
Programs and Algorithms of Numerical Mathematics 18 : Janov nad Nisou, June 1924, 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 1924, 2016. All the papers have been peerreviewed. The seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EUMATHSIN.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 19832014. 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 multiprocessor applications of computational methods.


Programs and Algorithms of Numerical Mathematics 19 : Hejnice, June 2429, 2018 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
These proceedings contain peerreviewed 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 2429, 2018. The seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EUMATHSIN.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 19832016. 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 multiprocessor applications of computational methods.


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 threedimensional flow governed by the NavierStokes 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.

 

The effect of irregular interfaces on the BDDC method for the NavierStokes equations
Hanek, M. ; Šístek, Jakub ; Burda, P.
We investigate the effect of interface irregularity on the convergence of the BDDC method for NavierStokes equations. A benchmark problem of a sequence of contracting channels is proposed to evaluate the robustness of the iterative solver with respect to element aspect ratios at the interface. Partitioners based on graph of the mesh and the geometry of the domain are compared. It is shown, that the convergence is significantly improved by avoiding irregular interfaces for the benchmark problem as well as for an industrial problem of oil flow in hydrostatic bearing.


Some practical aspects of parallel adaptive BDDC method
Šístek, Jakub ; Mandel, J. ; Sousedík, B.
We describe a parallel implementation of the Balancing Domain Decomposition by Constraints (BDDC) method enhanced by an adaptive construction of coarse problem. The method is designed for numerically difficult problems, where standard choice of continuity of arithmetic averages across faces and edges of subdomains fails to maintain the low condition number of the preconditioned system. Problems of elasticity analysis of bodies consisting of different materials with rapidly changing stiffness may represent one class of such challenging problems. The adaptive selection of constraints is shown to significantly increase the robustness of the method for this class of problems. However, since the cost of the setup of the preconditioner with adaptive constraints is considerably larger than for the standard choices, computational feasibility of the presented implementation is obtained only for large contrasts of material coefficients.


Incompressible fluids with temperature dependent viscosity  numerical analysis and computational simulations
Ulrych, Oldřich ; Málek, Josef (advisor) ; Dolejší, Vít (referee) ; Šístek, Jakub (referee)
Title: Incompressible fluids with temperature dependent visco sity, numerical analysis and computational simulations Author: RNDr. Oldřich Ulrych Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., DSc. Abstract: Flows of incompressible fluids connected with significant exchange of ther mal and mechanical energy and with material moduli varying with the temperature and the shear rate, are described by the balance equations for linear momentum and energy, complemented by suitable constitution equations for the Cauchy stress and the heat flux. Assuming sufficient smoothness of quantities involved, the energy balance equation exhibits several equivalent formulations. However, within the context of weak solution, these formulations are, in general, not equivalent. This thesis is based on the existence theory for the generalized NavierStokesFourier system describing planar flow of fluids with a shear and temperature dependent vis cosity. We specify parameters of a generalized powerlaw model under which weak formulations of balance equations are meaningful and both considered formulations of the energy balance equation are equivalent. Supported by the existence theory, we propose and numerically solve several problems pursuing the aim to systematically compare the...


Proceedings of the International Conference Applications of Mathematics 2015 : Prague, November 1821, 2015
Brandts, J. ; Korotov, S. ; Křížek, Michal ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
Professors Ivo Babuška, Milan Práger, and Emil Vitásek are renowned experts in numerical analysis and computational methods. Their fruitful scientific careers started in Prague, at the Institute of Mathematics of the Czechoslovak Academy of Sciences (now Czech Academy of Sciences). They collaborated there on various projects including the computational analysis of the construction technology for Orlík Dam. In 1966 they published their joint book entitled Numerical Processes in Differential Equations. It is an honor for the Institute of Mathematics to host a conference on the occasion of their birthdays.


Programs and Algorithms of Numerical Mathematics 17 : Dolní Maxov, June 813, 2014 : Proceedings of Seminar
Chleboun, J. ; Přikryl, Petr ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
This volume comprises peerreviewed papers that are based on invited lectures, survey lectures, short communications, and posters presented at the 17th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Dolní Maxov, Czech Republic, June 8–13, 2014. The seminar was organized by the Institute of Mathematics of the Academy of Sciences of the Czech Republic. It continued the previous seminars on mathematical software and numerical methods held (with only one exception) biannually in\nAlšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, and Prague in the period 1983–2012. The objective of this series of seminars is to provide a forum for presenting and discussing advanced topics in numerical analysis, singleor multiprocessor applications of computational methods, and new approaches to mathematical modeling.


An application of the BDDC method to the NavierStokes equations in 3D cavity
Hanek, M. ; Šístek, Jakub ; Burda, P.
We deal with numerical simulation of incompressible flow governed by the NavierStokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab) method. We present results for a 3D cavity problem computed on 32 cores of a parallel supercomputer.
