LEADER 04034nam 22006135 450 001 9910767513303321 005 20251009095200.0 010 $a3-031-13220-3 024 7 $a10.1007/978-3-031-13220-9 035 $a(MiAaPQ)EBC7133752 035 $a(Au-PeEL)EBL7133752 035 $a(CKB)25299466900041 035 $a(OCoLC)1350687456 035 $a(PPN)266349331 035 $a(DE-He213)978-3-031-13220-9 035 $a(EXLCZ)9925299466900041 100 $a20221108d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntegral Equation Methods for Evolutionary PDE $eA Convolution Quadrature Approach /$fby Lehel Banjai, Francisco-Javier Sayas 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (283 pages) 225 1 $aSpringer Series in Computational Mathematics,$x2198-3712 ;$v59 311 08$aPrint version: Banjai, Lehel Integral Equation Methods for Evolutionary PDE Cham : Springer International Publishing AG,c2022 9783031132193 320 $aIncludes bibliographical references and index. 327 $a1 Some examples of causal convolutions -- 2 Convolution quadrature for hyperbolic symbols -- 3 Algorithms for CQ: linear multistep methods -- 4 Acoustic scattering in the time domain -- 5 Runge-Kutta CQ -- 6 Transient electromagnetism -- 7 Boundary-field formulations -- 8 Parabolic problems -- 9 Data sparse methods and other topics. 330 $aThis book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and Runge?Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable. 410 0$aSpringer Series in Computational Mathematics,$x2198-3712 ;$v59 606 $aNumerical analysis 606 $aIntegral equations 606 $aDifferential equations 606 $aNumerical Analysis 606 $aIntegral Equations 606 $aDifferential Equations 615 0$aNumerical analysis. 615 0$aIntegral equations. 615 0$aDifferential equations. 615 14$aNumerical Analysis. 615 24$aIntegral Equations. 615 24$aDifferential Equations. 676 $a929.605 700 $aBanjai$b Lehel$01265944 702 $aSayas$b Francisco-Javier 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910767513303321 996 $aIntegral equation methods for evolutionary PDE$93073867 997 $aUNINA