Reference material preconditioning for FFT‐based solvers. Issue 1 (18th November 2019) - Ladecký, Martin; Pultarová, Ivana; Zeman, Jan; Vondřejc, Jaroslav
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.