This paper introduces a high-order accurate surface integral equation method for solving 3D electromagnetic scattering for dielectric objects with uniaxially anisotropic permittivity tensors. The N-Müller formulation is leveraged resulting in a second-kind integral formulation, and a finite-difference-based approach is used to deal with the strongly singular terms resulting from the dyadic Green's functions for uniaxially anisotropic media while maintaining the high-order accuracy of the discretization strategy. The integral operators are discretized via a Nyström-collocation approach, which represents the unknown surface densities in terms of Chebyshev polynomials on curvilinear quadrilateral surface patches. The convergence is investigated for various geometries, including a sphere, cube, a complicated NURBS geometry imported from a 3D CAD modeler software, and a nanophotonic silicon waveguide, and results are compared against a commercial finite element solver. To the best of our knowledge, this is the first demonstration of high-order accuracy for objects with uniaxially anisotropic materials using surface integral equations.
On the surface plasmonic waves excited by a dipole above anisotropic and spatially dispersive two-dimensional surfaces of infinite extent in planarly layered media
acousticHelmholtzFoam: an MPI-parallel unstructured finite-volume solver for frequency-domain acoustics in heterogeneous two-phase media with perfectly matched layers
