20th GAMM-Seminar Leipzig on
Numerical Methods for Non-Local Operators

Max-Planck-Institute for Mathematics in the Sciences
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  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
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  Abstract Ralf Hiptmair, Sat, 09.00-10.00 Previous Contents Next  
  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 are

  • 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.


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