|
|
Programs and Algorithms of Numerical Mathematics 18 : Janov nad Nisou, June 19-24, 2016 : proceedings of seminar
Chleboun, J. ; Kůs, Pavel ; Přikryl, Petr ; Segeth, Karel ; Šístek, Jakub ; Vejchodský, Tomáš
This book comprises papers that originated from the invited lectures, survey lectures, short communications, and posters presented at the 18th seminar Programs and Algorithms of Numerical Mathematics (PANM) held in Janov nad Nisou, Czech Republic, June 19-24, 2016. All the papers have been peer-reviewed. The seminar was organized by the Institute of Mathematics of the Czech Academy of Sciences under the auspices of EU-MATHS-IN.cz, Czech Network for Mathematics in Industry. It continued the previous seminars on mathematical software and numerical methods held (biennially, with only one exception) in Al šovice, Bratří kov, Janov nad Nisou, Ko řenov, L ázně Libverda, Dolní Maxov, and Prague in the period 1983-2014. The objective of this series of seminars is to provide a forum for presenting and discussing advanced theoretical as well as practical topics in numerical analysis, computer implementation of algorithms, new approaches to mathematical modeling, and single- or multi-processor applications of computational methods.
|
|
|
Implicit constitutive solution scheme for Mohr-Coulomb plasticity
Sysala, Stanislav ; Čermák, M.
This contribution summarizes an implicit constitutive solution\nscheme of the elastoplastic problem containing the Mohr-Coulomb yield cri-\nterion, a nonassociative \now rule, and a nonlinear isotropic hardening. The\npresented scheme builds upon the subdifferential formulation of the \now rule\nleading to several improvements. Mainly, it is possible to detect a position\nof the unknown stress tensor on the Mohr-Coulomb pyramid without blind\nguesswork. Further, a simplifed construction of the consistent tangent opera-\ntor is introduced. The presented results are important for an efficient solution\nof incremental boundary value elastoplastic problems.
|
|
|
On Finite Element Approximation of Flow Induced Vibration of Elastic Structure
Valášek, J. ; Sváček, P. ; Horáček, Jaromír
In this paper the fluid-structure interaction problem is studied on a simplified model of the human vocal fold. The problem is mathematically described and the arbitrary Lagrangian-Eulerian method is applied in order to treat the time dependent computational domain. The viscous incompressible fluid flow and linear elasticity models are considered. The fluid flow and the motion of elastic body is approximated with the aid of fininite element method. An attention is paid to the applied stabilization technique. The whole algorithm is implemented in an in-house developed solver. Numerical results are presented and the influence of different inlet boundary conditions is discused.
|
|
|
Remarks on inverse of matrix polynomials
Fischer, Cyril ; Náprstek, Jiří
Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation of the inversion problem.
|
|
|
A Generalized Limited-Memory BNS Method Based on the Block BFGS Update
Vlček, Jan ; Lukšan, Ladislav
A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in some sense for quadratic objective functions, but it does not guarantee that the direction vectors are descent for general functions. To overcome this difficulty and utilize the advantageous properties of the block BFGS update, a block version of the limited-memory BNS method for large scale unconstrained optimization is proposed. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency.
|
|
|
On the Optimization of Initial Conditions for a Model Parameter Estimation
Matonoha, Ctirad ; Papáček, Š. ; Kindermann, S.
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence Recovery After Photobleaching) experimental technique. The core idea resides in the maximization of a sensitivity measure, which depends on the initial condition. Numerical experiments show that the discretized optimal initial condition attains only two values. The number of jumps between these values is inversely proportional to the value of a diffusion coefficient D (characterizing the biophysical and numerical process). The smaller value of D is, the larger number of jumps occurs.
|
|
|
A particular smooth interpolation that generates splines
Segeth, Karel
There are two grounds the spline theory stems from -- the algebraic one (where splines are understood as piecewise smooth functions satisfying some continuity conditions) and the variational one (where splines are obtained via minimization of some quadratic functionals with constraints). We use the general variational approach called $it smooth interpolation$ introduced by Talmi and Gilat and show that it covers not only the cubic spline and its 2D and 3D analogues but also the well known tension spline (called also spline with tension). We present the results of a 1D numerical example that characterize some properties of the tension spline.
|
|
|
The role of Sommerville tetrahedra in numerical mathematics
Hošek, Radim
In this paper we summarize three recent results in computational geometry, that were motivated by applications in mathematical modelling of fluids. The cornerstone of all three results is the genuine construction developed by D. Sommerville already in 1923. We show Sommerville tetrahedra can be effectively used as an underlying mesh with additional properties and also can help us prove a result on boundary-fitted meshes. Finally we demonstrate the universality of the Sommerville's construction by its direct generalization to any dimension.
|
host ::
RSS.