Mathematical Modeling and Methods for High Performance Computing ****************************************************************************************** * ****************************************************************************************** # Mathematic, mathematical modeling, mathematical methods, mathematical models, mathematic numerical method, # Computing systems, nonlinear partial differential equations, PDEs, computational mathema # Numerical solving, numerical solution, numerical stability, numerical simulation # Calculus of variations, calculation # Matrix # High performance computing ****************************************************************************************** * Offer ****************************************************************************************** - Expert analysis of interdisciplinary problems in physics, mathematics and high-performan - Application of mathematical modeling in physics with particular focus to area of continu - Expert knowledge of mathematical analysis for problems in continuum physics and related - Expertise in theory of numerical methods and their application in modern HPC environment - Contact with wide network of local and international experts (EU-MATHS-IN, Nečas Center Modeling) - Development of models for complex materials from the basic principles to an efficient nu - Consultancy services in the field of mathematical modeling, analysis, numerical software ****************************************************************************************** * Expertise ****************************************************************************************** - Development of models for complex physical processes with analysis and numerical simulat - Mathematical modeling of mechanical, thermal and chemical processes in continuum mechani thermodynamics - Non-linear partial differential equations (PDEs) stemming from solid and fluid mechanics relevant problems - Modeling of flow problems in biomechanics for patient specific data - Models and numerical methods for industrial problems in glass melting, geomaterials, sha and electrochemical devices (fuel cells, batteries) - Analysis of computational methods, numerical stability and scalability - Computational mathematics related to numerical solving of challenging problems ****************************************************************************************** * Research Areas and Excellence ****************************************************************************************** Mathematical modeling aims to describe and study various phenomena using the language of m represents an indispensable tool in natural sciences, engineering, life and also social sc The uniqueness of the research consists in the fact that it is able to cover – at a very h level – all aspects of the mathematical modelling workflow, in particular development of m models, mathematical analysis of their properties, development of suitable numerical methods and their implementations optimally exploiting t computational power of current and near future high performance computing systems. Research and tutoring of young scientific generation in the given field is at Charles Univ subject of the group. ****************************************************************************************** * Main Recent Projects ****************************************************************************************** - Charles University UNCE (University Centre of Excellence) project: University Center Mat 2017) and its successor (2018–2023) titled University Center for Mathematical Modeling, Ap and Computational Mathematics: PI Josef Málek, other senior advisors Miroslav Bulíček, Ond Dolejší, Josef Ďurech, Jaroslav Hron, Luboš Pick, Vít Průša, Zdeněk Strakoš, Miroslav Tůma - ERC-CZ project MORE : PI Josef Málek, senior members of the team Endre Süli, Eduard Feir Strakoš, Martin Vohralík; Charles University, Prague, 2012–2017; see http://more.karlin.mf "http://more.karlin.mff.cuni.cz"] The collaborating members hold two ERC projects: - ERC AdG project MATHEF: PI Eduard Feireisl; Institute of Mathematics, Academy of Science Republic, 2013–2018 - ERC CoG project GATIPOR: PI Martin Vohralík, external collaborator Zdeněk Strakoš; INRIA France, 2015–2019 ****************************************************************************************** * Partnership and Collaboration ****************************************************************************************** *========================================================================================= * Academic Partners *========================================================================================= The group closely collaborates with leading researchers from institutions all over the wor - University of Oxford, - INRIA Paris - University of Heidelberg - TU Berlin - University of Washington at Seattle - Texas A&M University - University of Warsaw *========================================================================================= * Industry Partners *========================================================================================= The group has several ongoing partnerships and collaborations in applied areas, e.g.: - Glass Service – modeling and simulating float glass process - Masaryk Hospital Ústí nad Labem – investigation and numerical simulation of aneurysma - RS Dynamics – electrical impedance tomography of soft tissues - Preciosa – Image processing in quality analysis of jewelry stones - SHM Šumperk – Thermodynamic analysis of high pressure physics. Simulation of motion of c ****************************************************************************************** * Are you interested in this expertise? ****************************************************************************************** Please contact CPPT UK Web: www.cppt.cuni.cz/ [ URL "https://cppt.cuni.cz/"] Mail: transfer@cuni.cz Phone: +420 224 491 255 ****************************************************************************************** * Experts and their department ****************************************************************************************** Prof. RNDr. Josef Málek, Csc., DSc., Prof. Ing. Zdeněk Strakoš, DrSc. Mathematical Institute and Department of Numerical Mathematics Web: http://ncmm.karlin.mff.cuni.cz [ URL "http://ncmm.karlin.mff.cuni.cz"] ****************************************************************************************** * Klíčová slova ****************************************************************************************** # Matematika, matematické výpočty, matematické modelování # Nelineární parciální diferenciální rovnice, numerika, numerické problémy # Parciální, parciální diferenciální rovnice, řešení parciálních diferenciálních rovnic # Numerická simulace, numerická stabilita, numerické řešení, numerické metody, implementac metod # Matematické modely, matematická analýza # PDR