Would you like to have an academic career after finishing your master studies? Here you have an opportunity to enrol for *Computational Sciences* Doctoral Study Program focused on HPC. It is designated mainly for *Computational Sciences* Master Study Program graduates but also for graduates of related fields of study: mathematics, computer sciences, mechanical engineering, physics, or chemistry.

Within the study program you will be involved in solving both national and international projects IT4Innovations participates in. In the process of projects solving, studies, and realization of your doctoral diploma thesis you will have access not only to IT4Innovations National Supercomputing Center supercomputers but also to computational resources of other supercomputer centres participating, along with IT4Innovations, in PRACE European HPC infrastructure. You will gain rich practical experience in the exploitation of high performance computing in the Czech Republic as well as in the EU and with the making of related effective applications.

„I believe that the opportunity to use the supercomputers at the IT4Innovations National Supercomputing Center had an essential effect on my being awarded Fourier Prize. Anselm has not been in operation for a long time, yet I can hardly imagine my research work without exploitation of supercomputing resources at the IT4Innovations center.”

Michal Merta

Doctoral student

Researcher at IT4Innovations

- doc. RNDr. Jiří Bouchala, Ph.D.
- prof. Ing. Radim Briš, CSc.
- prof. RNDr. Zdeněk Dostál, DSc.
- doc. Ing. Sylva Drábková, Ph.D.
- doc. Mgr. Jiří Dvorský, Ph.D.
- doc. Ing. Radim Halama, Ph.D.
- prof. Ing. Petr Horyl, CSc., dr.h.c.
- prof. RNDr. Petr Jančar, CSc.
- Mgr. Branislav Jansík Ph. D.
- doc. RNDr. René Kalus, Ph.D.
- doc. Mgr. Petr Kovář, Ph.D.

- prof. Ing. Tomáš Kozubek, Ph.D.
- prof. RNDr. Milada Kozubková, CSc.
- prof. Ing. Jaromír Pištora, CSc.
- prof. Ing. Jana Seidlerová, CSc.
- prof. RNDr. Václav Snášel, CSc.
- doc. Dr. Ing. Eduard Sojka
- Ing. Jonáš Tokarský, Ph.D.
- prof. Ing. Ivo Vondrák, CSc.
- doc. Mgr. Vít Vondrák, Ph. D.
- prof. Ing. Ivan Zelinka, Ph.D.

- English – Mgr. Andrea Wlochová, Ph.D.
- German – PhDr. Šárka Sladovníková, Ph.D.
- Russian – Mgr. Václav Kubečka
- French – Mgr. Dagmar Klanicová
- Spanish – Mgr. Ivana Vašková, MBA

**Selected Language of Instruction**: English, German, Russian, Spanish, or French

Acceleration of the iterative process in Hybrid Total FETI method

The goal of the thesis is an acceleration of the iterative process in Hybrid Total FETI algorithm.

- Analysis, development, and implementation of preconditioners (variants of Dirichlet preconditioners) with suitable scaling techniques.
- Corrections of orthogonal basis built within iterative process.
- Analysis and implementation of suitable block Krylov subspace method to reduce global communication.

Real-time Large Scale Visualizations

The main goal of this work would be development and implementation of real-time in-situ visualization techniques for massively parallel sparse solvers developed at IT4Innovations. These solvers are able to solve billions of unknowns using hundreds of compute nodes. Visualization at this scale brings new challenges which will be addressed by this work using software defined visualization techniques. Part of the work will be development of visualization plugin for IT4Innovations in-house solver libraries.

Mixed Precision Solvers for Sparse Systems of Linear Equations

The main goal of this work will be research in area of mixed precision solvers for sparse systems of linear equations. Part of the work would also be an efficient implementation of developed methods for modern HPC architectures. New methods will be implemented into parallel solver libraries developed at IT4Innovations.

Highly parallel solvers for contact problems with friction

The project focuses on implementation of scalable algorithms for solution of large scale dynamic contact problems with friction. These problems lead after discretization to quadratic programming problems with convex constraints whose development based on the domain decomposition methods has long term tradition at IT4I, especially TFETI (Total Finite Element Tearing and Interconnecting) and its Hybrid version HTFETI. Performance optimization for future exascale supercomputers based on advanced computing and programming techniques and novel many-core accelerators will be developed and implemented to enable solutions of contact problems with billions of unknowns. The work is supported by the project H2020-MSCA-ITN EXPERTISE.

Optimization and highly parallel implementation of domain decomposition based solvers for water – turbines simulations

The project focuses on the development, implementation, and optimization of the highly parallel solvers of contact problems for large-scale water – turbines simulations, so that these solvers are able to fully utilize modern HPC architectures. The idea is based on the combination of the FETI type domain decomposition methods developed by the IT4I team and efficient algorithms employing active set strategy (MPRG, SMALSE, semismooth Newton method) and using all three parallelization techniques: MPI + OpenMP + vectorization to reduce the communication and to preserve the efficiency with increasing problem size. These solvers will be used for such problems as the simulation of the water – turbine bearing/shaft system, topological and parameter optimization of chosen water – turbine components or lifetime and limit states computation for stressed parts of water – turbines. The work is supported by the project H2020-MSCA-ITN EXPERTISE.

Optimization of selected logistics processes

Within the dissertation, the student will be involved in solving optimization problems in logistics focused on the problems requiring HPC for their solution either on the level of accelerators and per-node basis or multiple-node basis. The objective of this thesis will be the overview of state-of-the-art algorithms and subsequent design of the implementation of these algorithms using HPC technologies.

