Identification

Title

Comparisons between pseudospectral and radial basis function derivative approximations

Abstract

Fourier-based pseudospectral (PS) methods have been used since the 1970s for obtaining spectrally accurate solutions to PDEs in periodic geometries. Radial basis functions (RBFs) were introduced about the same time for interpolation on scattered nodes in irregular geometries. As was later recognized, they can also be used for accurate numerical solution of PDEs. Although the main strength of RBFs lies in their outstanding geometric flexibility, offering possibilities of spectral accuracy also over irregularly shaped finite domains, it is still of interest to compare them against Fourier-based PS methods in the extremely simple geometries (infinite or periodic domains) where the latter can also be used. Mostly by means of heuristic arguments and graphical illustrations based on Fourier analysis and numerical experiments, we show that there are notable differences (more pronounced in increasing numbers of dimensions) in how the two spectral approaches approximate derivatives.

Resource type

document

Resource locator

Unique resource identifier

code

http://n2t.net/ark:/85065/d7dj5g1h

codeSpace

Dataset language

eng

Spatial reference system

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Classification of spatial data and services

Topic category

geoscientificInformation

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keyword value

Text

originating controlled vocabulary

title

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reference date

date type

publication

effective date

2016-01-01T00:00:00Z

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date type

publication

effective date

2010-01-01T00:00:00Z

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Use constraints

Limitations on public access

None

Responsible organisations

Responsible party

contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

responsible party role

pointOfContact

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