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001451106 001__ 1451106
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001451106 019__ $$a1350687456
001451106 020__ $$a9783031132209$$q(electronic bk.)
001451106 020__ $$a3031132203$$q(electronic bk.)
001451106 020__ $$z9783031132193
001451106 020__ $$z303113219X
001451106 0247_ $$a10.1007/978-3-031-13220-9$$2doi
001451106 035__ $$aSP(OCoLC)1350617823
001451106 040__ $$aYDX$$beng$$erda$$epn$$cYDX$$dGW5XE$$dEBLCP$$dOCLCF$$dOCLCQ
001451106 049__ $$aISEA
001451106 050_4 $$aQA431
001451106 08204 $$a515/.45$$223/eng/20221130
001451106 1001_ $$aBanjai, Lehel,$$eauthor.
001451106 24510 $$aIntegral equation methods for evolutionary PDE :$$ba convolution quadrature approach /$$cLehel Banjai, Francisco-Javier Sayas.
001451106 264_1 $$aCham :$$bSpringer,$$c[2022]
001451106 264_4 $$c©2022
001451106 300__ $$a1 online resource (xix, 268 pages) :$$billustrations.
001451106 336__ $$atext$$btxt$$2rdacontent
001451106 337__ $$acomputer$$bc$$2rdamedia
001451106 338__ $$aonline resource$$bcr$$2rdacarrier
001451106 4901_ $$aSpringer series in computational mathematics ;$$vvolume 59
001451106 504__ $$aIncludes bibliographical references and index.
001451106 5050_ $$aIntro -- Preface -- Contents -- List of Symbols -- 1 Some Examples of Causal Convolutions -- 1.1 Abel's Equation and Duhamel's Principle -- 1.2 A Quick Review of Laplace Transforms and Causal Distributions -- 1.3 Convolution Form of Systems of Linear ODE -- 1.4 A One Dimensional `Scattering' Problem -- 1.5 A Transmission Problem for the Acoustic Wave Equation in 3D -- 2 Convolution Quadrature for Hyperbolic Symbols -- 2.1 Introduction to Operational Calculus -- 2.2 Discrete Convolutions by CQ -- 2.3 Derivation of CQ Using the z Transform -- 2.4 Yet Another Derivation of CQ
001451106 5058_ $$a2.5 Linear Multistep CQ Convergence Analysis -- 2.6 Positivity Conservation of CQ -- 2.7 Generalisation of CQ to Non-uniform Time-Steps -- 2.8 Combination with a Galerkin Discretisation -- 2.9 Hyperbolic Kernels Under Perturbation -- 3 Algorithms for CQ: Linear Multistep Methods -- 3.1 Computation of CQ Weights and Evaluation of Convolution -- 3.2 Solving a Discrete Convolutional System (All-Steps-at-Once) -- 3.3 Recursive, Marching-on-in-Time Implementation -- 3.4 Avoiding Limits to Accuracy Due to Round-Off -- 3.5 Examples -- 4 Acoustic Scattering in the Time Domain
001451106 5058_ $$a4.1 Acoustic Scattering by Bounded Obstacles -- 4.2 Superposition of Spherical Waves -- Two-Dimensional Problems -- 4.3 Construction via the Laplace Domain -- Integral Operators in the Laplace Domain -- 4.4 The Bamberger Ha-Duong Theory -- 4.5 Coercivity of the Acoustic Calderón Operator -- 4.6 Boundary Integral Formulation of Sound-Soft Scattering -- 4.7 Boundary Integral Formulation of Sound-Hard Scattering -- 4.8 Kirchhoff's Formula and the Direct Method -- 4.9 Full Discretisation: Sound Soft Scattering -- 4.10 Full Discretisation: Sound-Hard Scattering
001451106 5058_ $$a4.11 Absorbing (Linear and Nonlinear) Boundary Conditions -- Boundary Integral Representation of the Scattered Field -- Full-Discretisation of the Linear Problem -- Semi-discretisation in Time in the Nonlinear Case -- 4.12 Equivalence of CQ for TDBIE to Linear Multistep Discretisation of the PDE -- 4.13 Choice of the Linear Multistep Method -- 5 Runge-Kutta CQ -- 5.1 Implicit Differentiation with RK Methods -- 5.2 Operator Valued Functions -- 5.3 Convergence of RK CQ -- 5.4 Implementation of the RK-CQ Method and Simple Tests -- 5.5 Accuracy of RK-CQ and Comparison with Linear Multistep CQ
001451106 5058_ $$a5.6 Combination with a Galerkin Discretisation in Space -- 5.7 Sound-Soft Scattering Revisited -- 5.8 Details of Some Technical Proofs -- 6 Transient Electromagnetism -- 6.1 Maxwell Equation and the Electric Field Integral Equation -- 6.2 Maxwell Boundary Integral Operators in the Laplace Domain -- 6.3 Time-Domain Estimates for Scattering by a Perfect Conductor -- 6.4 Further Topics -- 7 Boundary-Field Formulations -- 7.1 Acoustic Scattering by Non-homogeneous, Penetrable Obstacle -- 7.2 Coupled Domain/Boundary Integral Formulation -- 7.3 Fully Implicit, Fully Discretised System
001451106 506__ $$aAccess limited to authorized users.
001451106 520__ $$aThis book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method. Properties of convolution quadrature, based on both linear multistep and RungeKutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book. Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.
001451106 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed November 30, 2022).
001451106 650_0 $$aIntegral equations.
001451106 650_0 $$aConvolutions (Mathematics)
001451106 650_0 $$aDifferential equations, Partial.
001451106 655_0 $$aElectronic books.
001451106 7001_ $$aSayas, Francisco-Javier,$$eauthor.
001451106 77608 $$iPrint version: $$z303113219X$$z9783031132193$$w(OCoLC)1334722333
001451106 830_0 $$aSpringer series in computational mathematics ;$$v59.
001451106 852__ $$bebk
001451106 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-13220-9$$zOnline Access$$91397441.1
001451106 909CO $$ooai:library.usi.edu:1451106$$pGLOBAL_SET
001451106 980__ $$aBIB
001451106 980__ $$aEBOOK
001451106 982__ $$aEbook
001451106 983__ $$aOnline
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