2012/4 - Natural Sciences and Technology
Permanent URI for this collection
ACC Journal, ročník XVIII 2012/4
Recenzovali:
Prof. RNDr. Jaromír Antoch, CSs. – Univerzita Karlova v Praze
doc. RNDr. Karel Najzar. CSc. - Univerzita Karlova v Praze
Recenzovali:
Prof. RNDr. Jaromír Antoch, CSs. – Univerzita Karlova v Praze
doc. RNDr. Karel Najzar. CSc. - Univerzita Karlova v Praze
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Browsing 2012/4 - Natural Sciences and Technology by Issue Date
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- ItemAdaptive inexact newton methods with a posteriori stopping criteria(Technická univerzita v Liberci, Česká republika, 2012) Ern, Alexandre; Vohralík., Martinspline-wavelet basis and a method for an inexact multiplication of wavelet stiffness matrix with
- ItemApplication of reconstruction operators in the discontinuous galerkin method(Technická univerzita v Liberci, Česká republika, 2012) Kučera, VáclavThis paper gives an overview of the main ingredients needed to incorporate reconstruction op- erators, as known from higher order finite volume (FV) and spectral volume (SV) schemes, into the discontinuous Galerkin (DG) method. Such an operator constructs higher order approxima- tions from the lower order DG scheme, increasing the order of convergence, while leading to a more efficient numerical scheme than the corresponding higher order DG scheme itself. We discuss theoretical, as well as implementational aspects and numerical experiments.
- ItemNumerical evaluation of rheological experiment(Technická univerzita v Liberci, Česká republika, 2012) Salač, Petr; Matoušek, IvoA viscoelastic simply supported rotationally symmetric body, fixed on a base, is considered. The body is loaded by a flat plunger, which moves in the direction of the z axis by a constant velocity v. In this work the reaction force is computed. This allows us to compare numerical results with data from rheological experiment (see [6], [7]). The variational formulation of the problem is derived and transformed to cylindrical coordinates. Some results of numerical calculations are presented.
- ItemMultiwavelets based on hermite cubic splines(Technická univerzita v Liberci, Česká republika, 2012) Černá, Dana; Finěk, Václav; Plačková, Gertathe convection-diffusion equation. We use an implicit scheme for the time discretization and
- ItemHP-discontinuous galerkin method for nonlinear problems(Technická univerzita v Liberci, Česká republika, 2012) Dolejší, Vítan adaptive wavelet-based method for a spatial discretization. We use a well-conditioned cubic
- ItemOn the problem of variability of interval data(Technická univerzita v Liberci, Česká republika, 2012) Finěk, Václav; Matonoha, Ctirada vector which we have recently proposed in [1, 2]. The theoretical advantages of our scheme
- ItemOptimal error estimates for nonstationary singularly perturbed problems for low discretization orders(Technická univerzita v Liberci, Česká republika, 2012) Vlasák, Miloslav; Roos, Hans–GöergWe consider an unsteady 1D singularly perturbed convection–diffusion problem. We discretize such a problem by the linear finite element method (FEM) on a Shishkin mesh and by a discon- tinuous Galerkin method in time. We present optimal a priori error estimates for low order time discretizations.
- ItemOn two flexible methods of 2-dimensional regression analysis(Technická univerzita v Liberci, Česká republika, 2012) Volf, PetrThe paper deals with the problem of non-parametric statistical modeling of 2-dimensional sur- faces from observed data, i.e. the regression analysis. In general, the model is constructed from a set of basal functions, as are the splines, gaussians and others. However, such model- ing means to estimate a large set of parameters (locations of functional units and parameters of their combination). We shall present two approaches allowing reduction of the number of needed parameters. Namely, a well known method of projection pursuit, and the less known method of Gordon surface. Further, we shall analyze possible serious consequences of sparse data to precision of model and uncertainty of prediction. Methods will be illustrated in artificial examples.
- ItemAdaptive wavelet scheme for convection-diffusion equations(Technická univerzita v Liberci, Česká republika, 2012) Černá, Dana; Finěk, VáclavOne of the most important part of adaptive wavelet methods is an efficient approximate multi- plication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time con- suming and its implementation is very difficult. Therefore, it is necessary to develop a well- conditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzero elements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices corresponding to the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number. In this contribution, we shortly review this construction and show several numerical tests.
- ItemAlgorithm for elimination of systems with sparse asymmetric reducible matrices(Technická univerzita v Liberci, Česká republika, 2012) Bittnerová, DanielaV článku je uveden algoritmus určený k nalezení optimálního či skoro optimálníhouspořádání prvků matice, která je řídká, nesymetrická a rozložitelná (reducibilní). Pomocítohoto algoritmu můžeme efektivněji řešit velké řídké soustavy lineárních rovnic. Uvedenýalgoritmus je modifikací známého algoritmu pro symetrické nerozložitelné matice.
