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Block Conjugate Gradient Iteration for Fourier‐Galerkin Homogenization of Periodic Media
Author(s) -
Mishra Nachiketa,
Vondřejc Jaroslav,
Zeman Jan
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510222
Subject(s) - homogenization (climate) , conjugate gradient method , mathematics , galerkin method , fourier transform , mathematical analysis , fourier series , trigonometry , conjugate , fourier analysis , algorithm , physics , finite element method , biodiversity , ecology , biology , thermodynamics
The Fourier‐Galerkin method is considered here for the solution of the unit cell problem that describes the homogenized properties of periodic materials in the scalar elliptic setting. The method is based on a Galerkin approximation with trigonometric polynomials and leads to linear systems suitable for iterative solvers. In [1], Zeman et al show the effectiveness of Conjugate gradients (CG) which is compared here with its block version (BCG). We show that the latter version outperforms the CG especially for anisotropic materials with non‐symmetric distribution of material properties. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)