Interpolating EFGM for computing continuous and discontinuous electromagnetic fields

Abstract

Purpose

This paper proposes an interpolating approach of the element‐free Galerkin method (EFGM) coupled with a modified truncation scheme for solving Poisson's boundary value problems in domains involving material non‐homogeneities. The suitability and efficiency of the proposed implementation are evaluated for a given set of test cases of electrostatic field in domains involving different material interfaces.

Design/methodology/approach

The authors combined an interpolating approximation with a modified domain truncation scheme, which avoids additional techniques for enforcing the Dirichlet boundary conditions and for dealing with material interfaces usually employed in meshfree formulations.

Findings

The local electric potential and field distributions were correctly described as well as the global quantities like the total potency and resistance. Since, the treatment of the material interfaces becomes practically the same for both the finite element method (FEM) and the proposed EFGM, FEM‐oriented programs can, thus, be easily extended to provide EFGM approximations.

Research limitations/implications

The robustness of the proposed formulation became evident from the error analyses of the local and global variables, including in the case of high‐material discontinuity.

Practical implications

The proposed approach has shown to be as robust as linear FEM. Thus, it becomes an attractive alternative, also because it avoids the use of additional techniques to deal with boundary/interface conditions commonly employed in meshfree formulations.

Originality/value

This paper reintroduces the domain truncation in the EFGM context, but by using a set of interpolating shape functions the authors avoided the use of Lagrange multipliers as well as of a penalty strategy. The resulting formulation provided accurate results including in the case of high‐material discontinuity.

Citation

Nelson Marques, G., Márcio Machado, J., Luis Lopes Verardi, S., Stephany, S. and Jonatas Preto, A. (2007), "Interpolating EFGM for computing continuous and discontinuous electromagnetic fields", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 5, pp. 1411-1438. https://doi.org/10.1108/03321640710823082