Guaranteed bounds on homogenized periodic media by FFT‐based Galerkin method. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Vondřejc, Jaroslav; Zeman, Jan; Marek, Ivo
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 563
• Page End: 564
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410269
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>An FFT‐based method, introduced by Moulinec and Suquet [1] in 1994, is an effective alternative to conventional Finite Element Method (FEM) for numerical homogenization of periodic media. Here, we summarize the recent variational reformulation and discretizations by Vondřejc et al. [2–6], which are based on conforming Galerkin approximations with trigonometric polynomials as basis functions. This insight, naturally leading to guaranteed bounds on homogenized matrix, opens a wide area of further investigations, which are also briefly discussed here. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)</p> </abstract>