A scheme to calculate higher-order homogenization as applied to micro-acoustic boundary value problems

Hardik A. Vagh; Alireza Baghai-Wadji

doi:10.1117/12.814424

30 December 2008 A scheme to calculate higher-order homogenization as applied to micro-acoustic boundary value problems

Proceedings Volume 7269, Micro- and Nanotechnology: Materials, Processes, Packaging, and Systems IV; 72690Q (2008) https://doi.org/10.1117/12.814424
Event: SPIE Smart Materials, Nano- and Micro-Smart Systems, 2008, Melbourne, Australia

Abstract

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

Citation Download Citation

Hardik A. Vagh and 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); https://doi.org/10.1117/12.814424

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