Adaptive wavelet scheme for convection-diffusion equations

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dc.contributor.authorČerná, Dana
dc.contributor.authorFiněk, Václav
dc.date.accessioned2017-11-02
dc.date.available2017-11-02
dc.date.issued2012
dc.description.abstractOne of the most important part of adaptive wavelet methods is an efficient approximate multi- plication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time con- suming and its implementation is very difficult. Therefore, it is necessary to develop a well- conditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices corresponding to the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number. In this contribution, we shortly review this construction and show several numerical tests.en
dc.formattextcs
dc.format.extent8 stran
dc.identifier.eissn1803-9790
dc.identifier.issn1803-9782
dc.identifier.otherACC_2012_4_04
dc.identifier.urihttps://dspace.tul.cz/handle/15240/21136
dc.language.isoen
dc.licenseCC BY-NC 4.0
dc.publisherTechnická univerzita v Liberci, Česká republikacs
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dc.relation.ispartofACC Journalen
dc.relation.isrefereedtrue
dc.subjectWaveleten
dc.subjectHermite cubic splinesen
dc.subjectsparse representationsen
dc.titleAdaptive wavelet scheme for convection-diffusion equationsen
dc.typeArticleen
local.accessopen
local.citation.epage39
local.citation.spage32
local.fulltextyesen
local.relation.issue4
local.relation.volume18
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