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Programy a algoritmy numerické matematiky 14
Chleboun, Jan ; Přikryl, Petr ; Segeth, Karel ; Vejchodský, Tomáš
The book contains papers presented at the international seminar Programs and algorithms of numerical Mathematics 14 (PANM 14), held in Dolni Maxov, Czech Republic, June 1-6, 2008. It is the fourteenth volume in the series of the PANM proceedings. The topics of contributions include numerical methods for fluid flow modelling, the finite element method, a posteriori error estimates, topics from numerical linear atgebra, etc.
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hp-metody konečných prvků adaptivní v prostoru i v čase: Přehled metodologie
Šolín, P. ; Segeth, Karel ; Doležel, I.
We present a new class of self-adaptive higher-order finite element methods (hp-FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methodology was used to solve various types of problems. In this paper we use a nonlinear combustion problem for illustration.
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Rezonanční chování kulového kyvadlového tlumiče
Fischer, Cyril ; Náprstek, Jiří
The pendulum damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the previous paper is performed. Both approaches are compared and conclusions are drawn.
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Metody s proměnnou metrikou s omezenou pamětí, založené na invariantních maticích
Vlček, Jan ; Lukšan, Ladislav
A new class of limited-memory variable metric methods for unconstrained minimization is described. Approximations of inverses of Hessian matrices are based on matrices which are invariant with respect to a linear transformation. As these matrices are singular, they are adjusted for a computation of direction vectors. The methods have the quadratic termination property, which means that they will find a minimum of a strict quadratic function with an exact choice of a step-length after a finite number of steps. Numerical experiments show the efficiency of this method.
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O Lagrangeových multiplikátorech v metodách s lokálně omezeným krokem
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
Trust-region methods are globally convergent techniques widely used, for example, in connection with the Newton's method for unconstrained optimization. One of the most commonly-used iterative approaches for solving the trust-region subproblems is the Steihaug-Toint method which is based on conjugate gradient iterations and seeks a solution on Krylov subspaces. The paper contains new theoretical results concerning properties of Lagrange multipliers obtained on these subspaces.
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Metody vnitřních bodů pro zobecněnou minimaxovou optimalizaci
Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan
A new class of primal interior point methods for generalized minimax optimization is described. These methods use besides a standard logarithmic barrier function also barrier functions bounded from below which have more favourable properties for investigation of global convergence. It deals with descent direction methods, where an approxmation of the Hessian matrix is computed by gradient differences or quasi-Newton updates. Two-level optimization is used. A direction vector is computed by a Choleski decompostition of a sparse matrix. Numerical experiments concerning two basic applications, minimization of a point maximum and a sum of absolute values of smooth functions, are presented.
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