Reference material preconditioning for FFT‐based solvers. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Ladecký, Martin; Pultarová, Ivana; Zeman, Jan; Vondřejc, Jaroslav
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900283
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Problems of finding effective material properties discussed in the classical works on homogenisation [1, 2] originate from asymptotic analysis of elliptic partial differential equations with oscillating anisotropic data. In 1994, Moulinec and Suquet [3] introduced an iterative algorithm for efficient determination of effective properties. In spite of its popularity and a deep research interest in this method, there are still some opportunities for improving its numerical effectiveness. We focus on preconditioning of related linear systems, which is necessary for solving large problems by iterative solvers. We introduce a general scheme for construction of preconditioning matrices based on some appropriate approximation of original material data.