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Journal Articles Applications of Mathematics Year : 2022

On the Maxwell-wave equation coupling problem and its explicit finite-element solution

Abstract

It is well known that in the case of constant dielectric permittivity and magnetic permeability, the electric field solving the Maxwell's equations is also a solution to the wave equation. The converse is also true under certain conditions. Here we study an intermediate situation in which the magnetic permeability is constant and a region with variable dielectric permittivity is surrounded by a region with a constant one, in which the unknown field satisfies the wave equation. In this case, such a field will be the solution of Maxwell's equation in the whole domain, as long as proper conditions are prescribed on its boundary. We show that an explicit finite-element scheme can be used to solve the resulting Maxwell-wave equation coupling problem in an inexpensive and reliable way. Optimal convergence in natural norms under reasonable assumptions holds for such a scheme, which is certified by numerical exemplification.
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Dates and versions

hal-03949048 , version 1 (20-01-2023)

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Vitoriano Ruas, Larisa Beilina. On the Maxwell-wave equation coupling problem and its explicit finite-element solution. Applications of Mathematics, 2022, pp.1-24. ⟨10.21136/AM.2022.0210-21⟩. ⟨hal-03949048⟩
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