The paper is concerned with the issues of modeling dynamic systems with interval parameters. In previous works, the authors proposed an adaptive interpolation algorithm for solving interval problems; the essence of the algorithm is the dynamic construction of a piecewise polynomial function that interpolates the solution of the problem with a given accuracy. The main problem of applying the algorithm is related to the curse of dimension, i.e., exponential complexity relative to the number of interval uncertainties in parameters. The main objective of this work is to apply the previously proposed adaptive interpolation algorithm to dynamic systems with a large number of interval parameters. In order to reduce the computational complexity of the algorithm, the authors propose using adaptive sparse grids. This article introduces a novelty approach of applying sparse grids to problems with interval uncertainties. The efficiency of the proposed approach has been demonstrated on representative interval problems of nonlinear dynamics and computational materials science.
A multiscale computational scheme is proposed for ion dynamics that allows modeling based on primary information—data on the chemical composition of the material and its crystal structure. The scheme includes quantum mechanical and molecular dynamics modeling as well as Monte Carlo simulation of ion and electron dynamics taking into account the real crystal structure. Approbation of the proposed approach is carried out on a silicon oxide memristive element. The results of computational experiments are presented that demonstrate the stages of growth and destruction of a conductive filament under the action of a time‐varying voltage.
A multiscale approach to discrete element modeling is presented. A distinctive feature of the method is that each macroscopic discrete element has an associated atomic sample representing the material’s atomic structure. The dynamics of the elements on macro and micro levels are described by systems of ordinary differential equations, which are solved in a self-consistent manner. A full cycle of multiscale simulations is applied to polycrystalline silicon. Macroscale elastic properties of silicon were obtained only using data extracted from the quantum mechanical properties. The results of computational experiments correspond well to the reference data.
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