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Mathematical modelling and computational methods in applied sciences and engineering - Modelling 2019
Blaheta, Radim ; Starý, Jiří ; Sysala, Stanislav
Modelling 2019 is an international conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering held in\nOlomouc, Czech Republic, in September 16 - 20, 2019. It aims to be a forum for an exchange of ideas, insights and experiences in different areas\nof mathematical modelling. It includes the fundamental formulation and analysis of mathematical models, the development of numerical methods and exploitation of capabilities of the contemporary high-performance computers or applications of mathematical modelling.\nThis conference belongs to a series of conferences previously held in Roznov in 2014 and 2009, in Pilsen in 2005 and 2001, and in Prague in 1998 and 1994. During the period of 25 years, the focus of the conference has been substantially enlarged. Besides the topics aiming at the development\nof numerical methods and analysis of mathematical models described by the partial differential equations, the conference relates to the inverse\nproblems, quantification of uncertainties in the input data, machine learning and exploitation of high-performance computing systems of petaflops and pre-exaflops performance. Increased attention is devoted to challenging industrial problems and collaboration with industry.
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SNA´19 - Seminar on numerical analysis.
Blaheta, Radim ; Starý, Jiří ; Sysalová, Dagmar
Seminar on Numerical Analysis 2017 (SNA'17) is a continuation in a series of SNA events held\nin different places in the Czech Republic and organized alternatively by Ostrava and Prague\ninstitutions. The SNA'17 is organized by the Institute of Geonics of the CAS in collaboration with\nVŠB - Technical University of Ostrava and IT4Innovations National Supercomputing Centre.\nConference location is one of the lecture rooms in New Aula of the VŠB-TU Ostrava.\nLet us note that SNA 2016 was reshaped to EMS School in Applied Mathematics (ESSAM)\ndevoted to mathematical modelling, numerical analysis and scientiffc computing. The SNA'17\nis turning back to more traditional winter event.\nIt provides opportunity for meeting and mutual information of the community working in computational\nmathematics and computer science, but an important part of SNA is devoted to the\nWinter School with tutorial lectures focused on selected important topics within the scope of\nnumerical methods and modelling.\nThis year, a part of the Winter School will be the course Parallel Linear Algebra (PLA) organized\nby the European research infrastructure PRACE, particularly by the French PRACE Advanced\nTraining Centre - Maison de la Simulation. Winter school lectures will cover the ongoing topics\nrelated to domain decomposition methods, interval computations and numerical veriffcation. The\nPLA course will provide lectures from the area of direct and iterative parallel solvers, as well as\npractical training with selected programs.
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Algebraic preconditioning for Biot-Barenblatt poroelastic systems
Blaheta, Radim ; Luber, Tomáš
Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.
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Professor Ivo Marek (1933-2017)
Blaheta, Radim ; Tůma, Miroslav
Ivo Marek, Professor at Charles University and the Czech Tec\nhnical University in Prague, was for many decades one of the best-known Czech ma\nthematicians, who contributed significantly to the development of computa\ntional methods and numerical analysis. At the same time, he was a teacher and a le\nading personality that integrated and influenced the Czech mathematical commu\nnity.
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Large-scale geosimulations using GEM and trilions
Blaheta, Radim ; Jakl, Ondřej ; Hrtus, Rostislav ; Kolcun, Alexej ; Kohut, Roman ; Starý, Jiří ; Turan, E.
The project deals with efficient solution of singular symmetric positive semidefinite problems. Our motivation arises from the \nneed to solve special problems of geotechnics, e.g. to perform upscaling analysis of geocomposites. In that and other applications we have to solve boundary problems with pure Neumann boundary conditions. We show that the stabilised PCG method with various preconditioners is a good choice for systems resulting from the numerical solution of Neumann problems, or more generally problems with a known small dimensional null space. The work was also taken as an opportunity to compare parallel implementations of the orresponding solvers, namely implementations in the in-house finite element software GEM and implementations employing components of the general Trilinos library. The studies show that the solvers based on GEM are highly competitive with its recognised counterpart.
