Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.
Journal article, 2024

In this paper, we address the approximation of the coupling problem for the wave equation and Maxwell’s equations of electromagnetism in the time domain in terms of electric field by means of a nodal linear finite element discretization in space, combined with a classical explicit finite difference scheme for time discretization. Our study applies to a particular case where the dielectric permittivity has a constant value outside a subdomain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this subdomain, Maxwell’s equations hold. Outside this subdomain, the wave equation holds, which may correspond to Maxwell’s equations with a constant permittivity under certain conditions. We consider as a model the case of first-order absorbing boundary conditions. First-order error estimates are proven in the sense of two norms involving first-order time and space derivatives under reasonable assumptions, among which lies a CFL condition for hyperbolic equations. The theoretical estimates are validated by numerical computations, which also show that the scheme is globally of the second order in the maximum norm in time and in the least-squares norm in space.

finite elements

lumped mass

absorbing boundary conditions

dielectric permittivity

piecewise linear

coupling problem

wave equation

Maxwell’s equations

explicit scheme

Author

Larisa Beilina

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

V. Ruas

Institut Jean Le Rond d'Alembert

Mathematics

22277390 (eISSN)

Vol. 12 7 936

Subject Categories

Computational Mathematics

Fluid Mechanics and Acoustics

Mathematical Analysis

DOI

10.3390/math12070936

More information

Latest update

8/7/2024 1