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Titlebook: Retarded Potentials and Time Domain Boundary Integral Equations; A Road Map Francisco-Javier Sayas Book 2016 Springer International Publish

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发表于 2025-3-21 16:41:04 | 显示全部楼层 |阅读模式
书目名称Retarded Potentials and Time Domain Boundary Integral Equations
副标题A Road Map
编辑Francisco-Javier Sayas
视频video
概述Full description of the rudiments of the vector-valued distributions as needed for the theory of time domain integral equations.First detailed exposition of the mathematical techniques for boundary in
丛书名称Springer Series in Computational Mathematics
图书封面Titlebook: Retarded Potentials and Time Domain Boundary Integral Equations; A Road Map Francisco-Javier Sayas Book 2016 Springer International Publish
描述This book offers a thoroughand self-contained exposition of the mathematics of time-domain boundaryintegral equations associated to the wave equation, including applications toscattering of acoustic and elastic waves. The book offers two differentapproaches for the analysis of these integral equations, including asystematic treatment of their numerical discretization using Galerkin(Boundary Element) methods in the space variables and ConvolutionQuadrature in the time variable. The first approach follows classical workstarted in the late eighties, based on Laplace transforms estimates. Thisapproach has been refined and made more accessible by tailoring thenecessary mathematical tools, avoiding an excess of generality. A secondapproach contains a novel point of view that the author and some of hiscollaborators have been developing in recent years, using the semigrouptheory of evolution equations to obtain improved results. The extension toelectromagnetic waves is explained in one of the appendices.
出版日期Book 2016
关键词Acoustics; Boundary integral equation; Retarded potentials; Variational methods; Wave equation; partial d
版次1
doihttps://doi.org/10.1007/978-3-319-26645-9
isbn_softcover978-3-319-79986-5
isbn_ebook978-3-319-26645-9Series ISSN 0179-3632 Series E-ISSN 2198-3712
issn_series 0179-3632
copyrightSpringer International Publishing Switzerland 2016
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发表于 2025-3-21 23:29:27 | 显示全部楼层
发表于 2025-3-22 00:27:01 | 显示全部楼层
From Laplace domain to time domain,nsforms. Our presentation will first restrict the kind of symbols (Laplace transforms) that we want to invert. Part of the material that follows is adapted (and modified) from the PhD dissertation of Antonio Laliena [61].
发表于 2025-3-22 05:42:29 | 显示全部楼层
Convolution Quadrature,ace and time domain looks somewhat unnatural but yields a general type of methods that can be easily used in black-box fashion. The method and much of its initial development are due to Christian Lubich. We will try not to be too heavy on notation for sequences by writing (..) to denote the sequence (..)..
发表于 2025-3-22 12:29:26 | 显示全部楼层
Patterns, extensions, and conclusions, have. We will next give two simple extensions of this theory, to problems defined on screens and to problems on linear elasticity. The chapter will finish with an overview of part of the literature and mentioning some work in progress.
发表于 2025-3-22 15:28:22 | 显示全部楼层
From time domain to Laplace domain,n, instead of thinking of functions of the space and time variables .(., .) we will think of functions of the time variable with values on a space of functions of the space variables, which amounts to considering the functions .(.) = .( ⋅ , .) (we will not change the name). In principle, our distrib
发表于 2025-3-22 17:31:00 | 显示全部楼层
From Laplace domain to time domain,r Theorem, which is a collection of results related to holomorphic extensions of the Fourier transform that can be understood as two-sided Laplace transforms. Our presentation will first restrict the kind of symbols (Laplace transforms) that we want to invert. Part of the material that follows is ad
发表于 2025-3-23 00:21:11 | 显示全部楼层
Convolution Quadrature,might seem bizarre at the beginning, this method ends up using data in the time domain but the Laplace transform of the operator. This mixture of Laplace and time domain looks somewhat unnatural but yields a general type of methods that can be easily used in black-box fashion. The method and much of
发表于 2025-3-23 04:27:37 | 显示全部楼层
The discrete layer potentials,let and Neumann problems associated with the wave equation. For the first one we will use a retarded single layer potential representation, and for the second one, a retarded double layer potential representation. We will detail the analysis of Galerkin semidiscretization error and some stability es
发表于 2025-3-23 06:38:38 | 显示全部楼层
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