#### Workshop on scientific computing 2022

May 26 - 29, 2022. Děčín, Czech Rep. + Online

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

### List of abstracts

###### Monika Balázsová
FNSPE CTU in Prague

Abstract:

In a numerical optimization problem the adjoint method allows us to compute the gradient of a functional or operator in an effective and cheap way. In this contribution we demonstrate the adjoint method on the optimization problem for heat equation with a Dirichlet boundary control and show some possible applications and numerical results.

Modeling Experiments in Freezing and Thawing of Porous Media
###### Michal Beneš, Michal Sněhota, Martina Sobotková
FNSPE CTU in Prague, Faculty of Civil Engineering, CTU in Prague

Abstract:

In the contribution, we discuss the modeling of freezing and thawing in a fully saturated porous medium at the experimental laboratory scale. The phase transition leaves the grains intact but involved in the heat transfer and mechanical interaction due to the difference in specific volumes of the liquid and solid phase. The model based on conservation laws of mass, energy and momentum is used for simulation of particular laboratory experiments.

Equivalent partial differential equation of the lattice Boltzmann method
FNSPE CTU in Prague

Abstract: 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).

LES and DNS of flow and scal dispersion in a street canyon
Faculty of Mathematics and Physics, Charles University, Institute of Thermomechanics CAS, Department of Atmospheric Physics MFF UK

Abstract:

In previous large eddy simulations (LES) and wind-tunnel measurements of several street-network configurations it was found that one particular configuration of building shapes poses a particular challenge to the numerical model and even the mean flow in the street canyon differs considerably between the measurement and the simulation.

To be able to conduct simulation for the analysis of the role of the coherent structures for the street canyon ventilation we need to be able to simulate this flow confidently. Therefore, a series of simulations that test the sensitivity of the LES simulations to various setup parameters were performed. Additionally, also direct numerical simulations were performed in a small domain with a reduced Reynolds number (while remaining fully turbulent). The parameters tested are the size of the domain - in particular when interested about persistent large scale structures and convergence of the flow towards a homogeneous mean, the subgrid model, the order of the finite difference approximation and lateral boundary conditions.

What is a proper boundary condition to solve eikonal equation on a non-convex domain?
###### Jooyoung Hahn
Slovak University of Technology

Abstract:

In this talk, boundary conditions to solve the eikonal equation are discussed in the case of non-convex computational domains. One of the proper conditions has been known as the Soner (or no-inflow) boundary condition written by an inequality. Considering an application to industrial problems, domains in three-dimensional space are discretized by polyhedral cells and a cell-centered finite volume method is used to solve the eikonal equation. We briefly check how the mentioned inequality boundary condition can be straightforwardly implemented in the finite volume method. If time permits, I would like to share a short working experience in a company as an applied mathematician. It is my personal story of how I could survive by working with others from the other world.

The Mortar Finite Element Method in Industrial Applications
###### Pavel Hron
Siemens Industry Software

Abstract:

The Mortar Finite Element Method allows the coupling of arbitrary nonconforming interface meshes. We exploit this capability and apply it to real 3D engineering applications in solid energy and solid mechanics. Advantageous properties of the devised algorithms comprise superior robustness as compared with the traditional node-to-segment approach, the absence of any unphysical user-defined parameters (e.g. penalty or Nitsche methods) and the possibility to condense the discrete Lagrange multipliers from the global system of equations.

Fast Evaluation of Modified Renyi Entropy for Fractal Analysis
FNSPE CTU in Prague, FNSPE CTU in Prague

Abstract:

A fractal dimension is a non-integer characteristic that measures the space filling of an arbitrary set. The conventional grid based methods usually provide a biased estimation of the fractal dimension, and therefore it is necessary to develop more complex methods for its estimation. A new characteristic based on the Parzen estimate formula is presented here as the modified Renyi entropy. A novel approach that employs the log-linear dependence of a modified Renyi entropy is used together with very fast implementation of epsilon search in k-d tree.

An alternative model of multicomponent diffusion based on a combination of the Maxwell-Stefan theory and continuum mechanics
###### Jiří Mikyška
FNSPE CTU in Prague

Abstract: TBA

Optimization with PDEs and connection to machine learning
###### Tomáš Oberhuber
FNSPE CTU in Prague

Abstract: In the presentation, we will show how to solve optimization problems with ordinary and partial differential equations by solving adjoint differential equations. We will show similarities with residual neural networks, convolution neural networks, and the backpropagation algorithm. We will point out difficulties arising from solving the optimization problems with partial differential equations.

