Workshop on scientific computing 2015

June 11-14, 2015
Department of Mathematics, FNSPE CTU in Prague
Děčín, Czech Republic

Bosson Cluster -- Building Cluster Solution on top of Open Source

David Fabian

Cluster Design, s.r.o.

Abstract:In the past decade, IT companies specialized in outsourcing of IT technologies have been dealing with two main problems -- how to fully utilize hardware and how to offer as stable environment as possible for the client applications. Computer clusters and virtualization are the answer to both of these issues. A computer cluster is a set of inter-connected computers (nodes) connected to a storage provider (storage array). Virtualization allows us to run multiple instances of an operating system side-by-side on a single hardware node. In this presentation, the Bosson cluster solution will be introduced. Bosson cluster joins together a common data-center hardware and a custom cluster stack software based heavily on the open-source software. Bosson cluster aims to be on-par with the traditional cluster solutions when it comes to stability and functions while reducing the cost of such a solution considerably.

TNL: FDM on GPU in C++

Tomáš Oberhuber


Abstract:We present Template Numerical Library with native support of CUDA for computations on GPUs. The library is written in C++ and it uses C++ templates extensively. The templated design of TNL allows to develop solvers of PDEs with GPU support relatively easily and almost without any knowledge of GPUs. The aim of TNL is to provide an easy to use tool for numerical mathematicians so that they may concentrate only to numerical methods but they can still profit from modern accelerators and parallel architectures. We will also discuss disadvantages of C++ templates and metaprogramming.

Tangential redistribution for mean-curvature driven evolution of surfaces

Daniel Ševčovič

Comenius University, Bratislava

Abstract:The main goal of this talk is to investigate tangential redistribution of points on evolving immersed manifolds. More precisely, we will analyse motion of surfaces or curves evolved in the normal direction by the curvature. Although the tangential velocity has no impact on the shape of evolved manifolds, it is an important issue in numerical approximation of any evolution model, since the quality of the mesh has a significant impact on the result of the computation. We analyse the volume-oriented and length-oriented tangential redistribution methods. We apply the proposed techniques to the particular case of mean
curvature evolution of surfaces in $\mathbb{R}^3$. We explain the numerical approximation of the model and present several experiments illustrating the performance of the redistribution techniques. This is a joint work based on the joint paper with M.Remesikova, K.Mikula and P.Sarkoci: Manifold evolution with tangential redistribution of points, SIAM J. Sci. Comput. 36-4 (2014).

A Phase Field Crystal Model for Active Particles

Francesco Alaimo

Technical University of Dresden

Abstract:Active systems, i.e. systems composed by particles that are intrinsically in non-equilibrium since they are self-propelled, exhibit a wide range of collective phenomena, such as cluster building or spontaneous organization in confined geometries. These phenomena have been observed both experimentally and numerically. We present
here a continuous approach to model the behaviour of such active particles: the Phase Field Crystal (PFC) method, a method that comes from dynamical density functional theory and that bridges the gap between microscopic theories and phase field approaches. We use a variation of the PFC, known as Vacancy Phase Field Crystal, and couple it to a polarization field that represents the orientation of the particles. With this continuous model we can reproduce the collective behaviour of active particles in many different geometries. This model is also a good starting point to include hydrodynamic interactions and therefore to describe in a continuous manner the motion of swimmers.

Radiality Order in Grid Design for Isotropic Diffusion Modeling

Jaromír Kukal


Abstract:Free isotropic diffusion in R^n was studied via spatial Fourier transform and Laplace transform in time domain to obtain traditional solution. The same technique was applied to centrosymmetric difference scheme of 2N+1 points. Direct comparison of both results in frequency domain via Taylor expansion will help to design various difference schemes with given order of radiality and accuracy. First results will be demonstrated on 2D schemes with tetragonal and hexagonal topology. Direct application to anisotropic diffusion is also possible but corresponding coefficients are not so nice fractions and formula orders can be decreased in particular cases.

Spectral methods for time-dependent vector-valued problems on the two-sphere

Simon Praetorius

Technical University of Dresden

Abstract:Vector-valued problem play an important role in the scientific area of computational
fluid dynamics and the description of liquid crystals, upon many others. In the flat-space, i.e. R2 or R3 , various different methods are available to solve the corresponding partial differential equations. Here we want to consider equations that live on the two-sphere S2 as a submanifold of R3 . For fluid mechanical applications the first available methods are based on spherical harmonics transform of the equations. This approach will be described and is applied to simple model problems of director field relaxation, as is relevant for liquid crystal on spherical shells.

First-principle Modeling of Nuclear Structure and Reactions in the Era of Petaflop Supercomputers

Tomáš Dytrych

Louisiana State University

Abstract:In this talk, I will give an overview of the first-principle modeling of structure and reactions of atomic nuclei that run on the world's most powerful supercomputers. I will discuss main challenges that hinders application of these methods for heavier nuclei and exotic isotopes that are key to understanding important astrophysical processes. I will introduce a novel method, the symmetry-adapted no-core shell model, and will show its promising potential for expanding the reach and predictive power of first-principle nuclear structure studies beyond their current limits.

Neutron Imaging of Trapped Gas Behaviour in Near-Saturated Heterogeneous Soils

Michal Sněhota


Abstract:Recently, a number of infiltration experiments have not proved the validity of standard Richards’ theory of the flow in soils with wide pore size distribution. Water flow in such soils under near-saturated conditions often exhibits preferential flow and temporal instability of the saturated hydraulic conductivity.

