Student workshop on scientific computing

June 12-15, 2014
Department of Mathematics, FNSPE CTU in Prague
Děčín, Czech Republic

Mixed-Hybrid Finite Element Method for Modeling Two-phase Compositional Flow in Unsaturated Porous Media

Jakub Solovský


Abstract:This work deals with solving problems of two phase flow and two phase compositional flow. We describe method for solving this type of problems, based on mixed-hybrid finite element method. The method is tested on one-dimensional problems and results are compared to exact solutions. Numerical experiments showed that solutions converge and the order of convergence is slightly smaller than one. The method is also used for solving problems of compositional flow and a single system and a sequential solver are compared. There is no significant difference between these solutions and the sequential solver is more efficient.

Mathematical modeling of spherical phase interfaces using density gradient theory and capillary waves

Barbora Planková


Abstract:Nucleation is a process of nano-droplet formation occurring in nature and industrial processes. This phenomena can be described by modeling spherical phase interfaces. Easiest way is to use the classical nucleation theory, however, its drawback is an assumption of the same surface tension as for the macroscopic interface. More sophisticated method, density gradient theory, describes it better; however, the
precision is still not satisfactory. We tried to include another model cof capillary waves which accounts of the thermal motion of molecules resulting in interface-undulation.

Modeling of Structural Behavior of Saturated Soil Induced by Freezing

Alexandr Žák


Abstract:This contribution deals with two scale approaches to the modeling of mechanical manifestation of saturated soils during their freezing and thawing.

The first approach involves a macro-scale description of the problem. It comprises the modified heat equation involving the phase transition of the water content and the system of the Navier equations describing deformations of the body. Computational studies of the model for the control of the structural conditions within the mechanical heterogeneous soil are shown.

The second approach represents a micro-scale description of the problem. The micro-scale model of the mutual thermo-mechanical interaction between soil grains and pore water during its phase transition is presented. The latest simulations of the micro-scale freezing dynamics are shown.

Anisotropic Surface Diffusion in Relative Geometry

Hung Hoang Dieu


Abstract:In this contribution, we deal with the anisotropic surface diffusion in the context of the heteroepitaxial growth. In order to incorporate the anisotropy into the model, we replace the isotropic Euclidean norm by another norm (known as the Finsler metric) exhibiting the desired anisotropy. Treating  in the motion law as a graph, we obtain a nonlinear parabolic PDE which is solved by the numerical scheme based on the method of lines where the spatial derivatives are approximated by finite differences. Finally, we show computational results with various anisotropy settings.

Interval Arithmetics for Global Optimization

Jakub Jánský


Abstract:After short remembering of basic principles of interval calculations, the presentation will be oriented to various methods of interval global optimization. The talk will be about branch and bound methods: Box Consistency, Min-Max, Gradient, and Newton Update Upper Bound ones. Two of them are traditional ones but the rest methods are original ones. All methods will be demonstrated and compared on various multimodal smooth functions in 2D. Methodological aspects of interval optimization in higher dimensions will be also discussed.

Introduction to the hardware and software architecture of the Hyperion cluster at FNSPE CTU Prague

Vít Hanousek


Abstract:Recently, a new high performance system has been installed at the Faculty of Nuclear Sciences and Physical Engineering, CTU Prague. Our team is currently finalizing the configuration of its software environment and the new system will shortly be made available for scientific computations. In this contribution, we reveal its hardware specifications and explain the function and configuration of some components of the software framework. We focus mainly on the interoperability of the MPI library, the resource manager, and the distributed parallel filesystem.

Numerical Simulation of Gas Flow and NAPL Vapor Transport in Soil

Ondřej Pártl


Abstract:Our research is focused on simulation of gas flow and NAPL vapor transport driven by gas flow in soil. In this contribution, our numerical results will be compared with experimental data, and some results of the simulations of the NAPL vapor transport in heterogeneous soil will be presented.
Moreover, we test a simple method of coupling incompressible free flow with porous media flow and we will present some results of the simulations based on this method.

MRI data segmentation using Allen-Cahn equation

Radek Máca


Abstract:The contribution presents a 3D (2D+time) segmentation of the real cardiac MRI data using the Allen-Cahn equation and its semi-implicit complementary volume discretization. In particular, the application is focused on the segmentation of the heart ventricles from the cine MRI data.

Multigrid method for linear complenetarity problem on GPU

Vladimír Klement


Abstract:This contribution presents the CUDA implementation of the parallel multigrid solver for the linear complenetarity problem. As a smoother, the Projected SOR method is used. The final algorithm efficiency is demonstrated on the constrained level-set method used in image segmentation. For this task the speed-up up to 3 was achieved on Nvidia GeForce GTX 480 compared to 12 core AMD Opteron.

Computational Analysis of the Conserved Mean-Curvature Flow for Open and Closed Curves in the Plane

Miroslav Kolář


Abstract:We present results of numerical solution of the evolution law for the constrained mean-curvature flow. This law originates in the theory of phase transitions for crystalline materials and describes the evolution of closed embedded curves with constant enclosed area. It can be shown that the enclosed area is preserved for open curves with ?fixed endpoints as well. The evolution law is reformulated by means of the direct method into the system of degenerate parabolic partial differential equations for the curve parametrization. This system is spatially discretized by means of the flowing finite volumes method and solved numerically by the explicit Runge-Kutta solver. We discuss the role of the tangential redistribution. Several qualitative and quantitative computational studies are presented as well.

Compositional Simulation of Two-Phase Flow in Porous Media Using VT-Flash

Ondřej Polívka


Abstract:We deal with the numerical simulation of compressible two-phase flow of a mixture composed of several components in porous media with species transfer between the phases. The mathematical model is formulated by means of the extended Darcy's laws for all phases, components continuity equations, constitutive relations, and appropriate initial and boundary conditions. The splitting of components among the phases is described using a formulation of the local thermodynamic equilibrium which uses volume, temperature, and moles as specification variables.

GPU implementation of the finite element method

Vítězslav Žabka


Abstract:Numerical approximation of partial differential equations by means of the finite element method leads to a system of linear equations. In case of some nonlinear evolution problems and implicit time-stepping schemes, the system matrix depends on time. During the numerical solution of such problems, the system matrix has to be updated after each time step. When implementing the solver on the GPU, special attention has to be paid to the matrix update because it can significantly affect performance of the implementation. This contribution deals with the process of assembling the system matrix by the finite element method on the GPU using an unstructured computational mesh. We present a general CUDA implementation of the finite element matrix assembly relying on a coloring of the mesh.