Two simple derivations of universal bounds for the C.B.S. inequality constant

summary:Universal bounds for the constant in the strengthened Cauchy-Bunyakowski-Schwarz inequality for piecewise linear-linear and piecewise quadratic-linear finite element spaces in 2 space dimensions are derived. The bounds hold for arbitrary shaped triangles, or equivalently, arbitrary matrix coefficients for both the scalar diffusion problems and the elasticity theory equations

An improved return-mapping scheme for nonsmooth yield surfaces: PART I - the Haigh-Westergaard coordinates

The paper is devoted to the numerical solution of elastoplastic constitutive initial value problems. An improved form of the implicit return-mapping scheme for nonsmooth yield surfaces is proposed that systematically builds on a subdifferential formulation of the flow rule. The main advantage of this approach is that the treatment of singular points, such as apices or edges at which the flow direction is multivalued involves only a uniquely defined set of non-linear equations, similarly to smooth yield surfaces. This paper (PART I) is focused on isotropic models containing: $a)$ yield surfaces with one or two apices (singular points) laying on the hydrostatic axis; $b)$ plastic pseudo-potentials that are independent of the Lode angle; $c)$ nonlinear isotropic hardening (optionally). It is shown that for some models the improved integration scheme also enables to a priori decide about a type of the return and investigate existence, uniqueness and semismoothness of discretized constitutive operators in implicit form. Further, the semismooth Newton method is introduced to solve incremental boundary-value problems. The paper also contains numerical examples related to slope stability with available Matlab implementation.Comment: 25 pages, 10 figure

HPC in Computational Micromechanics of Composite Materials

Proceedings of: Second International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2015). Krakow (Poland), September 10-11, 2015.This work was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and the COST NESUS project with an additional CZ MEYS LD15105 support

Analysis of fiber-reinforced concrete: micromechanics, parameter identification, fast solvers

Proceedings of: Third International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2016). Sofia (Bulgaria), October, 6-7, 2016.Ultrascale computing is required for many important applications in chemistry, computational fluid dynamics etc., see an overview in the paper Applications for Ultrascale Computing by M. Mihajlovic et al. published in the International Journal Supercomputing Frontiers and Innovations, Vol 2 (2015). In this abstract we shortly describe an application that involves many aspects described in the above paper - the multiscale material design problem. The problem of interest is analysis of the fiber reinforced concrete and we focus on modelling of stiffness through numerical homogenization and computing local material properties by inverse analysis. Both problems require a repeated solution of large-scale finite element problems up to 200 million degrees of freedom and therefore the importance of HPC and ultrascale computing is evident.The work is supported by COST Action IC1305 project Network for Sustainable Ultrascale Computing and a bilateral project of collaboration between the Institute of Geonics CAS and IICT BAS. Further support is through the projects LD15105 Ultrascale computing in geosciences and LQ1602 IT4Innovations excellence in science supported by the Ministry of Education, Youth and Sports of the Czech Republic

Finalisation of development and verification of Flow123d software within the DECOVALEX 2015 project

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 Decovalex-2015, 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

Overlapping domain decomposition preconditioners for elliptic and parabolic problems in primal and mixed form

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]

SNA´17 - Seminar on Numerical Analysis

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

Parallel Computing and FEM

The contribution describes application of parallel computing for numerical solution of boundary value problems like elasticity, heat conduction etc. by the finite element method (FEM). The main application concerns solution of large scale linear algebraic systems by domain decomposition methods

The 25th anniversary of the Institute of Geonics of the Academy of Sciences of the Czech Republic

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Annual report of the Institute of Geonics AS CR, v.v.i. 2010

The annual report of the Institute of Geonics AS CR presents the results of the activities of the institute in the year 2010. In particular chapters there is information considerig the results in the field of science and research, cooperation with universities and the application sphere, international collaboration, information about organization of various scientific conferences, participation in editorial and scientific boards etc. There is also information about organization, personal structure and the economy of the institution including audit. Final part is devoted to planned activities in the next period