Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: meshless finite differences method

Sortuj według:

Ogranicz wyniki do:

Application of the Monte Carlo method with meshless random walk procedure to selected scalar elliptic problems

Milewski S.

Archives of Mechanics

2019

Vol. 71, nr 4-5

337–-375

The combined stochastic-deterministic approach, which may be applied to the numerical analysis of a wide range of scalar elliptic problems of civil engineering, is presented in this paper. It is based on the well-known Monte Carlo concept with a random walk procedure, in which series of random paths are constructed. Additionally, it incorporates selected features of the meshless finite difference method, especially star selection criteria and a local weighted function approximation. The approach leads to the explicit stochastic formula relating one unknown function value with all a-priori known data parameters. Therefore, it allows for a fast and effective estimation of the solution value at the selected point(s), without the necessity of generation of large systems of equations, combining all unknown values. In such a manner, the proposed approach develops and extends the original standard Monte Carlo one toward analysis of boundary value problems with more complex shape geometry, natural boundary conditions, non-homogeneous right-hand sides as well as anisotropic and non-linear material models. The paper is illustrated with numerical results of selected elliptic problems, including a torsion problem of a prismatic bar, a stationary heat flow analysis with anisotropic and non-linear material functions, as well as an inverse heat problem. Moreover, the appropriate coupling with other deterministic methods (e.g., the finite element method) is considered.

Non-statistical physically reasonable technique for a posteriori estimation of experimental data error

Magiera J.

Computer Assisted Mechanics and Engineering Sciences

2006

Vol. 13, No. 4

593-611

In the paper presented is an application of the physically based global method (PBGM) to a posteriori estimation of experimental data error. It is proposed here to build data error measures by spanning a high ąuality physically reasonable smoothing fit to data and treat it as a reference field for error estimation in a very similar way it is done in the postprocessing type error estimates used widely in FE or meshless methods, where the higher order (superconvergent) solutions are used for building error estimates (post-processing type of error estimators). The new techniąue is different from classical methods of experimental data error estimation as it provides non-statistical estimates of the data error and as such it may be applied to a wider rangę of problems, including cases when only a single data set is available (e.g., destructive testing). And because the new approach builds the estimates while performing its standard physically based global-type approximation, it fully integrates other features of the PBGM approach like data interpolation, extrapolation or differentiation. In the paper the whole PBGM approach is presented, including the concept of the method formulated for the case of analysis of residual stress in railroad rails, discretisation with MFDM, then several PBGM a posteriori error estimates are introduced and results for test problems (benchmark and actual data) are shown.