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Note publique d'information : 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
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