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Programs and Algorithms of Numerical Mathematics 18 : Janov nad Nisou, June 19-24, 2016 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
This book comprises papers that originated from the invited lectures, survey lectures, short communications, and posters presented at the 18th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Janov nad Nisou, Czech Republic, June 19-24, 2016. All the papers have been peer-reviewed. The seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EU-MATHS-IN.cz, Czech Network for Mathematics in Industry. It continued the previous seminars on mathematical software and numerical methods held (biennially, with only one exception) in Al šovice, Bratří kov, Janov nad Nisou, Ko řenov, L ázně Libverda, Dolní Maxov, and Prague in the period 1983-2014. The objective of this series of seminars is to provide a forum for presenting and discussing advanced theoretical as well as practical topics in numerical analysis, computer implementation of algorithms, new approaches to mathematical modeling, and single- or multi-processor applications of computational methods.
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Programs and Algorithms of Numerical Mathematics 19 : Hejnice, June 24-29, 2018 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
These proceedings contain peer-reviewed papers that are based on the invited lectures, survey lectures, short communications, and posters presented at the 19th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in the International Center for Spiritual Rehabilitation, Hejnice, Czech Republic, June 24-29, 2018. The seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EU-MATHS-IN.cz, Czech Network for Mathematics in Industry, and with the financial support provided by the RSJ Foundation. It continued the previous seminars on mathematical software and numerical methods held (biennially, with only one exception) in Alšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, and Prague in the period 1983-2016. The objective of this series of seminars is to provide a forum for presenting and discussing advanced topics in numerical analysis, computer implementation of numerical algorithms, new approaches to mathematical modeling, and single- or multi-processor applications of computational methods.
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Multivariate smooth interpolation that employs polyharmonic functions
Segeth, Karel
We study the problém of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints. We present a procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines complemented with lower order polynomials therms. In general, such formulae can be very useful e.g. in geographic information systems or computer aided geometric design. A simple computational example is presented.
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Cosmology on Small Scales 2018: Dark Matter Problem and Selected Controversies in Cosmology
Křížek, Michal ; Dumin, Y. V.
According to the standard cosmological model, our Universe needs a significant amount of dark matter, about six times more than that of the usual baryonic matter, besides an even larger amount of dark energy. But to date, both dark matter and dark energy have remained conceptually elusive, without concrete evidence based on direct physical measurements. Yet another subtle issue is that the Friedmann equation – the cornerstone of modern cosmology – was derived from the system of ten Einstein’s equations applied to a perfectly symmetric universe, which is homogeneous\nand isotropic for every fixed time instant. So, the question is whether one can perform such excessive extrapolations and, in particular, at which scale the effect of Hubble expansion is manifested.
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Analysis of the turbulence parameterisations for the atmospheric surface layer
Caggio, Matteo ; Bodnár, Tomáš
The purpose of this short communication is to present a method that aims to express the turbulent variables in the atmospheric surface-layer in function of the stability of the atmosphere. The case of very stable conditions (strong strati cation), where theoretical approaches provide conflicting results (see Luhar et al. [11]), is analysed in detail to provide some insight into the limits of applicability for some of the most popular models of turbulence. The problem of the existence of the critical flux Richardson number is also taken into account.
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Artificial far-field pressure boundary conditions for wall-bounded stratified flows
Bodnár, Tomáš ; Fraunié, P.
This paper presents an alternative boundary conditions setup for the numerical simulations of stably stratifed flow. The focus of the tested computational setup is on the pressure boundary conditions on the arti cial boundaries of the computational domain. The simple three dimensional test case deals with the steady flow of an incompressible, variable density fluid over a low smooth model hill. The Boussinesq approximation model is solved by an in-house developed high-resolution numerical code, based on compact finite-difference discretization in space and Strong Stability Preserving Runge-Kutta method for (pseudo-) time stepping.
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Parallel domain decomposition solver for flows in hydrostatic bearings
Hanek, Martin ; Šístek, Jakub ; Burda, P. ; Stach, E.
We perform simulations of oil flow in hydrostatic bearings. Stationary incompressible three-dimensional flow governed by the Navier-Stokes equations is considered. The finite element method is used for discretization. The arising nonlinear system of algebraic equations is linearized using the Picard’s iteration, and the Balancing Domain Decomposition based on Constraints (BDDC) method is used to solve the linear systems of equations. The solver is first validated with an experiment for the case of a bearing without motion, and it is then applied to simulation of flow in a sliding bearing.
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Neglected gravitational redshift in detections of gravitational waves
Křížek, Michal ; Somer, L.
In 2016, the letter [1] about the first detection of gravitational waves was published. They were generated by two merging black holes that had approximately 36 and 29 Sun’s masses. However, the authors have not taken into account a large gravitational redshift of this binary system, which is a direct consequence of time dilation in a strong gravitational field. Thus the proposed masses are overestimated. In our paper we also give other arguments for this statement.
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Classification of distances in cosmology
Křížek, Michal ; Mészáros, A.
In cosmology many different distances are defined: angular, comoving, Euclidean, Hubble, light-year, luminosity, Minkowski, parallax, proper motion, redshift, ... distance. There is not one single natural distance, since the universe is expanding, curved, and we look back in time. In this survey paper we will concentrate on geometrical interpretations of the above-mentioned distances.
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