A partial differential equation approach to multidimensional extrapolation

In this short note, a general methodology for multidimensional extrapolation is presented. The approach assumes a level set function exists which separates the region of known values from the region to be extrapolated. It is shown that arbitrary orders of polynomial extrapolation can be formulated b...

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Bibliographic Details
Published in:	Journal of computational physics Vol. 193; no. 1; pp. 349 - 355
Main Author:	Aslam, Tariq D.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Inc 2004 Elsevier
Subjects:	Exact sciences and technology Extrapolation Function theory, analysis Level set Mathematical methods in physics Partial differential equation Partial differential equations Physics Level set Extrapolation Partial differential equation Partial differential equations
Online Access:	Get full text
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Summary:	In this short note, a general methodology for multidimensional extrapolation is presented. The approach assumes a level set function exists which separates the region of known values from the region to be extrapolated. It is shown that arbitrary orders of polynomial extrapolation can be formulated by simply solving a series of linear partial differential equations (PDEs). Examples of constant, linear and quadratic extrapolation are given.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0021-9991 1090-2716
DOI:	10.1016/j.jcp.2003.08.001