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

Vagh, H and Baghai - Wadji, A 2008, 'A scheme to calculate higher-order homogenization as applied to boundary value problems', in J.C. Chiao, A. J. H. Jariz, D. V. Thiel, C.Yang (ed.) Proceedings of SPIE, Volume 7269, Micro- and Nanotechnology: Materials, Processes, Packaging, and Systems IV, Bellingham, United States, 9-12 December, 2008.


Document type: Conference Paper
Collection: Conference Papers

Title A scheme to calculate higher-order homogenization as applied to boundary value problems
Author(s) Vagh, H
Baghai - Wadji, A
Year 2008
Conference name Micro- and Nanotechnology: Materials, Processes, Packaging, and Systems IV
Conference location Bellingham, United States
Conference dates 9-12 December, 2008
Proceedings title Proceedings of SPIE, Volume 7269, Micro- and Nanotechnology: Materials, Processes, Packaging, and Systems IV
Editor(s) J.C. Chiao, A. J. H. Jariz, D. V. Thiel, C.Yang
Publisher SPIE - The International Society for Optical Engineering
Place of publication Bellingham, United States
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 a form of homogenization which permits the establishment of a link with conventional Finite Element Method (FEM). © 2008 SPIE.
Subjects Numerical Solution of Differential and Integral Equations
Microelectronics and Integrated Circuits
Keyword(s) symbolic calculations
finite element method
quadratures
cubatures
Copyright notice © 2008 SPIE.
ISSN 0277-786X
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