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

被引：0
作者：
Larisa Beilina
Vitoriano Ruas
机构：
[1] Chalmers University of Technology and Gothenburg University,Department of Mathematical Sciences
[2] UMR 7190 CNRS - Sorbonne Université,Institut Jean Le Rond d’Alembert
来源：
Applications of Mathematics | 2023年 / 68卷
关键词：
constant magnetic permeability; dielectric permittivity; explicit scheme; finite element; mass lumping; Maxwell-wave equation; 65M12; 65M22; 65M60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：75 / 98
页数：23
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