This edited volume offers a state of the art overview of fast and robust
solvers for the Helmholtz equation. The book consists of three parts:
new developments and analysis in Helmholtz solvers, practical methods
and implementations of Helmholtz solvers, and industrial applications.
The Helmholtz equation appears in a wide range of science and
engineering disciplines in which wave propagation is modeled. Examples
are: seismic inversion, ultrasone medical imaging, sonar detection of
submarines, waves in harbours and many more. The partial differential
equation looks simple but is hard to solve. In order to approximate the
solution of the problem numerical methods are needed. First a
discretization is done. Various methods can be used: (high order) Finite
Difference Method, Finite Element Method, Discontinuous Galerkin Method
and Boundary Element Method. The resulting linear system is large, where
the size of the problem increases with increasing frequency. Due to
higher frequencies the seismic images need to be more detailed and,
therefore, lead to numerical problems of a larger scale. To solve these
three dimensional problems fast and robust, iterative solvers are
required. However for standard iterative methods the number of
iterations to solve the system becomes too large. For these reason a
number of new methods are developed to overcome this hurdle.
The book is meant for researchers both from academia and industry and
graduate students. A prerequisite is knowledge on partial differential
equations and numerical linear algebra.
