Non-reflecting boundary conditions for Maxwell's equations
Ralf Hiptmair (ETH Zürich)
A new discrete non-reflecting boundary condition for the time-dependent Maxwell
equations describing the propagation of an electromagnetic wave in an infinite
homogeneous lossless rectangular waveguide with perfectly conducting walls is
presented. It is derived from a virtual spatial finite difference discretization of
the problem on the unbounded domain. Fourier transforms are used to decouple
transversal modes. A judicious combination of edge based nodal values permits us to
recover a simple structure in the Laplace domain.
Switching back to the time domain the resulting absorbing boundary conditions
involve a temporal convolution integral with a kernel whose Laplace transform
is known. This can be tackled by a fast convolution algorithm, whose core ideas
- the adaptive approximation of complex contour integrals by means of the
trapezoidal rule, and
- to make use of the fact that temporal convolution with an exponential
function is related to the solution of an ordinary differential equation.