A finite volume method for the approximation of Maxwell’s equations in two space dimensions on arbitrary meshes. (English) Zbl 1207.78035
Summary: A new finite volume method is presented for discretizing the two-dimensional Maxwell equations. This method may be seen as an extension of the covolume type methods to arbitrary, possibly non-conforming or even non-convex, \(n\)-sided polygonal meshes, thanks to an appropriate choice of degrees of freedom. An equivalent formulation of the scheme is given in terms of discrete differential operators obeying discrete duality principles. The main properties of the scheme are its energy conservation, its stability under a CFL-like condition, and the fact that it preserves Gauss’ law and divergence free magnetic fields. Second-order convergence is demonstrated numerically on non-conforming and distorted meshes.
MSC:
| 78M10 | Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory |
Keywords:
finite volume method; Maxwell’s equations; dual mesh; non-conforming meshes; distorted meshes; Gauss’ law; divergence free fields; energy conservation; CFL stability conditionReferences:
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