Details

Title

1D and 2D finite-difference operators for periodic functions on arbitrary mesh

Journal title

Archives of Electrical Engineering

Yearbook

2022

Volume

vol. 71

Issue

No 1

Affiliation

Sobczyk, Tadeusz Jan : Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Cracow University of Technology, 24 Warszawska str., 31-155 Kraków, Poland

Authors

Keywords

arbitrary meshes ; finite-difference operators ; partial finite difference operators ; periodic functions ; two-variable periodic functions

Divisions of PAS

Nauki Techniczne

Coverage

265-275

Publisher

Polish Academy of Sciences

Bibliography

[1] Richtmayer R.D., Morton K.W., Difference methods for initial-value problems, J.Willey & Sons, New York (1967).
[2] Burden R.L., Faires J.D., Numerical analysis, PWS-Kent Pub. Comp., Boston (1985).
[3] Taflove A., Computational electrodynamics: the finite-difference time-domain method, Artech House, Boston – London (1995).
[4] Strikwerda J.C., Finite Difference Schemes and Partial Differential Equations, Society for Industrial and Applied Mathematics, Second Edition, Philadelphia (2004).
[5] LeVeque R.J., Finite difference methods for ordinary and partial differential equations, Society for Industrial and Applied Mathematics, Second Edition, Philadelphia (2007).
[6] Fortuna Z., Macukow B., Wasowski J., Numerical methods, WNT (in Polish), Warsaw (2009).
[7] Esfandiari R.S., Numerical Methods for Engineers and Scientists Using MATLABr, CRC Press, Taylor & Francis Group (2017).
[8] Zakrzewski K., Łukaniszyn M., Application of 3-D finite difference method for inductance calculation of air-core coils system, COMPEL International Journal of Computations and Mathematics in Electrical Engineering, vol. 13, no. 1, pp. 89–92 (1994).
[9] Demenko A., Sykulski J., On the equivalence of finite difference and edge element formulations in magnetic field analysis using vector potential, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33, no. 1/2, pp. 47–55 (2014).
[10] Huang J., LiaoW., Li Z., A multi-block finite difference method for seismic wave equation in auxiliary coordinate system with irregular fluid–solid interface, Engineering Computations, vol. 35, no. 1, pp. 334–362 (2018).
[11] Chapwanya M., Dozva R., Gift Muchatibaya G., A nonstandard finite difference technique for singular Lane-Emden type equations, Engineering Computations, vol. 36, no. 5, pp. 1566–1578 (2019).
[12] Mawlood M., Basri S., AsrarW., Omar A., Mokhtar A., Ahmad M., Solution of Navier-Stokes equations by fourth-order compact schemes and AUSM flux splitting, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 16, no. 1, pp. 107–120 (2006).
[13] Ivanovic M., Svicevic M., Savovic S., Numerical solution of Stefan problem with variable space grid method based on mixed finite element/finite difference approach, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 27, no. 12, pp. 2682–2695 (2017).
[14] Sobczyk T.J., Algorithm for determining two-periodic steady-states in AC machines directly in time domain, Archives of Electrical Engineering, Polish Academy of Science, Electrical Engineering Committee, vol. 65, no. 3, pp. 575–583 (2016), DOI: 10.1515/aee-2016-0041.
[15] Sobczyk T.J., Radzik M., Radwan-Pragłowska N., Discrete differential operators for periodic and two-periodic time functions, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 38, no. 1, pp. 325–347 (2019).
[16] Sobczyk T.J., Radzik M., A new approach to steady state analysis of nonlinear electrical circuits, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 37, no. 3, pp. 716–728 (2017).
[17] Sobczyk T.J., Radzik M., Tulicki J., Direct steady-state solutions for circuit models of nonlinear electromagnetic devices, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 40, no. 3, pp. 660–675 (2021), DOI: 10.1108/COMPEL-10-2020-0324.
[18] Sobczyk T.J., Jaraczewski M., Application of discrete differential operators of periodic functions to solve 1D boundary-value problems, COMPEL – The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Emerald Pub. Ltd., vol. 39, no. 4, pp. 885–897 (2020).
[19] Sobczyk T.J., 2D discrete operators for periodic functions, Proceedings IEEE Conference Selected Issues of Electrical Engineering and Electronics (WZZE), Zakopane, Poland, pp. 1–5 (2019), https://ieeexplore.ieee.org/document/8979992.
[20] Jaraczewski M., Sobczyk T., Leakage Inductances of Transformers at Arbitrarily Located Windings, Energies, vol. 13, no. 23, 6464 (2020), DOI: 10.3390/en13236464.

Date

2022.03.11

Type

Article

Identifier

DOI: 10.24425/aee.2022.140209
×