A second-order scheme for Maxwell's equations with dielectric permittivity discontinuities and total field-scattered field boundaries

Abstract

A finite volume scheme for numerical solution of Maxwell's equations in regions with dielectric permittivity discontinuities and total field-scattered field (TFSF) boundaries is proposed. The scheme is second-order accurate in space and time. The key idea is to choose stencils for approximation of derivatives used to increase the order of approximation so that they do not cross dielectric permittivity discontinuities or TFSF boundaries. Computational results verify second order of approximation of the proposed scheme.

Keywords:

• Maxwell's equations
• finite volume
• unstructured mesh
• second order
• discontinuous dielectric permittivity
• total field-scattered field

2010 AMS Subject Classifications :

• 65M08
• 65M12
• 65D25
• 78M12