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Titlebook: Numerical Methods and Analysis of Multiscale Problems; Alexandre L. Madureira Book 2017 The Author(s) 2017 Asymptotic Analysis.Elliptic Eq

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書目名稱Numerical Methods and Analysis of Multiscale Problems
編輯Alexandre L. Madureira
視頻videohttp://file.papertrans.cn/670/669039/669039.mp4
概述Offers an introduction to asymptotic analysis techniques and various finite element methods for elliptic problems.Presents numerous case studies on modeling techniques of multiscale PDEs, in one- and
叢書名稱SpringerBriefs in Mathematics
圖書封面Titlebook: Numerical Methods and Analysis of Multiscale Problems; Alexandre L. Madureira Book 2017 The Author(s) 2017 Asymptotic Analysis.Elliptic Eq
描述.This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. ?Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses ?examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods..The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters..
出版日期Book 2017
關(guān)鍵詞Asymptotic Analysis; Elliptic Equations; Finite Elements; Multiscale; Singular Perturbed Problems; partia
版次1
doihttps://doi.org/10.1007/978-3-319-50866-5
isbn_softcover978-3-319-50864-1
isbn_ebook978-3-319-50866-5Series ISSN 2191-8198 Series E-ISSN 2191-8201
issn_series 2191-8198
copyrightThe Author(s) 2017
The information of publication is updating

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An Application in Neuroscience: Heterogeneous Cable Equation,f the cable is much smaller than its length, it originates a singular perturbed behavior equation that does not differ substantially from what was investigated in Chap.?. Moreover, other interesting asymptotics arise when considering a large number of synapses..We also show here that the Multiscale
板凳
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Two-Dimensional Reaction-Diffusion Equations,this time we show how to deal with the boundary layer in a two-dimensional problem, assuming that the boundary is smooth. We then derive an estimate for non-smooth domains. Finally, we present a numerical scheme that is a variation of the Residual Free Bubble method that works well for the problem u
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Modeling PDEs in Domains with Rough Boundaries, and we show two ways to decrease such burden. When the wrinkles are periodic, one way is to avoid the expensive discretization of the rough domain altogether, replacing the rough domain by a smooth one and changing the boundary conditions in such a way that the geometry of the wrinkles is captured.
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Alexandre L. Madureirahe circuit’s computational performance, i.e. how fast a circuit can compute its outputs. Thus, conventionally, input data are supplied to a circuit in intervals greater than or equal to the delay of the circuit. For example, in the pipelined combinational circuit shown in Figure 5.1 where blocks of
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