Interpolating EFGM for computing continuous and discontinuous electromagnetic fields

Abstract

PurposeThis 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/approachThe 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.FindingsThe 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/implicationsThe 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 implicationsThe 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/valueThis 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.

New formulations for the hybrid meshless‐MoM method applied to 2D scattering problems

“…Although the MLS generates a smooth approximation for the unknown functions, its main weakness is the lack of the Kronecker delta property. 12,13 An interpolating MLS approximation (IMLS) can be obtained using singular weight functions in the definition of I in (7). Thus, it is possible to obtain shape functions which satisfy the Kronecker delta property.…”

“…where υ M are unknown coefficients to be determined and N Γ is the number of triangular shape functions over Γ. In (11) and (12), W is defined using Galerkin method, ie, the weight functions are also triangular functions Φ U , leading to matrices…”

“…in which ψ(ψ′)is the angle between vectors n and R (n′ and R), H 1 (2) is the second kind of Hankel function of order 1, and q = 1 or −1 if the segment has the Ith triangle side with positive or negative derivative, respectively. Equations (14) to (16) correspond to the EFIE (11) while (17) to (19) correspond to the MFIE (12). These sets of equations can be used individually, eg, (14) to (16) as in Resende et al, 9 or combined 3 to solve the equivalent external subproblem.…”