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Asymptotic analysis of solutions to transmission problems in solids with many inclusions

Nieves

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Abstract

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterized by two small parameters that determine the nominal diameter of individual inclusions and their separation within the cluster. These small parameters can be comparable to each other. Remainder estimates of the asymptotic approximation are rigorously justified. Numerical illustrations demonstrate the efficiency of the asymptotic approach when compared with benchmark finite element algorithms.


Read More: https://epubs.siam.org/doi/10.1137/16M1102586

Acceptance Date May 8, 2017
Publication Date Aug 22, 2017
Journal SIAM Journal on Applied Mathematics
Print ISSN 0036-1399
Publisher Society for Industrial and Applied Mathematics
Pages 1417 - 1443
DOI https://doi.org/10.1137/16M1102586
Keywords clouds of defects; transmission problems; approximations for large clusters; compound asymptotic approximations
Publisher URL http://epubs.siam.org/doi/10.1137/16M1102586

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