Browsing by Author "Kopal, Jiří"
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- ItemA note on adaptivity in factorized approximate inverse preconditioning(OVIDIUS UNIV PRESS, FAC MATHEMATICS & COMPUTER SCIENCE, BULEVARDUL MAMAIA 124, CONSTANTA, 900527, ROMANIA, 2020) Kopal, Jiří; Rozložník, Miroslav; Tůma, MiroslavThe problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram-Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix diagonalization in computation of electronic structures but approximating inverses is of an interest in parallel computations in general. Our approach uses adaptive dropping of the matrix entries with the control based on the computed intermediate quantities. Strategy has been introduced as a way to solve difficult application problems and it is motivated by recent theoretical results on the loss of orthogonality in the generalized Gram-Schmidt process. Nevertheless, there are more aspects of the approach that need to be better understood. The diagonal pivoting based on a rough estimation of condition numbers of leading principal submatrices can sometimes provide inefficient preconditioners. This short study proposes another type of pivoting, namely the pivoting that exploits incremental condition estimation based on monitoring both direct and inverse factors of the approximate factorization. Such pivoting remains rather cheap and it can provide in many cases more reliable preconditioner. Numerical examples from real-world problems, small enough to enable a full analysis, are used to illustrate the potential gains of the new approach.
- ItemGeneralized Gram-Schmidt Process: Its Analysis and Use in Preconditioning(Technická Univerzita v Liberci, ) Kopal, Jiří
- ItemModelování transportu radionuklidů obsažených v granitové vodě v heterogenním horninovém prostředí(Technická Univerzita v Liberci, 2008) Kopal, JiříPráce pojednává o modelování transportu radionuklidů v granitovém prostředí a je motivována problematikou hlubinného úložiště radioaktivního odpadu. Cílem je porovnat významnost jednotlivých procesů, které retardaci radionuklidů v granitovém prostředí ovlivňují. První kapitoly jsou pojaty jako teoretický základ a uvádí šířku problematiky, které se práce věnuje. Stavba hydrogeologického modelu je ucelená - od popisu fyzikálních jevů přes tvorbu diskrétního matematického modelu až po jeho řešení. Práce zmiňuje i širší souvislosti, které jsou s hydrogeologickým modelováním spjaty s cílem uvést čtenáře co nejpodrobněji do komplexní problematiky. Nedílnou součástí práce je i numerická implementace, která navazuje na převzaté zdrojové kódy a rozšiřuje jejich funkčnost. Poslední kapitola práce se věnuje vyhodnocení výstupů simulací s teoreticky odvozenými poznatky a porovnává významnost jednotlivých procesů, které na transport v heterogenním granitovém prostředí působí.
- ItemPiezoelektrické transformátory ve tvaru disku s klínovitě dělenou elektrodou(Technická Univerzita v Liberci, 2006) Kopal, Jiří; Erhart, JiříThe aim of the bachelor thesis is measuring the frequency characteristics of the transformation ratio (of the voltage gain) of the piezoelectric transformers in the form of disc with the wedge-shaped electrode, which were designed for the function in the mode of the plane shear oscillations. The introduction presents the piezoelectric effect, findings about the piezoelectric materials, their microstructure and mainly the ferroelectric (piezoelectric) ceramics. The thesis afterwards aims at the piezoelectric transformers, their qualities, types and modes of the oscillations. The practical part of the thesis begins with the preparation of the specimens then follows the measuring of their frequency characteristics of the voltage gain during different loading of the output (real impedance). The characteristics of the gain coefficient and the shifting of the resonant frequency with the loading of the output circuit are mainly stressed during the appraising of the results. The transformers are being compared with each other (the key parameter is the proportion of the surfaces of the electrodes), but also the overtones in the spectrum of each single transformer. It could be specified, what ratio of the electrodes is being reached the maximum of the voltage gain at. The results of the effort could serve to the optimalization of the design of the piezoelectric transformers, in some cases for further research.