- ItemFinite element and boundary element solution of nuclear waste repository thermal dimensioning problem(Technická univerzita v Liberci, Česká republika, 2012) Hokr, Milan; Novák, JosefWe solve the thermal dimensioning problem of the deep geological spent nuclear fuel repository, which means to estimate the maximum temperature in the repository caused by the heat generation of the spent fuel. We use a combination of the boundary element method for the exterior problem of heat discharge to the infinity and finite element method for a near- field thermal problem with a boundary condition expressed by the far-field problem solution. This combination is implemented within the simulation software ANSYS as the “far-field element”. The far-field element solution confirmed to well represent the heat discharge, in comparison with the variant of a standard FEM far-field problem solution and conventional boundary conditions (constant temperature or zero heat flow).
- ItemOn a sparse representation of laplacian(Technická univerzita v Liberci, Česká republika, 2012) Černá, Dana; Finěk, Václav; Ondračková., ZdenaThe paper is concerned with theoretical and computational issues of a numerical resolution of
- ItemIteration-discretization methods for some variational inequality(Technická univerzita v Liberci, Česká republika, 2012) Cegielski, Andrzej; Grossmann, ChristianIterační metody pro řešení variačních nerovností v Hilbertových prostorech nekonečné dimenze vyžadují diskretizaci. To vede k řešení posloupnosti variačních nerovností v prostorech konečné dimenze. Tato práce se věnuje iteračním metodám, které vyžadují pouze konečný počet kroku˚ na každé diskretizační úrovni. Nejprve je studována abstraktní úloha a následně konkrétní úloha optimálního řízení s eliptickou stavovou rovnicí a s omezeními na řídící proměnnou. Diskretizace je provedena pomocí posloupnosti do sebe vnořených po částech lineárních, spojitých, konformních konečných prvku.
- ItemOptimization problems under two-sided (max; min)–linear Inequalities constraints(Technická univerzita v Liberci, Česká republika, 2012) Gad, Mahmoudas well as numerical examples will be presented.
- ItemNumerical solution of reaction-diffusion equations(Technická univerzita v Liberci, Česká republika, 2012) Lamač, JanThe subject of the presented paper is a mathematical analysis and numerical solution of the sys- tem of nonlinear nonstationary reaction-diffusion equations. Firstly, using the invariant region technique, the proof of both the existence and uniqueness of the solution and problem data con- tinuous dependence is carried out. After time discretization of the problem the Galerkin finite elements method is applied and a priori error estimates of the method are derived. A suitable mesh adaptivity is discussed as well. The method is finally implemented and tested on several examples.
- ItemParallel approach to the solution of stationary reaction-diffusion problem(Technická univerzita v Liberci, Česká republika, 2012) Bímová, DanielaČlánek je věnován paralelnímu řešení dvoudimenzionálního stacionárního reakčně-difúzníhoproblému. Pomocí paralelního přístupu k reprezentaci lineární algebry vytvoříme paralelníalgoritmus pro výpočet numerického řešení dvoudimenzionálního stacionárního reakčnědifúzníhoproblému. Porovnáme časy potřebné k výpočtu přibližného řešení systému (lineárních)diferenciálních rovnic pro různě velkou matici soustavy numerickou metodou sdruženýchgradientů na 1, 2, 3 a 4 procesorech.
- ItemNumerical solution of the mew equation by the semi-implicit numerical scheme(Technická univerzita v Liberci, Česká republika, 2012) Hozman, JiříIn this paper we deal with the development of a numerical method for the solution of the mo- dified equal width wave (MEW) equation – a very important equation with a cubic nonlinearity describing a large number of physical phenomena. The crucial idea of introduced approach is based on the discretization of the MEW equation with the aid of a combination of the discontin- uous Galerkin (DG) method for the space semi-discretization and the backward Euler method for the time discretization. The appended numerical experiments investigate the conservative properties of the MEW equation related to mass, momentum and energy, and illustrate the po- tency of this scheme, consequently.
- ItemMultiplication by wavelet matrix - effective implementation(Technická univerzita v Liberci, Česká republika, 2012) Šimůnková, MartinaStiffness matrix of the Dirichlet problem (auI)I = f with a homogeneous boundary value condition in a spline wavelet basis has O(n log n) non-zero elements [4]. We show that for a constant function a it is just O(n) and moreover we show that it can be stored in O(1) elements. This leads to a linear-time algorithm for multiplication by the wavelet matrix.