30 December 2008 A scheme to calculate higher-order homogenization as applied to micro-acoustic boundary value problems
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Current technological challenges in materials science and high-tech device industry require the solution of boundary value problems (BVPs) involving regions of various scales, e.g. multiple thin layers, fibre-reinforced composites, and nano/micro pores. In most cases straightforward application of standard variational techniques to BVPs of practical relevance necessarily leads to unsatisfactorily ill-conditioned analytical and/or numerical results. To remedy the computational challenges associated with sub-sectional heterogeneities various sophisticated homogenization techniques need to be employed. Homogenization refers to the systematic process of smoothing out the sub-structural heterogeneities, leading to the determination of effective constitutive coefficients. Ordinarily, homogenization involves a sophisticated averaging and asymptotic order analysis to obtain solutions. In the majority of the cases only zero-order terms are constructed due to the complexity of the processes involved. In this paper we propose a constructive scheme for obtaining homogenized solutions involving higher order terms, and thus, guaranteeing higher accuracy and greater robustness of the numerical results. We present
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Hardik A. Vagh, Alireza Baghai-Wadji, "A scheme to calculate higher-order homogenization as applied to micro-acoustic boundary value problems", Proc. SPIE 7269, Micro- and Nanotechnology: Materials, Processes, Packaging, and Systems IV, 72690Q (30 December 2008); doi: 10.1117/12.814424; https://doi.org/10.1117/12.814424


Finite element methods


Partial differential equations

Materials science

Standards development

Computer engineering

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