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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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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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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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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.
Fulltext: content.csg -  PDF
Plný tet: UGN_0438747 - PDF
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High performance computing in micromechanics
Blaheta, Radim ; Hrtus, Rostislav ; Jakl, Ondřej ; Starý, Jiří
By micromechanics we understand analysis of the macroscale response of materials through investigation of processes in their microstructure. Here by the macroscale, we mean the scale of applications, where we solve engineering problems involving materials like different metals and composites in aircraft design or rocks and concrete in a dam construction. Different applications are characterized by different characteristic size. At macroscale the materials mostly look as homogeneous or they are idealized as homogeneous or piecewise homogeneous. A substantial heterogeneity is hidden and appears only after more detailed zooming view into the material.
Fulltext: content.csg - PDF
Plný tet: UGN_0426823 - PDF
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Source localization for EEG patterns relevant to motor imagery BCI control
Bobrov, P. ; Frolov, A. ; Húsek, Dušan ; Tintěra, J.
This work concerns spatial localization of sources of EEG patterns the most specific for control of the motor imagery based BCI. In our previous work we have shown that performance of Bayesian BCI classifier can be drastically improved by extraction of the most relevant independent components of the EEG signal. This paper presents the results of spatial localization of electrical brain activity sources which activity is reflected by the extracted components. The localization was performed by solving the inverse problem in EEG source localization, using individual finite-element head models. The sources were located in central sulcus (Brodmann area 3a), in the superior regions of post- and precentral gyri, and supplementary motor cortex.
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