%0 Journal Article
%@nexthigherunit 8JMKD3MGPCW/46JKC45
%@holdercode {isadg {BR SPINPE} ibi 8JMKD3MGPCW/3DT298S}
%@archivingpolicy denypublisher denyfinaldraft24
%@issn 0168-9274
%@resumeid 8JMKD3MGP5W/3C9JHQP
%@usergroup administrator
%3 Ddomingues_Adaptive wavelet representation.pdf
%@dissemination WEBSCI
%@secondarykey INPE-10650-PRE/6112
%A Domingues, Margarete Oliveira,
%A Gomes, S. M,
%A Diaz, L. M. A.,
%T Adaptive wavelet representation and differentiation on block-structured grids
%B Applied Numerical Mathematics
%8 dec
%D 2003
%V 47
%N 3-4
%P 421-437
%2 cptec.inpe.br/walmeida/2004/04.22.08.51.06
%4 cptec.inpe.br/walmeida/2004/04.22.08.51
%K wavelet analysis, finite differences, adaptive grids,equations.
%X This paper considers a new adaptive wavelet solver for two-dimensional systems based on an adaptive block refinement (ABR) method that takes advantage of the quadtree structure of dyadic blocks in rectangular regions of the plane. The computational domain is formed by non-overlapping blocks. Each block is a uniform grid, but the step size may change from one block to another. The blocks are not predetermined, but they are dynamically constructed according to the refinement needs of the numerical solution. The decision over whether a block should be refined or unrefined is taken by looking at the magnitude of wavelet coefficients of the numerical solution on such block. The wavelet coefficients are defined as differences between values interpolated from a coarser level and known function values at the finer level. The main objective of this paper is to establish a general framework for the construction and operation on such adaptive block-grids in 2D. The algorithms and data structure are formulated by using abstract concepts borrowed from quaternary trees. This procedure helps in the understanding of the method and simplifies its computational implementation. The ability of the method is demonstrated by solving some typical test problems. (C) 2003 IMACS. Published by Elsevier B.V. All rights reserved.
%@language English
%@copyholder SID/SCD
%@e-mailaddress fabia@cptec.inpe.br
%@secondarytype PRE PI
%@area MET
%@group DMA-INPE-MCT-BR
%@affiliation CPTEC, Inst Nacl Pesquisas Espaciais, Caixa Postal 515, BR-12221970 Sao Jose Dos Campos, SP, Brazil,
%@affiliation CPTEC, Inst Nacl Pesquisas Espaciais, BR-12221970 Sao Jose Dos Campos, SP, Brazil,