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Field name	Details
Dewey Class	518
Title	Modern Solvers for Helmholtz Problems ([EBook]) / edited by Domenico Lahaye, Jok Tang, Kees Vuik.
Added Personal Name	Lahaye, Domenico editor.
	Tang, Jok editor.
	Vuik, Kees editor.
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Birkh?ser, , 2017.
Physical Details	XII, 243 p. 54 illus., 39 illus. in color : online resource.
Series	Geosystems Mathematics 2510-1544
ISBN	9783319288321
Summary Note	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.:
Contents note	I Algorithms: new developments and analysis -- II Algorithms: practical methods and implementations -- III Industrial applications. .
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-319-28832-1
Links to Related Works	Subject References: Algebra . Difference and Functional Equations . Difference equations . Functional equations . Linear and Multilinear Algebras, Matrix Theory . Mathematics . Matrix theory . Numerical Analysis . Partial differential equations . Authors: Lahaye, Domenico . Tang, Jok . Vuik, Kees . Corporate Authors: SpringerLink (Online service) . Series: Geosystems Mathematics . Classification: 518 .

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Modern Solvers for Helmholtz Problems

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