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Dokončení vývoje a ověření SW Flow123d v rámci projektu DECOVALEX 2015
Blaheta, Radim ; Maryška, J. ; Březina, J. ; Stebel, J. ; Šembera, J. ; Balvín, A. ; Bruský, I. ; Hasal, Martin ; Michalec, Zdeněk ; Staš, Lubomír ; Sysala, Stanislav
Tato závěrečná zpráva shrnuje průběh prací a výsledky za celé období řešení projektu. Obsahem je modelování úloh podle zadání projektu Decovalex-2015, vývoj softwaru Flow123d a příprava podkladů pro jeho standardizaci s využitím porovnání výsledků se zahraničními týmy. Tým TUL se účastnil řešení úloh Task C1 (THMC procesy v jednotlivé puklině) pomocí softwaru Geochemist’s Workbench a vlastního nástroje TrAper pro propojení mezi chemií a deformací a Task C2 (proudění a transport v okolí tunelu Bedřichov) s pomocí softwaru Flow123d. Tým ÚGN se účastnil řešení úlohy Task A, zaměřené na sycení bentonitové zátky v jílové hornině a uzavírání mezery, s pomocí softwaru COMSOL Multiphysics. Výsledkem řešení jsou společné zprávy mezinárodních týmů a články ve speciálním čísle časopisu. Vyvinuté modely a získané zkušenosti přispívají k možnostem predikovat jevy v úložišti vyhořelého jaderného paliva. Dalším výsledkem je sada dokumentů k softwaru Flow123d. Všechny jsou ke zprávě připojeny jako přílohy.
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Overlapping domain decomposition preconditioners for elliptic and parabolic problems in primal and mixed form
Blaheta, Radim
In this lecture, we concern the numerical solution of PDE problems and describe overlapping domain decomposition, which provides a tool for the construction of parallelizable Schwarz type iterative solvers and preconditioners. The idea of using overlapping domain decomposition goes back to Schwarz alternating method from 1870, see [1]. The analysis of this alternating iterative method was evolved by great mathematicians, see e.g. S.L. Sobolev (1936), R. Courant and D. Hilbert (1937), S.G. Michlin (1951), M. Práger (1958), I. Babuška (1958), F.E. Browder (1958). The use of overlapping domain decomposition for parallel computations started in the late eighties in the work of M. Dryja and O. Widlund [4], P.L. Lions [5, 6], S. Nepomnyaschikh [7] and others and continue up to the present days. The origin of the alternating Schwarz method is nicely described in [8].
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SNA´17 - Seminar on Numerical Analysis
Blaheta, Radim ; Starý, Jiří ; Sysalová, Dagmar
Seminar on Numerical Analysis 2017 (SNA'17) is a continuation in a series of SNA events held in different places in the Czech Republic and organized alternatively by Ostrava and Prague institutions. TheSNA'17isorganizedbytheInstituteofGeonicsoftheCASincollaborationwith VŠB - Technical University of Ostrava and IT4Innovations National Supercomputing Centre. Conference location is one of the lecture rooms in New Aula of the VŠB-TU Ostrava. Let us note that SNA 2016 was reshaped to EMS School in Applied Mathematics (ESSAM) devoted to mathematical modelling, numerical analysis and scientific computing. The SNA'17 is turning back to more traditional winter event. It provides opportunity for meeting and mutual information of the community working in computational mathematics and computer science, but an important part of SNA is devoted to the Winter School with tutorial lectures focused on selected important topics within the scope of numerical methods and modelling.
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A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems
Axelsson, Owe ; Blaheta, Radim ; Hasal, Martin
The paper overviews and compares some block preconditioners for the solution of saddle point systems, especially systems arising from the Brinkman model of porous media flow. The considered preconditioners involve different Schur complements as inverse free Schur complement in HSS (Hermitian - Skew Hermitian Splitting preconditioner), Schur complement to the velocity matrix and finally Schur complement to a regularization block in the augmented matrix preconditioner. The inverses appearing in most of the considered Schur complements are approximated by simple sparse approximation techniques as element-by-element and Frobenius norm minimization approaches. A special interest is devoted to problems involving various Darcy, Stokes and Brinkman flow regions, the efficiency of preconditioners in this case is demonstrated by some numerical experiments.
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Výroční zpráva o činnosti a hospodaření za rok 2015
Blaheta, Radim
Výroční zpráva o činnosti Ústavu geoniky AV ČR, v.v.i. v roce 2015 popisuje aktivity ústavu \na jejich výsledky v uplynulém roce. Zpráva je členěna předepsaným způsobem a v \njednotlivých kapitolách informuje o výsledcích vědy a výzkumu v oblastech výzkumných\naktivit ústavu. Je zde popsáno zapojení ústavu do mezinárodních výzkumných programů, \ndo projektů strategických směrů AV 21, do programů Strukturálních fondů EU, do \nspolupráce s aplikační sférou a vysokými školami. Zpráva podává informaci o mezinárodní \nspolupráci, o organizaci vědeckých konferencí, účasti v redakčních a vědeckých radách \napod. Podává také informace o organizaci, o personálním složení a činnosti orgánů ústavu, \no ekonomickém fungování instituce, včetně auditu.
Plný tet: UGN_0460562 -  PDF
Plný text: content.csg - PDF
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