Distributed Source Scheme to solve the classical form of Poisson equation using 3-D Finite-Difference Method for improved accuracy and unrestricted source position

Nithin Kumar Goona, Saidi Reddy Parne and S. Sashidhar

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 190, issue C, 965-975

Abstract: The Finite-Difference Method (FDM) despite being old and simple is not being used as rigorously as its counterpart Finite Element Method (FEM) for solving partial differential equations. This study aims to examine and improve the accuracy of FDM by eliminating significant sources of error. Since an expression for exact potential from the most accurate Method of Moment (MoM) is available in 3-D electrostatics, the classical form of Poisson equation is chosen for this study such that the error due to boundary conditions can be eliminated. The error due to the source term in the Poisson equation is studied with a single source and different grid densities by applying FDM in 3-D. Since the error is only present in the immediate surroundings of the source, a Distributed Source Scheme (DSS) has been proposed to reduce error due to the source term. A modified DSS i.e., Truncated Distributed Source Scheme (TDSS) is applied for the practical implementation of DSS. The maximum error in FDM when the source term is present has been reduced from 8.151% to 0.00091% with DSS. With the application of TDSS, it is shown that the maximum error can be maintained well below 0.1% for truncation values n > 15. The error due to source at off-center and off-grid positions was computed using TDSS and the maximum error is observed to be less than 0.05% and 0.01%, respectively. With off-grid error being low due to TDSS, it is shown that sources in TDSS can now take any position irrespective of grid nodes, which is forbidden in FDM with an average maximum error of 0.026%. It is also shown that DSS can also be used to find the charge distribution for a given potential distribution. While still maintaining the simplicity, improved accuracy and unrestricted source positions are achieved in FDM with exact boundary conditions using DSS.

Keywords: Finite-Difference Method; Poisson equation; Exact boundary values; Numerical methods (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475421002482
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:190:y:2021:i:c:p:965-975

DOI: 10.1016/j.matcom.2021.06.025

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().