Synopses & Reviews
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.
Synopsis
Wave propagation is studied in all branches of engineering science and finite element methods have been established for many years as a universal method for analyzing numerical mechanics. Using a variety of applications from engineering science, this book presents the state of the art in finite element analysis of wave propagation.
Table of Contents
The governing equations of time-harmonic wave propagation.- Analytical and variational solutions of exterior Helmholtz problems.- Discretization methods for exterior Helmholtz problems.- Finite element error analysis and control.- Computational Simulation of Elastic Scattering.