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Reference material preconditioning for FFT‐based solvers
Author(s) -
Ladecký Martin,
Pultarová Ivana,
Zeman Jan,
Vondřejc Jaroslav
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900283
Subject(s) - fast fourier transform , computer science , mathematics , focus (optics) , iterative method , partial differential equation , scheme (mathematics) , elliptic partial differential equation , algorithm , mathematical optimization , mathematical analysis , physics , optics
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.