Wave propagation is studied in all branches of engineering science. The physical effects are used in technical devices such as acoustic sensors, electromagnetic antennas and radars or microwave cookers. This book studies the numerical solution of wave propagations using finite element methods.
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.
