Computation of unsteady electromagnetic scattering about 3D complex bodies in free space with high-order difference potentials

Journal of Computational Physics. 2024. Vol. 498. Article 112705.

Petropavlovsky S., Tsynkov S., Turkel E.

We extend the previously developed high-order accurate method for acoustic scattering to electro-magnetic scattering, i.e., from the scalar setting to a vector setting. First, the governing Maxwell’s equations are reduced from their original first-order form to a system of second-order wave equa-tions for the individual Cartesian components of electromagnetic field. In free space, these wave equations are uncoupled. Yet at the boundary of the scatterer, the variables that they govern (i.e., Cartesian field components) remain fully coupled via the boundary conditions that account for the specific scattering mechanism. Next, the wave equations are equivalently replaced with Calderon’s boundary equations with projections obtained using the method of difference poten-tials and a compact high-order accurate scheme. The Calderon’s boundary equations are combined with the boundary conditions and the overall system is solved by least squares. The resulting vec-tor methodology (electromagnetic) inherits many useful properties of the scalar one (acoustic). In particular, it offers sub-linear computational complexity, does not require any special treatment of the artificial outer boundary, and has the capacity to solve multiple similar problems at a low individual cost per problem. We demonstrate the performance of the new method by computing the scattering of a given impinging wave about a double-cone hypersonic shape.

Keywords: уравнения Максвелла, Maxwell’s equations, The Huygens’ principle, метод разностных потенциалов, High-order compact schemes on Cartesian grids, Calderon’s boundary equations with projections