Cell tracking based on image segmentation in 2D+ and 3D+time microscopy data
###### Seol Ah PARK, Tamara Sipka, Zuzana Kriva, George Lutfalla, Mai Nguyen-Chi, Karol Mikula
Slovak University of Technology in Bratislava, LPHI, CNRS, Univ. Montpellier, Montpellier, France

Abstract:

We introduce the new cell tracking algorithm for time-lapse images. By using the segmented images, the time-relaxed Eikonal equation is solved inside every segmented cell to find the approximate cell centers. Next, the approximate cell centers form trajectories when the segmented cells overlap each other in the temporal direction. Finally, these firstly formed trajectories are connected by computing a tangent allowing us to estimate the direction of movement of the cells. The results of trajectories obtained from the proposed cell tracking method are presented visually and quantitatively.

On a numerical shape optimization approach to the exterior Bernoulli problem via the coupled complex boundary method
###### Julius Fergy Rabago
Institute of Science and Engineering, Kanazawa University

Abstract:

We propose a shape optimization formulation of the exterior Bernoulli problem using the the so-called coupled complex boundary method.

The idea of this approach is to transform the overdetermined problem to a complex boundary value problem with a complex Robin boundary condition coupling the Dirichlet and Neumann boundary conditions on the free boundary. Then, we optimize the cost function constructed by the imaginary part of the solution in the whole domain in order to identify the free boundary. To numerically solve the minimization problem, we compute the shape gradient of the cost functional and apply iterative algorithm based on a Sobolev gradient scheme via finite element method. We illustrate the feasibility of the method through several numerical examples, both in two and three spatial dimensions.

Analysis of the well-conditioned method of fundamental solutions for the Laplace equation
###### Koya Sakakibara
Okayama University of Science

Abstract:

The method of total solution (MFS for short) is a mesh-free numerical solution method for potential problems, and under certain conditions, the error decays exponentially for the number of approximation points. On the other hand, the condition number of the coefficient matrix of the collocation equation increases exponentially, and efforts have been made to overcome this ill-conditioning. In this talk, we consider the MFS-QR method proposed by Antunes (2018), which uses QR decomposition to replace the basis functions and prove that the error decays exponentially despite the condition number being O(1).

Numerically Efficient Optimization of Kinetic Parameters of the VR-1 Experimental Nuclear Reactor
###### Pavel Strachota, Sebastian Nývlt, Jan Rataj, Aleš Wodecki
FNSPE CTU in Prague, FNSPE CTU in Prague, Department of Nuclear Reactors

Abstract: We present a work in progress 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 in small-scale reactors where the spatial distribution of fuel and other components in the reactor core can be neglected. We solve the ODE-constrained minimization problem to determinine 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 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. The results of both approaches in terms of accuracy, robustness and computational costs are compared.

Lattice on fire -- Lattice Boltzmann Method for non-isothermal reactive flows
###### Robert Straka
AGH University of Science and Fiction

Abstract:

A Lattice Boltzmann Method (LBM) is able to - more or less - efficiently solve Navier-Stokes equations (NSE) together with Advection-Diffusion-Reaction equations (ADRE) for passive scalars. Simplified models of combustion could be easily solved by the LBM, especially when one could neglect radiation, temperature dependence of material properties, and other stuff related to non-ideal gases. Such idealized models of the combustion are good starting point & playground, that could be followed by further refinement and enhancement towards more complex and accurate ones. The application of the LBM in problems related to combustion will be presented, the premixed combustion of a propane-air mixture and the combustion of a solid fuel.

Formulation of reaction terms for reactive transport problems
###### Jan Šembera
Technical University of Liberec

Abstract: In reaction problem modelling appear many difficulties. One of them is even its correct mathematical formulation. Some remarks and a derivation of one specific example problem mathematical formulation will be presented.

Construction of Fermat-Torricelli points by means of semi-definite optimization methods
###### Daniel Ševčovič
Comenius University Bratislava

Abstract:

In this talk we construct Fermat-Torricelli points by means of semi-definite optimization techniques and methods. Fermat-Torricelli point is a minimizer of distances from a given set of points in the Euclidean space. We show how the Fermat-Torricelli point can be constructed by means of semi-definition programming technique. Various examples will be presented in this talk.

Quantitative cardio MR examination and new imaging options
###### Jaroslav Tintěra, Dana Kautznerová
IKEM Prague, ZRIR, IKEM, Praha

Abstract:

The issue of quantitative cardio MR examinations is discussed within the currently used methods. The lecture also serves as an introduction to the mapping of relaxation times and the clinical use of a quantitative approach to MR images. There are also some new techniques that increase the effectiveness of examinations, especially for severe patients.

Renyi Entropy Derived Distribution for Returns of Financial Assets
###### Quang Van Tran
FNSPE CTU in Prague

Abstract:

We derive a new distribution using Renyi entropy principle with maximum entropy method under the absolute moment constraints. The new distribution has four parameters: two shape parameters and the remaining two are location and scale parameters. The density of this distribution is smooth and twice differentiable which allows its parameters to be estimated by maximum likelihood estimation method. This distribution can capture the heavy tail property of returns of financial assets and we use it to model returns of various financial assets and compare its ability to model this property with other heavy tail distributions often used for this purpose.