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Green's Kernels and Meso-Scale Approximations in Perforated Domains (Paperback, 2013 ed.)
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Green's Kernels and Meso-Scale Approximations in Perforated Domains (Paperback, 2013 ed.)
Series: Lecture Notes in Mathematics, 2077
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Total price: R2,241
Discovery Miles: 22 410
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There are a wide range of applications in physics and structural
mechanics involving domains with singular perturbations of the
boundary. Examples include perforated domains and bodies with
defects of different types. The accurate direct numerical treatment
of such problems remains a challenge. Asymptotic approximations
offer an alternative, efficient solution. Green's function is
considered here as the main object of study rather than a tool for
generating solutions of specific boundary value problems. The
uniformity of the asymptotic approximations is the principal point
of attention. We also show substantial links between Green's
functions and solutions of boundary value problems for meso-scale
structures. Such systems involve a large number of small
inclusions, so that a small parameter, the relative size of an
inclusion, may compete with a large parameter, represented as an
overall number of inclusions. The main focus of the present text is
on two topics: (a) asymptotics of Green's kernels in domains with
singularly perturbed boundaries and (b) meso-scale asymptotic
approximations of physical fields in non-periodic domains with many
inclusions. The novel feature of these asymptotic approximations is
their uniformity with respect to the independent variables. This
book addresses the needs of mathematicians, physicists and
engineers, as well as research students interested in asymptotic
analysis and numerical computations for solutions to partial
differential equations.
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