
Programs and Algorithms of Numerical Mathematics 21 : Jablonec nad Nisou, June 1924, 2022 : Proceedings of Seminar
Chleboun, J. ; Kůs, Pavel ; Papež, Jan ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub
These proceedings contain peerreviewed papers that are based on the invited lectures, short communications, and posters presented at the 21st seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Merkur Hotel, Jablonec nad Nisou, Czech Republic, June 1924, 2022.\nThe 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 nancial 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, Prague, and Hejnice in the period 19832020. 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.


Programs and Algorithms of Numerical Mathematics 20 : Hejnice, June 2126, 2019 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Rozložník, Miroslav ; Segeth, Karel ; Šístek, Jakub
This book comprises papers that originated from the invited lectures, survey lectures, short communications, and posters presented at the 20th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Hejnice, Czech Republic, June 2126, 2020. 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. 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.


Efficient scalable solvers for incompressible flow problems
Mitro, Erik ; Hron, Jaroslav (advisor) ; Rozložník, Miroslav (referee)
In this thesis, the different solution methods for saddlepoint systems aris ing from fluid dynamics are studied. The main emphasis is on Krylov subspace methods with effective preconditioning techniques for saddlepoint systems ob tained from finite element discretization of the NavierStokes equations. Two preconditioning techniques are presented: pressureconvectiondiffusion precon ditioning (PCD) and leastsquare commutator preconditioning (LSC). Both pre conditioners are validated on two benchmarks: liddriven cavity and flow around cylinder. From the computational point of view, we focus on comparing the performance of used solvers, with emphasis on our implementation of PCD pre conditioning. All numerical simulations are performed by software Firedrake. 1


MAT TRIAD 2019: Book of Abstracts
Bok, J. ; Hartman, David ; Hladík, M. ; Rozložník, Miroslav
This volume contains the Book of abstracts of the 8th International Conference on Matrix Analysis and its Applications, MAT TRIAD 2019. The MATTRIAD conferences represent a platform for researchers in a variety of aspects of matrix analysis and its interdisciplinary applications to meet and share interests and ideas. The conference topics include matrix and operator theory and computation, spectral problems, applications of linear algebra in statistics, statistical models, matrices and graphs as well as combinatorial matrix theory and others. The goal of this event is to encourage further growth of matrix analysis research including its possible extension to other fields and domains.


Reduced communication algoritms: theory and practice
Slevínský, Rostislav ; Tůma, Miroslav (advisor) ; Rozložník, Miroslav (referee)
Development in the parallel computing environment in the last decade comes with the need of being able to use these in solving large algebraic systems. In this thesis, we focus on the Krylov subspace methods (namely the conjugate gradient method) as one of the most powerful tools and the possibilities of their parallelization. We discuss the communication avoiding Krylov subspace methods and various problems introduced by the parallelization e.g. loss of orthogonality or delay of convergence. Application of the Krylov subspace methods comes usually with some preconditioner, therefore part of this thesis is dedicated to the preconditioning in parallel computing environments.


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.


Applications of Mathematics. Special Issue  SNA ´17
Rozložník, Miroslav ; Sysala, Stanislav
This isssue of Applications of Mathematics is devoted to the Seminar on Numerical Analysis 2017 (SNA’17) held in New Aula of the VŠB—Technical University of Ostrava, January 30–February 3, 2017, and organized by the Institute of Geonics of the Czech Academy of Sciences in collaboration with IT4Innovations National Supercomputing Centre. The history of Seminar on Numerical Analysis (SNA) goes back to 2003. In 2005–2015, SNA was organized annually by the Institute of Geonics and Institute of Computer Science of the Czech Academy of Sciences in cooperation with Charles University in Prague, Czech Technical University, and VŠB—Technical University\nof Ostrava. Since 2016, Seminar on Numerical Analysis is organized alternatively on a biannual basis with the EMS School in Applied Mathematics (ESSAM). The scope of the seminar ranges from mathematical modeling and simulation of challenging engineering problems, to methods of numerical mathematics, numerical linear algebra, and high performance computing. An important part of SNA has\nbeen devoted to its Winter School with several longer lectures or tutorials focused on selected topics within the scope of the meeting. This year part of the Winter School was also the course Parallel Linear Algebra organized within the French PRACE Advanced Training Centre Maison de la Simulation. SNA’17 was attended by 77 participants, who presented six invited Winter School lectures, 24 short communications, and several posters.


Approximations by lowrank matrices and their applications
Outrata, Michal ; Tůma, Miroslav (advisor) ; Rozložník, Miroslav (referee)
Consider the problem of solving a large system of linear algebraic equations, using the Krylov subspace methods. In order to find the solution efficiently, the system often needs to be preconditioned, i.e., transformed prior to the iterative scheme. A feature of the system that often enables fast solution with efficient preconditioners is the structural sparsity of the corresponding matrix. A recent development brought another and a slightly different phe nomenon called the data sparsity. In contrast to the classical (structural) sparsity, the data sparsity refers to an uneven distribution of extractable information inside the matrix. In practice, the data sparsity of a matrix ty pically means that its blocks can be successfully approximated by matrices of low rank. Naturally, this may significantly change the character of the numerical computations involving the matrix. The thesis focuses on finding ways to construct Choleskybased preconditioners for the conjugate gradi ent method to solve systems with symmetric and positive definite matrices, exploiting a combination of the data and structural sparsity. Methods to exploit the data sparsity are evolving very fast, influencing not only iterative solvers but direct solvers as well. Hierarchical schemes based on the data sparsity concepts can be derived...

 
 