An intact sample of coarse sandy loam from Cambisol series containing naturally developed vertically connected macropore was investigated during recurrent ponding infiltration (RPI) experiments conducted during period of 30 hours. RPI experiment consisted of two ponded infiltration runs, each followed by free gravitational draining of the sample. Three-dimensional neutron tomography (NT) image of the dry sample was acquired before the infiltration begun and then repeatedly during steady state flow. The dynamics of the wetting front advancement was investigated by a sequence of neutron radiography (NR) images. As a next stage, the experiment was repeated on a composed sample packed of fine ceramic and coarse sand. Series of infiltrations was conducted with various initial water contents.

The neutron tomography data quantitatively showed that both in natural soil sample with macropore and in the composed sample air was gradually transported from the region of soil matrix to the macropores or to the coarser preferential pathway. This supports the hypothesis on strong influence of entrapped air (residual gas phase) amount and spatial distribution on infiltration into heterogeneous soils. The effect of air trapping on soil hydraulic properties will be discussed in the talk.

LBM simulation of industrial scale furnace

Robert Straka

AGH Krakow

Abstract:Lattice Boltzmann method is used in the numerical simulation of an industrial scale steelworks furnace located in Ostrowiec. Such type of furnaces are used for a heat treatment of a steel load before its further processing. In this talk we focus on the flue-gas flow inside the furnace chamber where the cylindrical metal load is located. Results from the different setup of gas-fired burners' parameters will be examined and compared.

Modelling of Athermal Phase Transitions in Materials by Phase-Field Method

Michal Beneš


Abstract:The contribution compares the phase-field models for phase transitions in materials accompanying the phase change from liquid to solid controlled by the heat transport, and the athermal transformation between e.g. beta and omega phases. The liquid-solid transition is described by the temperature distribution and by the position of the solid phase approximated by the phase field, whereas the beta-omega phase transition is described by the elastoplastic phase-field model where the transition is described by the crystallographic orientations (phase fields) given by the difference between the beta and omega structures and by plastic deformation and strain hardening. We discuss both models and indicate their numerical treatment in the context of real materials.

Error Estimate vs. Experimental Convergence Measurement of the Finite Volume Scheme for the Allen-Cahn Equation

Pavel Strachota


Abstract:The Allen-Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion PDE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce a model initial boundary-value problem for the isotropic variant of the equation. Its numerical solution by the method of lines is then considered, using a finite volume scheme for spatial discretization. The main part of the contribution is the derivation of the error estimate for the solution of the resulting semidiscrete scheme. Subsequently, sample numerical simulations in two and three dimensions are presented and the experimental convergence measurement is discussed in the context of the obtained theoretical results.

Software for parameter tuning and postprocessing of segmentations obtained from automatic algorithms based on PDEs

Róbert Špir

Slovak Technical University in Bratislava

Abstract:In this talk we present a new software tool that can be used for tuning of parameters and postprocessing of the results obtained from automated segmentation algorithms applied to biomedical images. The quality of the results is highly dependent on the quality of the input data and can be tuned using many parameters of the model based on partial differential equations. Obtaining good parameters for certain dataset can be difficult and tedious process. Using this new tool one can see the impact of parameter change on the segmentation result in real time and quickly find a set of good parameters that can be used on the whole dataset. The software can also be used to improve and modify the segmentation result so it will better fit the original data.

Non-Equilibrium Mass Transfer Model for Complete Volatilization of Trapped Non-Aqueous Phase Fluids in Vadose Zone

Radek Fučík


Abstract:We present a robust and efficient numerical model of mass transfer from trapped non-aqueous liquid phase (NAPL) source in the unsaturated zone and subsequent transport of the generated vapor subjected to air flow. Such a model allows for the investigation of mass transfer rates from NAPL sources under variable air and water flow for the study of vapor transport in the vadose zone, with applications to soil vapor extraction and vapor intrusion. The model simulates both near-local-equilibrium and rate limited mass transfer behavior. The model uses the mixed-hybrid finite element (MHFE) numerical scheme to solve the governing equations and is appropriately implemented to achieve high computational efficiency and accuracy. The model is applied to study a laboratory investigation conducted in a two-dimensional test tank simulating the volatilization of a NAPL pool placed in the unsaturated zone. Based on this numerical and experimental study, we propose a modified Gilliland-Sherwood model that includes an inverse proportionality to the Péclet number that can describe both near equilibrium and advection induced, rate-limited mass transfer.

Semi-implicit numerical methods for advection equation

Peter Frolkovič

Slovak Technical University in Bratislava

Abstract:In this talk we present recent results concerning the development of a class of second order accurate semi-implicit numerical methods for the solution of advection equations. The proposed methods are unconditionally stable for arbitrary (positive) Courant number. The resulting algebraic equation for numerical solution can be solved in an efficient way by e.g. fast sweeping method.

Comparison of numerical methods on a benchmark problem of tracer transport in a combined 3D and 2D domain

M. Hokr, A. Balvín

Technical University of Liberec

Abstract:The solved problem is inspired by a real case of water inflow into a tunnel, with measured natural tracers determining travel time between the surface and the tunnel. The main feature is a contact of a 3D rock continuum domain in contact with a 2D fracture. There are several numerical issues. One is a sensitivity of the tracer transport on diffusion parameters and a numerical scheme, where either the numerical diffusion or the problem-scale dispersion in the flow pattern control the tunnel tracer evaluation curve. The second is the interaction between 3D and 2D in a configuration containing a singularity - we demonstrate the problem and show its minor effect for particular set of parameters. Own software Flow123D and the commercial FEFLOW are used for the calculations.