Uniform Preconditioners of Linear Complexity for Problems of Negative Order-Reference-Cited by-同舟云学术

Uniform Preconditioners of Linear Complexity for Problems of Negative Order

Published:2020-12-02 Issue:2 Volume:21 Page:469-478
ISSN:1609-4840
Container-title:Computational Methods in Applied Mathematics
language:en
Short-container-title:

Author:

Stevenson Rob¹,van Venetië Raymond¹^ORCID

Affiliation:

1. Korteweg-de Vries Institute for Mathematics , University of Amsterdam , P.O. Box 94248, 1090 GE Amsterdam , Netherlands

Abstract

Abstract We propose a multi-level type operator that can be used in the framework of operator (or Caldéron) preconditioning to construct uniform preconditioners for negative order operators discretized by piecewise polynomials on a family of possibly locally refined partitions. The cost of applying this multi-level operator scales linearly in the number of mesh cells. Therefore, it provides a uniform preconditioner that can be applied in linear complexity when used within the preconditioning framework from our earlier work [Uniform preconditioners for problems of negative order, Math. Comp. 89 (2020), 645–674].

Funder

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Computational Mathematics,Numerical Analysis

Reference14 articles.

1. M. Bebendorf, Approximation of boundary element matrices, Numer. Math. 86 (2000), no. 4, 565–589.

2. J. H. Bramble, J. E. Pasciak and P. S. Vassilevski, Computational scales of Sobolev norms with application to preconditioning, Math. Comp. 69 (2000), no. 230, 463–480.

3. S. H. Christiansen and J.-C. Nédélec, Des préconditionneurs pour la résolution numérique des équations intégrales de frontière de l’acoustique, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 7, 617–622.

4. T. Führer, A. Haberl, D. Praetorius and S. Schimanko, Adaptive bem with inexact pcg solver yields almost optimal computational costs, Numer. Math. 141 (2019), no. 4, 967–1008.

5. W. Hackbusch, A Sparse Matrix Arithmetic Based on ℋ-Matrices. Part I: Introduction to ℋ-Matrices, Computing 62 (1999), no. 2, 89–108.

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