In the first part of the talk, a brief overview of the development of nonoverlapping domain decomposition methods will be given. The focus will be on the iterative substructuring methods using primal unknowns. The Balancing Domain Decomposition based on Constraints (BDDC) by C. Dohrmann will be used for describing these concepts. Next, two extensions of the original BDDC method will be discussed. The first is an adaptive generation of the coarse space to enhance its robustness, e.g. for finite element problems with variable coefficients. The second is an extension of the method to multiple levels, an approach to improving scalability of the method for parallel computations. Our open-source implementation of this Adaptive Multilevel BDDC method, the BDDCML library, will be presented.
In the second part of the talk, we will discuss combination of this solver with the finite element method using an adaptive mesh refinement (AMR). AMR is challenging in the context of distributed memory parallel FEM in general. The treatment of hanging nodes will be also described. Of particular interest is the effect of disconnected subdomains, a typical output of the employed mesh partitioning based on space-filling curves.
The talk will be concluded with numerical results for benchmark Poisson and linear elasticity problems.

The present talk will focus on rotating disk dynamics by introducing a novel signal-processing method geared towards capturing the dynamics of such systems. The method exploits multiple sensors and is thus capable of handling spatially complex transient dynamics. Rotating disks identification methods rely on special features of rotating elements, e.g. cyclic-symmetry, gyroscopic effects, directional whirling and circumferentially traveling deformations, all have a physical meaning and are exploited in the proposed approach.
The ‘eyes’ of ‘Smart Rotating Machines’ are the sensors and the accompanied, real-time signal processing methods play the role of a ‘brain’ in the assessment of measured data. Indeed ‘smart’ also means combining advanced sensing capabilities with an electronic brain which is aware of the underlying physics laws to which the model obeys. At the moment, it seems that the pendulum leans heavily towards numerical modeling. Finite Element models are the basis for analysis and design, while testing and measurements provide only limited verification means for some of the model parameters due to poor deployment and simplistic signal processing procedures. The new method narrows the gap between models and experiment and it illustrates what can be gained when they are added.
The presentation will highlight the advantages of model-based signal processing over past and presently used methods and will try to point to a path leading from older methods and techniques towards present, state-of-the-art methods and further into the future where smart machines will have ‘eyes’ and ‘brains’.
Specifically, the presentation will describe spatial, temporal and directional decomposition of rotating machine vibrations during rapid rotational accelerations. Real time signal processing methods that exploit Hilbert transform based decompositions; directional order-tracking and time-frequency maps will be demonstrated via simulations and experiments. The spatial and temporal decomposition method enables a Smart-Machine to assess true stress and strain on parts rotating relative to an array of sensors and thus help to enhance safety.
One additional topic will be briefly shown if time allows: active detection of imbalance for high-speed modes, using slow rotation data.

We discuss the thermodynamically consistent modeling of semiconductor devices from the mathematical point of view. The task lies in coupling of several physical effects that occur on different temporal or spatial scales, namely optics via the Maxwell equations, charge transport
via drift-diffusion models and quantum mechanical processes in embedded quantum dots, wires or layers.
Using the framework of GENERIC, which is an acronym for General Equations for Non-Equilibrium Reversible Irreversible Coupling, we construct suitable hybrid models that are thermodynamically consistent in the sense that for the isolated system we have energy conservation and positive entropy production. The conservative dynamics is driven by a Hamiltonian structure involving the energy, whereas the dissipative dynamics is driven by an entropic gradient system.

Jedním z často diskutovaných témat současnosti je charakter a příčiny oteplování podnebí pozorované v posledních 100–150 letech a předpověď jeho budoucího vývoje. Odpovědi na tyto otázky se hledají zejména pomocí klimatických a meteorologických modelů vycházejících ze současného (nedokonalého) stavu poznání procesů v atmosféře, hydrosféře i litosféře. Ke kalibraci modelů se vedle observatorních dat používají i proxy data o historii klimatu v delších časových obdobích. Jednou z paleoklimatických metod poskytujících proxy data je rekonstrukce historie povrchové teploty z křivek vyjadřujících chod teploty s hloubkou. Přednáška se zaměří na principy a výsledky této metody.

Fokker–Planck equation is one of the most important tools for investigation of dynamic systems under random excitation. Finite Element Method represents very effective solution possibility particularly when transition processes are investigated or more detailed solution is needed. However, a number of specific problems must be overcome. They follow predominantly from the large multi-dimensionality of the Fokker–Planck equation, shape of the definition domain and usual requirements on the nature of the solution which are out of a conventional practice of the Finite Element employment. Unlike earlier studies it is coming to light that multi-dimensional simplex elements are the most suitable to be deployed. Moreover, new original algorithms for the multi-dimensional mesh generating were developed as well as original procedure of the governing differential and algebraic systems assembling and subsequent analysis. Finally, an illustrative example is presented together with aspects typical for the problem with large multi-dimensionality.

Damage is a phenomenon/concept in continuum mechanics of solid materials undergoing various degradation processes with numerous applications in engineering and in computational mechanics and (geo)physics. Combination with inertial effects may be important modelling issue to prevent various undesired effects otherwise occuring in quasistatic models. Various damage models and their variants as a phase-field fracture will be overviewed. Also, several numerical approaches will be presented, amenable to compute vibrations or waves emitted during fast damage/fracture, together with various extensions of the basic scenario, combining mass or heat transfer, or plasticity.