Discrete non-local boundary conditions for split-step Padé approximations of the one-way Helmholtz equation

Authors:
Matthias Ehrhardt;Andrea Zisowsky
Affiliations:
Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany;Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623 Berlin, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

This paper deals with the efficient numerical solution of the two-dimensional one-way Helmholtz equation posed on an unbounded domain. In this case, one has to introduce artificial boundary conditions to confine the computational domain. The main topic of this work is the construction of the so-called discrete transparent boundary conditions for state-of-the-art parabolic equation methods, namely a split-step discretization of the high-order parabolic approximation and the split-step Pade algorithm of Collins. Finally, several numerical examples arising in optics and underwater acoustics illustrate the efficiency and accuracy of our approach.