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Solving an elasto-plastic problems by Newton-like methods
Byczanski, Petr ; Sysala, Stanislav
In this contribution, we will apply the semismooth Newton methods with and without damping to solving a one-time step problem in elesto-plasticity. First, we briefly describe the elasto-plastic model and formulate the corresponding one-time step problem in the form of the non-linear variational equation. Then we characterize the used numerical methods. Finally, we illustrate the methods on a 2D numerical example.
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Mnohoúrovňové modelování geomateriálů a iterační řešiče
Blaheta, Radim ; Byczanski, Petr ; Harasim, Petr
The knowledge of microstructure in combination with properties of the constituents and mathematical modelling can be used for investigation of the properties of geomaterials at application scale. We investigate problems with both deterministic knowledge of microstructure, derived from X-ray CT scans, and stochastic one. The stochastic generation is also used for a systematic study of robustness of iterative solvers, particularly for Schwarz methods for PDE problems discretized by mixed FEM.
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Modifikovaná nehladká Newtonova metoda: numerický příklad
Byczanski, Petr ; Sysala, Stanislav
The modified semismooth Newton method is introduced in this contribution. The modification is based on a ``damping" in each Newton iteration. The damping coefficient are computed by a minimisation problem. The method is described on an abstract problem with the main convergence results. Then it is applied to solving an elasto-plastic problem with hardening and illustrated on a numerical example.
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Search of local maximum of function, algorithm "postup06"
Byczanski, Petr
Local maximum of differentiable function is found by sequential change of argument. In the neighbourhood of each proceed point is function approximated with only 2 elements of Taylor expansion. The change of argument is primary bounded by keeping certain level accuracy of approximation.
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Víceúrovňové hierarchické předpodmínění (úvod do problematiky)
Blaheta, Radim ; Byczanski, Petr
The paper describes hierarchical decompositions and AMLI preconditioners, analysis of hierarchical decomposition methods through CBS constant in 2D and 3D, discusses robustness with respect to anisotropy and element shape and introduces fully algebraic AMLI with aggregation or agglomeration. Finally, the paper discusses recent results concerning algebraic theory of AMLI for nonconforming FEś.
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Adaptive base method
Byczanski, Petr
The adaptive base method is designated for the repeated solution of a system of linear equations with a constant regular matrix and slowly changing right hand side. The method is based on an adaptive construction of the orthonormal basis in right hand side vector space. If the approximation of current right hand side in actual basis is sufficiently exact, then the corresponding solution with limited precision is directly given by the stored inverse of basis.
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