Adaptive wavelet scheme for convection-diffusion equations
dc.contributor.author | Černá, Dana | |
dc.contributor.author | Finěk, Václav | |
dc.date.accessioned | 2017-11-02 | |
dc.date.available | 2017-11-02 | |
dc.date.issued | 2012 | |
dc.description.abstract | One 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.format | text | cs |
dc.format.extent | 8 stran | |
dc.identifier.eissn | 1803-9790 | |
dc.identifier.issn | 1803-9782 | |
dc.identifier.other | ACC_2012_4_04 | |
dc.identifier.uri | https://dspace.tul.cz/handle/15240/21136 | |
dc.language.iso | en | |
dc.license | CC BY-NC 4.0 | |
dc.publisher | Technická univerzita v Liberci, Česká republika | cs |
dc.relation.isbasedon | ČERNÁ , D.; FINĚK, V, V.: Construction of optimally conditioned cubic spline wavelets on the interval. Adv. Comput. Math. 34, pp. 519-552, 2011. | |
dc.relation.isbasedon | ČERNÁ , D.; FINĚK, V.: Construction of optimally conditioned cubic spline wavelets on the interval. Adv. Comput. Math. 34, pp. 519-552, 2011 | |
dc.relation.isbasedon | Č ERNÁ , D.; FINĚ K, V.: Approximate multiplication in adaptive wavelet methods. Sub- mitted. | |
dc.relation.isbasedon | COHEN, A.; DAHMEN, V.; DEVORE, R.: Adaptive Wavelet Schemes for Elliptic Oper- ator Equations - Convergence Rates. Math. Comput. 70, pp. 27-75, 2001. | |
dc.relation.isbasedon | COHEN, A.: Numerical Analysis of Wavelet Methods. Elsevier Science, Amsterdam, 2003. | |
dc.relation.isbasedon | COHEN, A.; DAHMEN, V.; DEVORE, R.: Adaptive wavelet techniques in numerical simulation. Encyclopedia of Computational Mathematics 1, pp. 157-197, 2004. | |
dc.relation.isbasedon | COHEN, A.; DAHMEN, V.; DEVORE, R.: Adaptive wavelet methods II - Beyond the elliptic case. Foundations of Computational Mathematics 2, pp. 203-245, 2002. | |
dc.relation.isbasedon | DAHLKE, S.; FORNASIER, M.; RAASCH, T.; STEVENSON, R.; WERNER, M.: Adap- tive Frame Methods for Elliptic Operator Equations: The Steepest Descent Approach. IMA J. Numer. Anal. 27, pp. 717-740, 2007. | |
dc.relation.isbasedon | STEVENSON, R.: Adaptive Solution of Operator Equations Using Wavelet Frames. SIAM J. Numer. Anal. 41, pp. 1074-1100, 2003. | |
dc.relation.isbasedon | DIJKEMA, T.J.; SCHWAB, Ch.; STEVENSON, R.: An adaptive wavelet method for solv- ing high-dimensional elliptic PDEs. Constructive approximation 30, pp. 423-455, 2009. | |
dc.relation.ispartof | ACC Journal | en |
dc.relation.isrefereed | true | |
dc.subject | Wavelet | en |
dc.subject | Hermite cubic splines | en |
dc.subject | sparse representations | en |
dc.title | Adaptive wavelet scheme for convection-diffusion equations | en |
dc.type | Article | en |
local.access | open | |
local.citation.epage | 39 | |
local.citation.spage | 32 | |
local.fulltext | yes | en |
local.relation.issue | 4 | |
local.relation.volume | 18 |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- ACC_2012_4_04.pdf
- Size:
- 94.64 KB
- Format:
- Adobe Portable Document Format
- Description:
- Článek