Multi-Stage Filtering of Numerical Solutions With an Application to the Hele-Shaw Problem

DOI

10.2991/aisr.k.201029.034How to use a DOI?

Keywords

error estimation, improving the reliability of calculations, acceleration of convergence

Abstract

This work is devoted to improving the accuracy and reliability of computer-generated information in mathematical modeling of physical and technological processes. A method of filtering numerical results for the solutions of different problems is presented for estimating the errors and increasing the accuracy. This method includes a formal two-stage rule for choosing the standard and testing. It is shown that the proposed method allows avoiding the uncertainty and limitations of the Runge and Romberg rules for estimating the errors of numerical data. The proposed method is used to analyze numerical solutions of an electrochemical machining modeling problem. The developed numerical method for solving this problem includes the definition of two conformal mappings. One of them is a conformal mapping of the semicircle region of the parametric plane on a band of the complex potential plane. This function is represented as the sum of a known function with singularities and a function without singularities defined as the Laurent series with known coefficients. The second conformal mapping is used to determine the relationship between the parametric plane and the physical one. We use the Laurent series for this and its coefficients are determined by the method of collocations for the boundary condition fulfillment. The forms of the surface to be machined during its processing with an ellipsoidal cross-section electrode tool are obtained. The carried out investigation of the error dependencies on the numbers of stored coefficients of the series shows that these dependencies are the sums of exponential functions. The error estimates of the studied parameters obtained by filtering are given.

Copyright

© 2020, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Vladimir Zhitnikov
AU  - Nataliya Sherykhalina
AU  - Aleksandra Sokolova
AU  - Sergey Porechny
PY  - 2020
DA  - 2020/11/10
TI  - Multi-Stage Filtering of Numerical Solutions With an Application to the Hele-Shaw Problem
BT  - Proceedings of the 8th Scientific Conference on Information Technologies for Intelligent Decision Making Support (ITIDS 2020)
PB  - Atlantis Press
SP  - 178
EP  - 185
SN  - 1951-6851
UR  - https://doi.org/10.2991/aisr.k.201029.034
DO  - 10.2991/aisr.k.201029.034
ID  - Zhitnikov2020
ER  -