Abstract
An alternating direction implicit (ADI), scheme for the wide-angle
finite-difference beam propagation method (FD-BPM) based on the wide angled
Pade multistep method is presented. The scheme incorporates an iterative
technique for correction of the operator splitting error. The resulting
equations are efficiently solved by the Thomas algorithm for tri-diagonal
band matrices. The dispersion characteristics, accuracy and stability of the
scheme is verified analytically and numerically for the cases of a plane
wave propagating at fixed angle to the assumed propagation direction of the
algorithm and the three dimensional angled propagation of a Gaussian beam.
The computational requirements of the method are assessed against a standard
wide-angle Pade multistep method that uses direct and iterative sparse
matrix solvers.
© 2009 IEEE
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