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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Eliminating the pollution effect in Helmholtz problems by local subscale correction
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by Daniel Peterseim PDF
Math. Comp. 86 (2017), 1005-1036 Request permission


We introduce a new Petrov-Galerkin multiscale method for the numerical approximation of the Helmholtz equation with large wave number $\kappa$ in bounded domains in $\mathbb {R}^d$. The discrete trial and test spaces are generated from standard mesh-based finite elements by local subscale correction in the spirit of numerical homogenization. The precomputation of the correction involves the solution of coercive cell problems on localized subdomains of size $\ell H$, $H$ being the mesh size and $\ell$ being the oversampling parameter. If the mesh size and the oversampling parameter are such that $H\kappa$ and $\log (\kappa )/\ell$ fall below some generic constants and if the cell problems are solved sufficiently accurately on some finer scale of discretization, then the method is stable and its error is proportional to $H$. Pollution effects are eliminated in this regime.
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Additional Information
  • Daniel Peterseim
  • Affiliation: Rheinische Friedrich-Wilhelms-Universität Bonn, Institute for Numerical Simulation, Wegelerstr. 6, 53115 Bonn, Germany
  • MR Author ID: 848711
  • Email:
  • Received by editor(s): November 27, 2014
  • Received by editor(s) in revised form: October 17, 2015
  • Published electronically: August 3, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1005-1036
  • MSC (2010): Primary 65N12, 65N15, 65N30
  • DOI:
  • MathSciNet review: 3614010