Workshop on scientific computing 2023

May 25 - 28, 2023. Děčín, Czech Rep. + Online

Departments of Software Engineering and Mathematics
FNSPE CTU in Prague, Czech Republic

List of abstracts

Pore-scale Model of Soil Freezing
Michal Beneš, Alexandr Žák and Tissa H. Illangasekare
FNSPE, CTU in Prague, FNSPE, CTU in Prague and Colorado School of Mines, Golden, USA

Abstract: We present results of the finite-element simulation of ice nucleation and growth in pores of a saturated porous medium. The ice volume expansion leads to structural changes. The ice phase is captured by the phase-field method including anisotropy. We discuss computational results and future steps in the model development.

Equivalent Partial Differential Equations for LBM and LBMAT: Open Problems
Radek Fučík
FNSPE, CTU in Prague


A general method for the derivation of equivalent finite difference equations (EFDEs) and subsequent equivalent partial differential equations (EPDEs) presented for a general matrix lattice Boltzmann method (LBM). The method can be used for both the advection diffusion equations and Navier-Stokes equations in all dimensions. In principle, the EFDEs are derived using a recurrence formula. A computational algorithm is proposed for generating sequences of matrices and vectors that are used to obtain EFDEs coefficients. The resulting EFDEs and EPDEs are derived for selected velocity models and include the single relaxation time, multiple relaxation time, and cascaded LBM collision operators. The algorithm for the derivation of EFDEs and EPDEs is implemented in C++ using the GiNaC library for symbolic algebraic computations. Its iplementation is available under the terms and conditions of the GNU general public license (GPL). The talk will summarize open problems for EPDEs for LBM with source terms.

Numerical aspects of Smoothed Particle Hydrodynamics Method in hydraulic applications
Tomáš Halada, Luděk Beneš
FME, CTU in Prague


SPH is a mesh-free particle Lagrangian method that can successfully solve problems that are difficult or even impossible to handle with a conventional mesh-based method. We use a weakly compressible formulation of the SPH method (WCSPH) for free-surface flow and discuss some of its numerical aspects. Two hydraulic application are presented, free-surface flow in open channels with a complex geometry and simulation of mechanical mixing. These applications are used to highlight some numerical issues of the method, that need to be addressed and which are not clear from the standard, widely used benchmarks. Problems with negative pressure, pressure oscillations and numerical viscosity are discussed. Emphasis is placed on the additional stabilizing diffusive terms, realization of viscous terms, artificial viscosity and its relation to physical viscosity. Moreover, some additional improvement based on regularization techniques (PST) are mentioned, which eventually leads to a modern and promising Quasi-Lagrangian and Arbitrary Lagrangian-Eulerian schemes. Recent results from both of these applications are presented and analyzed in terms of the numerical aspects of the weakly compressible SPH method, and some improvements are suggested based on this analysis.

Parallel performance of STAR-CCM+
Pavel Hron
Siemens Industry Software


One of the key requirements of commercial Computational Fluid Dynamics (CFD) based simulation software is great parallel scalability. The parallel performance of STAR-CCM+ is evaluated on several industrial test cases for both, modern CPU and GPU architectures. The computational times on high-end hardware can be reduced from weeks to hours.

Recent updates in development of the Data Acquisition System of the AMBER experiment
Vladimír Jarý, Bc. Jan Vondruška. Ing. Martin Zemko
FNSPE, CTU in Prague


Modern experiments in high energy physics strongly depend on effient data acquistion (DAQ) systems. In this contribution, we will focus on the DAQ system of the AMBER experiment at CERN laboratory in Geneva, Switzerland. We briefly introduce overall hardware architecture of the system, then we will present the software part that is used mainly for run control, configuration, and monitoring.

Often, it is necessary to access the system remotely. However, as the main parts of the software are desktop applications with Qt-based graphical user interface, the remote access requires fast and stable network connection. We analyse the possibility to replace selected configuration tools with web applications. We also propose to develop library of functions to implement a common command line library that would cover the most important aspects of the control and monitoring functionality. The combination of both approaches would greatly reduce requirements on the connection and would simplify the remote work. 

We discuss the current state of the implementation of the proposed applications. We summarize the contribution by giving outlook into the future development. 

