Approximation of the high-frequency Helmholtz kernel by nested directional interpolation: error analysis View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-09

AUTHORS

Steffen Börm, Jens M. Melenk

ABSTRACT

We present and analyze an approximation scheme for a class of highly oscillatory kernel functions, taking the 2D and 3D Helmholtz kernels as examples. The scheme is based on polynomial interpolation combined with suitable pre- and post-multiplication by plane waves. It is shown to converge exponentially in the polynomial degree and supports multilevel approximation techniques. Our convergence analysis may be employed to establish exponential convergence of certain classes of fast methods for discretizations of the Helmholtz integral operator that feature polylogarithmic-linear complexity. More... »

PAGES

1-34

References to SciGraph publications

Journal

TITLE

Numerische Mathematik

ISSUE

1

VOLUME

137

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00211-017-0873-y

DOI

http://dx.doi.org/10.1007/s00211-017-0873-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1084019513


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