
SNA'21  Seminar on Numerical Analysis
Starý, Jiří ; Sysala, Stanislav ; Sysalová, Dagmar
Seminar on Numerical Analysis 2021 (SNA'21) is the 15th meeting in aseries of SNA events.The previous meetings were held in Ostrava 2003, 2005, Monínec 2006,Ostrava 2007,Liberec 2008,Ostrava 2009,Nové Hrady 2010, Rožnov 2011, Liberec 2012, Rožnov 2013, Nymburk 2014, Ostrava 2015, 2017, and 2019. SNA events help to bring together the Czech research community working in the field of numerical mathematics and computer simulations.The scope of the seminar ranges from mathematical modelling and simulation of challenging engineering problems, to methods of numerica lmathematics, numerical linear algebra, and high performance computing. SNA'21 has about 80 participants. Its programme includes the traditional Winter School with tutorial lectures focused on selected important topics within the scope of the seminar.This year, the Winter School includes the following lectures:


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 highperformance 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 highperformance computing systems of petaflops and preexaflops performance. Increased attention is devoted to challenging industrial problems and collaboration with industry.


Reliable computation and local mesh adaptivity in limit analysis
Sysala, Stanislav ; Haslinger, Jaroslav ; Repin, S.
The contribution is devoted to computations of the limit load for a perfectly plastic model with the von Mises yield criterion. The limit factor of a prescribed load is defined by a specific variational problem, the socalled limit analysis problem. This problem is solved in terms of deformation fields by a penalization, the finite element and the semismooth Newton methods. From the numerical solution, we derive a guaranteed upper bound of the limit factor. To achieve more accurate results, a local mesh adaptivity is used.


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.


Implicit constitutive solution scheme for MohrCoulomb plasticity
Sysala, Stanislav ; Čermák, M.
This contribution summarizes an implicit constitutive solution\nscheme of the elastoplastic problem containing the MohrCoulomb yield cri\nterion, a nonassociative \now rule, and a nonlinear isotropic hardening. The\npresented scheme builds upon the subdifferential formulation of the \now rule\nleading to several improvements. Mainly, it is possible to detect a position\nof the unknown stress tensor on the MohrCoulomb pyramid without blind\nguesswork. Further, a simplifed construction of the consistent tangent opera\ntor is introduced. The presented results are important for an efficient solution\nof incremental boundary value elastoplastic problems.


Finalisation of development and verification of Flow123d software within the DECOVALEX 2015 project
Blaheta, Radim ; Maryška, J. ; Březina, J. ; Stebel, J. ; Šembera, J. ; Balvín, A. ; Bruský, I. ; Hasal, Martin ; Michalec, Zdeněk ; Staš, Lubomír ; Sysala, Stanislav
This final report summarizes the progress of work and results for the whole period of the project. The subject is modelling of tasks within the project Decovalex2015, development of Flow123d software, and preparation of documents for its standardization using the comparison results with foreign teams. TUL team participated in Task C1 (THMC processes in a single fracture) using the software Geochemist’s Workbench and their own tool TrAper for connecting chemistry and deformation and Task C2 (flow and transport in the vicinity of the tunnel Bedřichov) using Flow123d software. Task C2 also includes the formulation of the assignment and coordination of the solution of other teams. The ÚGN team participated in Task A, focusing on saturation of bentonite seals in clay rock and closing the gap, with the help of the COMSOL Multiphysics software. The outputs are the joint report by international teams and papers in a special issue of a journal. The developed models and lessons learned contribute to the ability to predict phenomena in the deep geological repository. Another result is a set of documents for the Flow123d software. All of which are attached to the report as attachments.


Bending of Beam with Free Ends on Nonlinear Subsoil
Sysala, Stanislav
A semicoercive problem with a beam on a unilateral elastic subsoil of Winkler type is investigated in the contribution. Firstly, the existence, the uniqueness and the continuous dependence on data of the problem solution are discussed. Secondly, the problem is approximated by the finite element method, where the subsoil is replaced by insulated "springs" due to a numerical quadrature. The relations between the original problem and the family of approximated problems are introduced. Thirdly, suitable numerical methods of Newton type are introduced. The convergence analysis of the methods is investigated. The dependence of the methods on the discretization parameter and the load is also discussed. And finally, some of the theoretical results are illustrated on numerical examples.


Solving an elastoplastic problems by Newtonlike methods
Byczanski, Petr ; Sysala, Stanislav
In this contribution, we will apply the semismooth Newton methods with and without damping to solving a onetime step problem in elestoplasticity. First, we briefly describe the elastoplastic model and formulate the corresponding onetime step problem in the form of the nonlinear variational equation. Then we characterize the used numerical methods. Finally, we illustrate the methods on a 2D numerical example.


Modifikovaná nehladká Newtonova metoda: numerický příklad
Byczanski, Petr ; Sysala, Stanislav
The modified semismooth Newton method is introduced in this contribution. The modification is based on a ``damping" in each Newton iteration. The damping coefficient are computed by a minimisation problem. The method is described on an abstract problem with the main convergence results. Then it is applied to solving an elastoplastic problem with hardening and illustrated on a numerical example.


Numerická ilustrace teoretických výsledků pro nelineární semikoercivní nosníkovou úlohu
Sysala, Stanislav
The semicoercive problem of a beam on a unilateral elastic subsoil of Winkler's type is considered. The aim of this contribution is numerically illustrate some basic results of the problem, which are summarised in the contribution. Concretely, we are interested in dependence of the problem solution on an external load, the error estimates of approximated solutions and the convergence properties of used numerical methods subject to the load.
