance in the preparation of this proceedings volume. Jyviiskylii, Gary C. Cohen February 2003 Erkki H eikkola Patrick loly Pekka Neittaanmiiki Contents Part I Invited Presentations Dispersive Properties of High Order Finite Elements Mark Ainsworth...3 ...

Solving efficiently the wave equations involved in modeling acoustic, elastic or electromagnetic wave propagation remains a challenge both for research and industry. To attack the problems coming from the propagative character of the solution, the author constructs higher-order numerical methods to reduce the size of the meshes, and consequently the time and space stepping, dramatically improving storage and computing times. This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem. A central role is played by the notion of the dispersion relation for analyzing the methods. The last chapter is devoted to unbounded domains which are modeled using perfectly matched layer (PML) techniques. Numerical examples are given.

This book surveys higher-order finite difference methods and develops various mass-lumped finite (also called spectral) element methods for the transient wave equations, and presents the most efficient methods, respecting both accuracy and stability for each sort of problem.

These proceedings include articles of the Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2003), held in Jyviiskylii, Finland, from June 30 to July 4, 2003. As in the previous five conferences in this series, its program covered a broad range of topics related to the mathematical modeling and numerical simulation of wave phenomena. Topics of specific interest included various areas of acoustics, electromagnetics, elasticity, and related optimization and inverse problems. In addition to the nine invited presentations, we selected for this confer- ence 152 high-level papers from over 20 countries, especially from Europe. Most of them are contained in this book. They provide an extensive overview on the recent developments in the theoretical and applied wave propagation. The conference was organized by the University of Jyviiskylii and the Institut National de Recherche en Informatique et en Automatique (INRIA) in cooperation with Jyviiskylii Congresses. The editors would like to thank the organizing institutions and the in- ternational scientific committee for their efforts in the preparation of this conference.We are also grateful to all the authors of the papers for their contributions to these proceedings. Special acknowledgment is due to Ms. Dominique Potherat, to Ms. Helene Chanut and to Ms. Marja-Leena Ranta- lainen for their valuable assistance in the preparation of this proceedings volume. Jyviiskylii, Gary C. Cohen February 2003 Erkki H eikkola Patrick loly Pekka Neittaanmiiki Contents Part I Invited Presentations Dispersive Properties of High Order Finite Elements Mark Ainsworth...3 ...

This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem of its spurious-free approximations. Treatment of unbounded domains by Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML) is described and analyzed in a separate chapter. The two last chapters deal with time approximation including local time-stepping and with the study of some complex models, i.e. acoustics in flow, gravity waves and vibrating thin plates. Throughout, emphasis is put on the accuracy and computational efficiency of the methods, with attention brought to their practical aspects.This monograph also covers in details the theoretical foundations and numerical analysis of these methods. As a result, this monograph will be of interest to practitioners, researchers, engineers and graduate students involved in the numerical simulationof waves.