Approximation and interpolation employing divergence-free radial basis functions with applications

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dc.contributor.advisor Narcowich , Francis J . en_US
dc.contributor.committeeMember Pasciak , Joseph E . en_US
dc.creator Lowitzsch , Svenja en_US
dc.date.accessioned 2004 -09 -30T01 :40 :21Z
dc.date.accessioned 2014 -02 -18T22 :28 :02Z
dc.date.available 2004 -09 -30T01 :40 :21Z
dc.date.available 2014 -02 -18T22 :28 :02Z
dc.date.created 2003 -05 en_US
dc.date.issued 2004 -09 -30T01 :40 :21Z
dc.identifier.uri http : / /hdl .handle .net /1969 .1 /21
dc.description.abstract Approximation and interpolation employing radial basis functions has found important applications since the early 1980's in areas such as signal processing , medical imaging , as well as neural networks . Several applications demand that certain physical properties be fulfilled , such as a function being divergence free . No such class of radial basis functions that reflects these physical properties was known until 1994 , when Narcowich and Ward introduced a family of matrix -valued radial basis functions that are divergence free . They also obtained error bounds and stability estimates for interpolation by means of these functions . These divergence -free functions are very smooth , and have unbounded support . In this thesis we introduce a new class of matrix -valued radial basis functions that are divergence free as well as compactly supported . This leads to the possibility of applying fast solvers for inverting interpolation matrices , as these matrices are not only symmetric and positive definite , but also sparse because of this compact support . We develop error bounds and stability estimates which hold for a broad class of functions . We conclude with applications to the numerical solution of the Navier -Stokes equation for certain incompressible fluid flows . en_US
dc.format.extent 1064009 bytes
dc.format.medium electronic en_US
dc.format.mimetype application /pdf
dc.language.iso en _US en_US
dc.publisher Texas A &M University en_US
dc.rights I hereby certify that , if appropriate , I have obtained and attached hereto a written permission statement from the owner (s ) of each third party copyrighted matter to be included in my thesis , dissertation , or project report , allowing distribution as specified below . I certify that the version I submitted is the same as that approved by my advisory committee . I hereby grant to Texas A &M University or its agents the non -exclusive license to archive and make accessible , under the conditions specified below , my thesis , dissertation , or project report in whole or in part in all forms of media , now or hereafter known . I retain all other ownership rights to the copyright of the thesis , dissertation or project report . I also retain the right to use in future works (such as articles or books ) all or part of this thesis , dissertation , or project report . en_US
dc.subject incompressible Navier -Stokes equation en_US
dc.title Approximation and interpolation employing divergence -free radial basis functions with applications en_US
dc.type Book en
dc.type.genre Electronic Dissertation en_US
dc.type.material text en_US
dc.format.digitalOrigin born digital en_US

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Approximation and interpolation employing divergence-free radial basis functions with applications. Available electronically from http : / /hdl .handle .net /1969 .1 /21 .

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