Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations

Highlights: • Multidomain spectral method with Sommerfeld condition for the Helmholtz equation. • Sommerfeld condition imposed exactly at infinity being a finite point on the grid. • Spherical and prolate spheroidal domains considered. We present a multi-domain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed, as well as the interaction of a radiating dipole with a nano-particle.