Geospatial data storage and processing on the HPC infrastructure

Processing of large spatial data presents the current topic in the field of HPC, namely in the area of processing Earth observation data. Within the dissertation, the state-of-the-art methods for processing and storing spatiotemporal data will be developed and tested. The emphasis will be placed on efficient use of HPC in geospatial analyses.

Detection methods of dynamic properties of mechanical systems

There are many phenomena in engineering showing periodic, quasi periodic or irregular, chaotic patterns. The main aim is to research those phenomena on suitable systems using standard and new analytical and simulation methods.

Discrete dynamic systems on the lattice

The study of discrete dynamic systems created on the lattice type space have a big potential, namely in connections with the cellular automata. The main aim is to research dynamic properties of systems generated by coupled lattice maps given by classical and new models; the study will be supported by massive simulations.

Quantitative characteristic of the solution of difference equations

The theory of difference equations is used for the modeling through the scientific fields. Relevant models, or solutions of suitable difference equations are showing stable and unstable behaviors. The main aim of the thesis is to study analytical and simulation tools that quantify dynamical properties of difference equations.

Monte Carlo simulations at quantum chemistry accuracy

The main focus of the work will be on the development, testings, and pilot applications of software solutions for linking codes for Monte Carlo simulations with quantum chemistry libraries. Pilot calculations will be performed on selected subnano- and nanoscopic complexes. The work will be done in cooperation with Instituto de Física Fundamental – Consejo Superior de Invetsigationes Científicas, Madrid, Spain.

Formation of molecular ions in cold rare-gas plasmas

Implementation of numerical models as well as their use in dynamical calculations of elementary collisions between ionic rare-gas clusters with rare-gas atoms. The main goal consists in detailed understanding of recombination processes and in providing a microscopic base for subsequent macroscopic modelings of cold rare-gas plasmas, plasma generators optimization, and their possible use in biomedical practice. The work will be done in cooperation with Université Paul Sabatier, Toulouse, France.

Modelling of transport properties of molecular ions of helium in air

The thesis focuses on microscopic modeling of collision processes of helium ions with nitrogen (and oxygen) molecules to be used in plasma generators optimization for biomedical applications.

Modelling of transport properties of molecular ions of argon in air

The thesis focuses on microscopic modeling of collision processes of argon ions with nitrogen (and oxygen) molecules to be used in plasma generators optimization for biomedical applications.

Algorithms of numerical linear algebra for new parallel architectures

Optimization of basic algorithms of numerical linear algebra is currently very essential task to speedup solution process of very complex numerical models. Increasing number of computational clusters allow massive parallel implementation of these algorithms. In addition, many of these algorithms are known by their excellent parallel scalability. One of fundamental changes in accelerating of these computations on parallel computers is the use of accelerators like MIC or GPU units on each node of computational cluster. However, this needs review of current algorithms and optimization of current codes for use on such systems to sustain or improve the scalability of original algorithms.

HPC modelling in environmental sciences

Application of numerical methods for modelling in hydrology, geology or numerical tools for modelling of air pollution shows to be essential part of environmental sciences. However, these numerical models exceed possibilities of standard computers due to their computational complexity. In addition, uncertainties in model parameters make these models even more complex. Therefore the use of high performance computing facilities like computational clusters shows to be unavoidable. Unfortunately very often, standard algorithms are not able effectively exploit such the computing resources. Therefore it is necessary to adapt these algorithms for such the computing environment or develop brand new ones, which will be able to solve these very complex problems efficiently.

Parallel solution of inverse problems

The main goal of inverse problems, which appear very often within the solution of physical problems, is the identification of parameters and input data of the mathematical model describing given physical problem. As an example we can use identification of sources of air or water pollution, hydrological parameters of for flood modelling or shape, material and topological optimization problems in engineering. All mentioned inverse problems typically solve many problems similar to original one that differ only in perturbed parameters and input data. This implies extreme requirements for computational resources, which could be effectively utilized only parallelizing the solution process and applying effective solution methods.

**prof. RNDr. Zdeněk Dostál, DSc.**,**doc. Ing. Radim Halama, Ph.D.**,**prof. Ing. Petr Horyl, CSc., dr.h.c.**,**Mgr. Branislav Jansík, Ph.D.**,**doc. RNDr. René Kalus, Ph.D.**,**prof. Ing. Tomáš Kozubek, Ph.D.**,**prof. Ing. Jaromír Pištora, CSc.**,**prof. RNDr. Václav Snášel, CSc.**,**prof. Ing. Ivo Vondrák, CSc.**,**doc. Mgr. Vít Vondrák, Ph.D.**

**prof. RNDr. Radim Blaheta, CSc.**, Ústav geoniky AV ČR Ostrava,**doc. Ing. Marek Brandner, Ph.D.**, Západočeská univerzita v Plzni,**prof. RNDr. Petr Čárský, DrSc.**, Ústav fyzikální chemie J. Heyrovského AV ČR,**prof. Ing. Jaroslav Kruis, Ph.D.**, České vysoké učení technické v Praze,**prof. RNDr. Ivo Nezbeda, DrSc.**, Ústav chemických procesů AV ČR a Univerzita JEP v Ústí nad Labem,**prof. RNDr. Jozef Noga, DrSc.**, Ústav anorganickej chémie SAV, Prírodovedecká fakulta Univerzity Komenského, Bratislava,**prof. Ing. Pavel Tvrdík, CSc.**, České vysoké učení technické v Praze

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