%0 Journal Article
%@holdercode {isadg {BR SPINPE} ibi 8JMKD3MGPCW/3DT298S}
%@nexthigherunit 8JMKD3MGPCW/3ESGTTP
%X In 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 Maxwells equation numerical solutions.
%@mirrorrepository sid.inpe.br/mtc-m19@80/2009/08.21.17.02.53
%8 Aug.
%N 8
%T Grid structure impact in sparse point representation of derivatives
%@secondarytype PRE PI
%K Wavelets, Multiresolution analysis, Adaptivity, Sparse grids, Finite differences, Consistency analysis.
%@archivingpolicy denypublisher denyfinaldraft24
%@usergroup administrator
%@usergroup marciana
%@usergroup simone
%@group LAC-CTE-INPE-MCT-BR
%3 grid structure.pdf
%@secondarykey INPE--PRE/
%@secondarymark A2_CIÊNCIA_DA_COMPUTAÇÃO A2_ENGENHARIAS_III B1_ENGENHARIAS_IV B1_GEOCIÊNCIAS A1_INTERDISCIPLINAR A2_MATEMÁTICA_/_PROBABILIDADE_E_ESTATÍSTICA
%@issn 0377-0427
%2 sid.inpe.br/mtc-m19@80/2010/06.01.14.11.12
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@affiliation Universidade de Aveiro
%@affiliation Universidade Estadual de Campinas
%@affiliation Universidade Estatual de Campinas
%@affiliation Universidade de Aveiro
%@affiliation Campus Universitário de Santiago
%B Journal of Computational and Applied Mathematics
%@versiontype publisher
%P 2377-2389
%4 sid.inpe.br/mtc-m19@80/2010/06.01.14.11
%@documentstage not transferred
%D 2010
%V 234
%@doi 10.1016/j.cam.2010.02.035
%A Domingues, Margarete de Oliveira,
%A Ferreira, Paulo J. S. G.,
%A Gomes, Sônia M.,
%A Gomide, Anamaria,
%A Pereira, José R.,
%A Pinho, Pedro,
%@dissemination WEBSCI; PORTALCAPES.
%@area COMP