Image segmentation techniques by means of evolving curves
Miroslav Kolář
CTU in Prague

Abstract: In this talk we focus on the problem of image segmentation by means of the flow of smooth parametrized curves. Particular reason for the choice of direct description of moving segmentation curve is simplistic descritption and easiness to recover geometrical information of the segmented object. The motivation is in the medical imaging, nd more precisely, in retrieving the geometrical information of tumor slices.

Numeric Formulas for Fractional Laplacian and Fractional Gradient
Jaromír Kukal, Michal Beneš
FNSPE, CTU in Prague

Abstract: New difference schemes for fractional Laplacian and fractional gradient wil be presented for 1 < alpha < 2. They are develped  for regular meshes (linear, tetragonal, cubic, hexagonal, dodecahedral) and have maximum possible approximation order 4 - alpha in all grid cases and any function from C4 class. The approximation error has been verified numerically. The hexagonal and dodecahedral meshes are recommended for radially symmetric solutions.

Programming GPU in TNL
Tomáš Oberhuber
FNSPE, CTU in Prague


Numerical simulation of dislocation multiple cross-slip
Petr Pauš
FNSPE, CTU in Prague


Our contribution deals with the phenomenon in material science called multiple cross-slip of dislocations in slip planes. The numerical model is based on a mean curvature flow equation with additional forcing terms included. The curve motion in 3D space is treated using our tilting method, i.e., mapping of a 3D situation onto a single plane where the curve motion is computed. The physical forces acting on a dislocation curve are evaluated in the 3D setting.

Numerical Optimization of Neumann Boundary Condition for thermal lens construction
Jakub Solovský, Aleš Wodecki, Monika Balázsová, Kateřina Škardová, Tomáš Oberhuber
FNSPE, CTU in Prague / RERI, FNSPE, CTU in Prague


The refractive index of thermo-optic materials changes significantly with temperature. This property allows for a layer of material with a certain temperature profile to act as a lens with desired optical properties.

The goal is to find the heat fluxes through the domain boundary that result in the given temperature profile at the given time.

We solve the PDE-constrained optimization problem using the gradient descent method. For the computation of the objective function gradient, we employ the approach based on solving the adjoint equation for Lagrange multipliers.

Both the primary and adjoint problems are solved by the Mixed-Hybrid Finite Element Method with fully implicit discretization in time.

We demonstrate that the temperature profiles given by Zernike polynomials on a circular domain can be obtained.

Numerically Efficient Determination of Kinetic Parameters of the VR-1 Nuclear Reactor based on Experimental Data and ODE-Constrained Optimization
Pavel Strachota, Sebastian Nývlt, Jan Rataj, Aleš Wodecki
FNSPE, CTU in Prague


We follow up on the work presented at WS2022 aimed at determining the correct contributions of different classes of delayed neutrons to the kinetics of the VR-1 experimental nuclear reactor. The facility is installed at the Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague. We consider the system of equations of point kinetics, which is a system of linear ODE with source terms. This model can be used provided that the spatial distribution of reaction parameters inside the nuclear reactor core evolves slowly with respect to the reaction dynamics. We solve the ODE-constrained minimization problem to determine the correct values of the model parameters based on experimental measurement of reactor power output response to the changes in reactivity. The difference between the results of the simulations and the experiments is minimized by several gradient descent techniques. For the computation of the gradient, we employ both the direct method (sensitivity analysis) and the adjoint method based on solving the adjoint equation for Lagrange multipliers. We demonstrate the advantages of the adjoint approach, discuss the influence of ODE solver accuracy, properties of the individual gradient descent variants, and the structure of the local minima of the cost functional.

Lattice Boltzmann Method and reacting flows
Robert Straka
AGH University of Science and Technology

Abstract: Combustion problems are usually described by a set of Navier-Stokes equations (NSE) together with Advection-Diffusion-Reaction equations (ADRE) for scalar quantities. We use a Lattice Boltzmann Method (LBM) to solve a system of equations related to simplified models of combustion i.e. we neglect radiation, temperature dependence of material properties, and assume ideal gases. Examples of solid state fuel combustion will be presented.

The overview of image reconstructions in Computed Tomography
Lucie Súkupová
IKEM, Prague


Computed Tomography (CT) is an imaging technique that uses X-ray radiation to generate axial slices of patients from acquired data. Acquired data are in the form of attenuation profiles in the sinogram space that can be filtered (here or in the frequency space), and then backprojected to the image space. One of major developments in reconstructions was use of iterative reconstructions (IR) of different types, firstly hybrid IR, later model-based IR that uses forward and backforward projections. Unfortunately, IR changes the texture of noise that negatively affects image appearance. These days, use of artificial intelligence is beneficial because it keeps the noise texture unchanged, but the magnitude can be decreased.

