2025-12-27
00:12 |
Parallel implementation of immersed boundary adaptive FEM or how to avoid mesh generation in a mesh-based method
Šístek, Jakub
Finite element method (FEM) typically relies on computational meshes composed of elements forming a nonoverlapping partition of the computational domain. However, generating these meshes of suffcient quality can be challenging and time-consuming, especially for very complex geometries used, e.g. in 3D printing. As a potential remedy, ideas of the immersed boundary method have been incorporated into FEM. We present a parallel implementation of an immersed boundary adaptive FEM. In order to achieve suffcient resolution at the boundary, local mesh re nement driven towards boundary is used. For large meshes distributed over a large number of processors, the resulting systems have to be solved by parallel iterative solvers. We present the method and demonstrate its performance for a complex problem of linear elasticity with meshes re ned adaptively towards the area with the largest stress for achieving better accuracy within these regions.
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2025-12-27
00:12 |
Adaptive mesh refinement and a posteriori error estimates
Vejchodský, Tomáš
This short contribution is intended mainly for mathematicians who are not specialists in numerical analysis but would like to understand better the fundamental features of the nite element method. First, we review the nite element method for linear elliptic partial differential equations of second order. Then we concentrate on the main ideas of a priori and a posteriori error estimates, convergence and adaptive mesh re nement. We especially emphasize the pioneering convergence result of Professor Miloš Zlámal and present some modern results from the theory of the nite element method. We use several numerical examples to illustrate the presented results.
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2025-12-27
00:12 |
Professor Miloš Zlámal - his life and work
Křížek, Michal
A brief biography of Professor Miloš Zlámal is presented. Then we focus on the mathematical problems he dealt with. In the rst period there were various properties of analytical solutions of ordinary and partial differential equations. His main results are in the theory of the nite element method as the minimum angle condition guaranteeing convergence, curved nite elements, uperconvergence, the so-called mortar nite elements and semiconductor equations.
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2025-12-27
00:12 |
Profesor Miloš Zlámal - život a dílo
Franců, J. ; Křížek, Michal
Je podán stručný životopis a přehled nejdůležitějších matematických výsledků prof. Miloše Zlámala, našeho předního českého numerického matematika. V roce 1968 Zlámal publikoval v Numerische Mathematik stěžejní článek, v němž dokázal konvergenci numerické metody konečných prvků pro řešení parciálních diferenciálních rovnic.
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2025-12-16
16:40 |
Programs and Algorithms of Numerical Mathematics 22 : Hejnice, June 23-28, 2024 : Proceedings of Seminar
Chleboun, J. ; Papež, Jan ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
These proceedings comprise peer-reviewed papers based on the invited lectures, short communications, and poster presentations from the 22nd seminar Programs and Algorithms of Numerical Mathematics (PANM), held at Hejnice Monastery, Czech Republic, from June 23 to 28, 2024.\nThe seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EU-MATHS-IN.CZ, the Czech Network for Mathematics in Industry, with nancial support from the RSJ Foundation. Continuing the tradition of its predecessors, PANM 2024 followed a long-standing series of biennial (with one exception) seminars on mathematical software and numerical methods, held in various locations|including Alšovice, Bratříkov, Janov nad Nisou, Kořenov, Lázně Libverda, Dolní Maxov, Prague, Hejnice, and Jablonec nad Nisou - since its inception in 1983. The primary objective of these seminars is to provide a platform for discussing advanced topics in numerical analysis, the implementation of numerical algorithms, novel approaches to mathematical modelling, and computational methods for both single- and multi-processor applications.
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2025-07-05
00:00 |
Simplified mathematical models of fluid-structure-acoustic interaction problem motivated by human phonation process
Valášek, Jan ; Sváček, P.
Human phonation process represents an interesting and complex problem of fluid-structure-acoustic interaction, where the deformation of the vocal folds (elastic body) are interplaying with the fluid flow (air stream) and the acoustics. Due to its high complexity, two simplified mathematical models are described - the fluid-structure interaction (FSI) problem describing the self-induced vibrations of the vocal folds, and the fluid-structure-acoustic interaction (FSAI) problem, which also involves aeroacoustic phenomena. The FSI model is based on the incompressible Navier-Stokes equations in the ALE formulation coupled with the linear elasticity model. Both the fluid and structural models are approximated using finite element methods, and the influence of different inlet boundary conditions is discussed in detail. For the FSAI model, an aeroacoustic hybrid approach is used, incorporating the Lighthill analogy or the perturbed convective wave equation. The acoustic results strongly depend on the proper choice of the computational acoustic domain (i.e. vocal tract model). Further, the spatial and frequency distributions of sound sources computed from the FSI solution are compared for both used approaches. The final frequency spectra of acoustic pressure at the mouth position are also analyzed for both approaches.
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2025-07-05
00:00 |
On fluid structure interaction problems of the heated cylinder approximated by the finite element method
Vacek, Karel ; Sváček, P.
This study addresses the problem of the flow around circular cylinders with mixed convection. The focus is on suppressing the vortex-induced vibration (VIV) of the cylinder through heating. The problem is mathematically described using the arbitrary Lagrangian-Eulerian (ALE) method and Boussinesq approximation for simulating fluid flow and heat transfer. The fluid flow is modeled via incompressible Navier-Stokes equations in the ALE formulation with source term, which represent the density variation due to the change of temperature. The temperature is driven by the additional governing transport equation. The equations are numerically discretized by the finite element method (FEM), where for the velocity-pressure couple the Taylor-Hood (TH) finite element is used and the temperature is approximated by the quadratic elements. The proposed solver is tested on benchmark problems.
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2025-07-05
00:00 |
Spherical RBF interpolation employing particular geodesic metrics and trend functions
Segeth, Karel
The paper is concerned with spherical radial basis function (SRBF) interpolation. We introduce particular SRBF interpolants employing several different geodesic metrics and a single trend function. Interpolation on a sphere is an important tool serving to processing data measured on the Earth's surface by satellites. Nevertheless, our model physical quantity is the magnetic susceptibility of rock measured in different directions. We construct a general SRBF formula and prove conditions sufficient for its existence. Particular formulae with specified geodesic metrics, trend and SRBFs are then constructed and tested on a series of magnetic susceptibility examples. The results show that this interpolation is sufficiently robust in general.
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2025-07-05
00:00 |
Performance of parallel QR factorization methods on the NVIDIA Grace CPU Superchip
Břichňáč, V. ; Šístek, Jakub
This article studies several algorithms for QR factorization based on hierarchical Householder reflectors organized into elimination trees, which are particularly suited for tall-and-skinny matrices and allow parallelization. We examine the effect of various parameters on the performance of the tree-based algorithms. The work is accompanied with a custom implementation that utilizes a task-based runtime system (OpenMP or StarPU). The same algorithm is implemented in the PLASMA library. The performance evaluation is done on the recent NVIDIA Grace CPU Superchip.
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2025-07-05
00:00 |
Coupled vibroacoustic problem inspired by human phonation
Valášek, Jan ; Hubálek, J.
The contribution deals with the 2D vibro-acoustic model inspired by human phonation. Its aim is to demonstrate the in uence of vocal fold compliance on acoustic resonant frequencies. Vibro-acoustic coupling is highlighted under speci c conditions, particularly when elastic and acoustic frequencies coincide, as seen in phonation into tubes or straws of suitable lengths used in voice therapy. Here, vocal folds vibrations are modelled using linear elasticity theory and acoustics is described by wave equation. Both coupled subproblems are formulated in the frequency domain and numerically approximated by the nite element method. In the end the numerical results of the obtained resonant frequencies and their analysis are presented.
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