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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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Modelling 2014
Blaheta, Radim ; Starý, Jiří ; Sysalová, Dagmar
MODELLING 2014 is a conference on Mathematical Modelling and Computational Methods in Applied Sciences and Engineering, which is held in Roznov pod Radhostem, Czech Republic, in June 2 - 6, 2014. The conference is organized by the IT4Innovations Centre of Excellence, Institute of Geonics AS CR, V’B-Technical University of Ostrava and International Association for Mathematics and Computers in Simulations (IMACS). MODELLING 2014 aims to be a forum for an exchange of ideas, insights and experience in di erent areas of mathematical modelling from numerical methods and computer aspects to applications of mathematical modelling methods. This international conference belongs to a series of conferences held in Roºnov 2009, Pilsen 2005, Pilsen 2001, Prague 1998 which started 20 years ago in Prague 1994. Main topics of the conference include computational modelling in engineering and science: multiscale modelling, multiphysics modelling, progress in discretization methods, effcient solvers, nonlinear problems, reliable computations, challenging applications of mathematical modelling methods, exploiting massively parallel computing facilities.
Plný tet: UGN_0438747 - PDF
Plný text: content.csg - PDF
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Dokončení vývoje a ověření SW Flow123D v rámci projektu DECOVALEX 2015
Hokr, M. ; Maryška, J. ; Březina, J. ; Šembera, J. ; Balvín, A. ; Bruský, I. ; Blaheta, Radim ; Hasal, M. ; Michalec, Zdeněk ; Staš, Lubomír
V rámci činností mezinárodního projektu DECOVALEX připadajících na ČR (SÚRAO) je cílem dokončit vývoj a ověřit kvalitu a vhodnost použití SW Flow123D pro výpočtové modelování sdružených termo-hydro-mechanicko-chemických (THMC) procesů na puklinovém granitovém prostředí bedřichovských tunelů.
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The history of measurement of rock mechanical properties at the Institute of Geonics AS CR
Konečný, Pavel ; Blaheta, Radim
The rock testing and evaluation of parameters for description of rock behaviour is an important part of the research at the Institute of Geonics AS CR since its foundation as an independent institute of the Czechoslovak Academy of Sciences in 1982. Focusing on mechanical testing, the first testing device, the hydraulic press EDZ 100H made in GDR with maximum force 1000 kN, was acquired in 1980, when only a branch of the Mining Institute existed in Ostrava. This equipment was substantially extended in the eighties by two „small“ mechanical presses FPZ 100 (max. force 100kN) and FPZ 10 (max. force 10kN) purchased in 1987 from GDR. But a really great progress came with the mechanical press ZWICK 1494 (500 kN) controlled by computer with a possibility of recording and processing the data. This press was bought from ZWICK Ulm (FRG) in 1985. The deformation measurement was realized by the dial test indicators. The described equipment was used for rock testing with focus on elastic behaviour and uniaxial strength limits, which were required for solving engineering problems mostly related to the coal mining.
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