A bicomplex finite element method for wave propagation in homogeneous media

Abstract

Purpose

The purpose of this paper is to present the advantageous applicability of the bicomplex analysis in the context of the Finite Element Method (FEM). This method can be applied for wave propagation problems in various environments.

Design/methodology/approach

In this paper, the bicomplex number system is introduced and accordingly the differential equation for time-harmonic Maxwell’s equations in homogeneous media is derived in detail. Besides that, numerical simulations of wave propagation are performed and compared to the traditional approach based on classical FEM related to the Helmholtz equation. The appropriate error norm is investigated for different discretizations.

Findings

The results show that the use of bicomplex analysis in FEM leads to the higher accuracy of the electromagnetic field determination compared to the traditional Helmholtz approach. By using the bicomplex-valued formulation, the complex-valued electric and magnetic fields can be found directly and no additional FEM calculations are necessary to get the whole field.

Originality/value

The direct bicomplex formulation overcomes the use of the second order derivatives, which leads to the higher accuracy. In general, accurate calculations of the wave propagation in FEM is still an open problem and the approach described in this paper is a contribution to this class of problems.

Citation

Reum, T. and Toepfer, H. (2020), "A bicomplex finite element method for wave propagation in homogeneous media", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 39 No. 5, pp. 1031-1039. https://doi.org/10.1108/COMPEL-01-2020-0010