A scalable multilevel domain decomposition solver for immersed boundary finite element method
Jakub Šístek
Institute of Mathematics of the Czech Academy of Sciences


Immersed boundary finite element method (FEM) presents an attractive approach to simulations avoiding the generation of large body-fitted meshes. This can be tedious and challenging for complex geometries as well as for very fine meshes distributed over a parallel computer and adaptively refined during a computation. However, the price to pay are more complicated formulations for the weak enforcement of Dirichlet boundary conditions, poor conditioning of stiffness matrices, and nonstandard numerical integration at the vicinity of the boundary.

We develop multilevel balancing domain decomposition by constraints (BDDC) method tailored to the solution of the linear systems arising in the context of immersed boundary FEM with parallel adaptive grid refinement. A crucial challenge is presented by fragmenting of subdomains, which has two sources: i) the partitioning strategy based on a space-filling curve, and ii) extraction of the elements contributing to the stiffness matrix.

We present these concepts, the challenges, our implementation, and numerical results for the Poisson problem on complex geometries from engineering. This is joint work with Fehmi Cirak, Eky Febrianto, Matija Kecman, and Pavel Kůs.

Effect of spatial and temporal resolution on the accuracy of motion tracking using 2D and 3D cine cardiac magnetic resonance imaging data
Kateřina Škardová, Tarique Hussain, Martin Genet, Radomír Chabiniok
FNSPE, CTU in Prague


This contribution explores how the spatial and temporal resolution of cardiac MRI cine images can affect the accuracy of the extracted left ventricle motion. Using a previously validated finite-element-based image registration method, the study was conducted on three subjects, for which both standard 2D cine stack (SA) and 3D cine MRI series imaging were acquired. Additionally, artificial SA-like cine image series were created from the 3D cine images to further augment the dataset. The study evaluated image series with various combinations of spatial and temporal resolution for each subject. Results indicated a strong correlation between slice thickness and the accuracy of extracted longitudinal displacement.

New methods in MRI data reconstruction: Deep learning and Artificial inteligence
Jaroslav Tintěra
IKEM, Prague


Recently, new software to reconstruct highly accelerated data from under-sampled acquisition has appeared commercially available. This SW utilizes  several modern mathematical methods to effectively denoise acquired data and also to increase sharpness of reconstructed magnetic resonance images (MRI). It includes tailored noise analysis (spatially selective noise mask), deep learning and also artificial intelligence methods based on large data sets training.

We will present first experience with this new technology and also we want to show both the clear benefit from using it but also potential risk of artifacts coming with reconstruction techniques.   

Bankruptcy prediction by a combined approach of LDA and ANN with robust whitening
Quang Van Tran
FNSPE, CTU in Prague

Abstract: We propose a new approach prediction of firm’s bankruptcy in which the neural network is combined with linear discriminant analysis. We also try to improve LDA algorithm with the introduction of the robust covariance matrix. We verify the applicability of our approaches on a relatively large-scale dataset of Polish firms in manufacturing sector in period 2000-2013. The results of our analysis show that this approach can correctly classify all cases of non-bankrupted firms (in-sample and out-of-sample) and the rate of correct prediction of bankrupted firms is over eighty percent for the given dataset.

Dynamic mode decomposition and its application to the flutter analysis
Jan Valášek
Institute of Mathematics, CAS


In this talk the dynamic mode decomposition (DMD) method will be introduced. It is a data-driven and model-free method which decomposes a given set of signals to DMD modes and associated DMD eigenvalues. Thus it offers a very interesting alternative to the proper orthogonal decomposition (POD) and similar methods usually used for the low-rank representation of the high-dimensional data. The advantage of DMD is better physical interpretation of the decomposition as the DMD modes have monofrequency content and the complex DMD eigenvalues provide the frequency as well as the growth/decay rate of particular mode. Moreover the DMD has solid theoretical underpinnings given by the Koopman operator. The disadvantage of DMD is a relative ambiguity of DMD mode selection which are not sorted as in the case POD decomposition. Finally an application example of the DMD analysis to the numerical simulation of flutter vibrations is presented.