2012/4 - Natural Sciences and Technology
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ACC Journal, ročník XVIII 2012/4
Recenzovali:
Prof. RNDr. Jaromír Antoch, CSs. – Univerzita Karlova v Praze
doc. RNDr. Karel Najzar. CSc. - Univerzita Karlova v Praze
Recenzovali:
Prof. RNDr. Jaromír Antoch, CSs. – Univerzita Karlova v Praze
doc. RNDr. Karel Najzar. CSc. - Univerzita Karlova v Praze
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Browsing 2012/4 - Natural Sciences and Technology by Author "Finěk, Václav"
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- ItemAdaptive wavelet scheme for convection-diffusion equations(Technická univerzita v Liberci, Česká republika, 2012) Černá, Dana; Finěk, VáclavOne 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.
- ItemMultiwavelets based on hermite cubic splines(Technická univerzita v Liberci, Česká republika, 2012) Černá, Dana; Finěk, Václav; Plačková, Gertathe convection-diffusion equation. We use an implicit scheme for the time discretization and
- ItemOn a sparse representation of laplacian(Technická univerzita v Liberci, Česká republika, 2012) Černá, Dana; Finěk, Václav; Ondračková., ZdenaThe paper is concerned with theoretical and computational issues of a numerical resolution of
- ItemOn the problem of variability of interval data(Technická univerzita v Liberci, Česká republika, 2012) Finěk, Václav; Matonoha, Ctirada vector which we have recently proposed in [1, 2]. The theoretical advantages of our scheme