Abstract
In this chapter, we outline the method of frequency filtering decomposition (FFD) proposed in [186] for the construction of factorized preconditioners for the systems of linear equations arising in usual FE conforming approximations for elliptic problems. Here we also consider possible extensions of this technique to approximate the Schur complements on the interface [113]. Further generalizations of this approach by using tangential FFD and adaptive filtering were developed in [183] and in [184]. In the case of symmetric positive definite block-tridiagonal matrices with constant block entries, a new interpretation for the TFFD techniques (which also simplifies a theoretical analysis) was considered in [38].
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© 2004 Springer-Verlag Berlin Heidelberg
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Khoromskij, B.N., Wittum, G. (2004). Frequency Filtering Techniques. In: Numerical Solution of Elliptic Differential Equations by Reduction to the Interface. Lecture Notes in Computational Science and Engineering, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18777-3_6
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DOI: https://doi.org/10.1007/978-3-642-18777-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20406-0
Online ISBN: 978-3-642-18777-3
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