LEADER 04370nam 22006975 450 001 9910254290103321 005 20200704071952.0 024 7 $a10.1007/978-3-319-28832-1 035 $a(CKB)3710000001083940 035 $a(DE-He213)978-3-319-28832-1 035 $a(MiAaPQ)EBC4816307 035 $a(PPN)199768854 035 $a(EXLCZ)993710000001083940 100 $a20170302d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModern Solvers for Helmholtz Problems /$fedited by Domenico Lahaye, Jok Tang, Kees Vuik 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (XII, 243 p. 54 illus., 39 illus. in color.) 225 1 $aGeosystems Mathematics,$x2510-1544 311 $a3-319-28831-8 311 $a3-319-28832-6 320 $aIncludes bibliographical references at the end of each chapters. 327 $aI Algorithms: new developments and analysis -- II Algorithms: practical methods and implementations -- III Industrial applications. . 330 $aThis edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to be more detailed and, therefore, lead to numerical problems of a larger scale. To solve these three dimensional problems fast and robust, iterative solvers are required. However for standard iterative methods the number of iterations to solve the system becomes too large. For these reason a number of new methods are developed to overcome this hurdle. The book is meant for researchers both from academia and industry and graduate students. A prerequisite is knowledge on partial differential equations and numerical linear algebra. 410 0$aGeosystems Mathematics,$x2510-1544 606 $aNumerical analysis 606 $aPartial differential equations 606 $aMatrix theory 606 $aAlgebra 606 $aDifference equations 606 $aFunctional equations 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aDifference and Functional Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12031 615 0$aNumerical analysis. 615 0$aPartial differential equations. 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aDifference equations. 615 0$aFunctional equations. 615 14$aNumerical Analysis. 615 24$aPartial Differential Equations. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aDifference and Functional Equations. 676 $a530.124 702 $aLahaye$b Domenico$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aTang$b Jok$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aVuik$b Kees$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254290103321 996 $aModern Solvers for Helmholtz Problems$91562273 997 $aUNINA