Grid structure impact in sparse point representation of derivatives

dc.creatorDomingues, MO
dc.creatorFerreira, PJSG
dc.creatorGomes, SM
dc.creatorGomide, A
dc.creatorPereira, JR
dc.creatorPinho, P
dc.date2010
dc.dateAUG 15
dc.date2014-11-18T05:34:18Z
dc.date2015-11-26T16:51:42Z
dc.date2014-11-18T05:34:18Z
dc.date2015-11-26T16:51:42Z
dc.date.accessioned2018-03-28T23:38:28Z
dc.date.available2018-03-28T23:38:28Z
dc.identifierJournal Of Computational And Applied Mathematics. Elsevier Science Bv, v. 234, n. 8, n. 2377, n. 2389, 2010.
dc.identifier0377-0427
dc.identifierWOS:000279071200002
dc.identifier10.1016/j.cam.2010.02.035
dc.identifierhttp://www.repositorio.unicamp.br/jspui/handle/REPOSIP/68467
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/68467
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/68467
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1276052
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionIn the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions. (C) 2010 Elsevier B.V. All rights reserved.
dc.description234
dc.description8
dc.description2377
dc.description2389
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.descriptionFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.descriptionCNPq [308632/2006-0, 308680/2007-3]
dc.descriptionFAPESP [2004/06880-3, 2007/52015-0]
dc.languageen
dc.publisherElsevier Science Bv
dc.publisherAmsterdam
dc.publisherHolanda
dc.relationJournal Of Computational And Applied Mathematics
dc.relationJ. Comput. Appl. Math.
dc.rightsfechado
dc.rightshttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dc.sourceWeb of Science
dc.subjectWavelets
dc.subjectMultiresolution analysis
dc.subjectAdaptivity
dc.subjectSparse grids
dc.subjectFinite differences
dc.subjectConsistency analysis
dc.subjectInterpolating Wavelets
dc.subjectSchemes
dc.titleGrid structure impact in sparse point representation of derivatives
dc.typeArtículos de revistas


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