This paper presents some theoretical and numerical investigations concerning the fast computation of an exterior wave field to a scatterer by the Beam Propagation Method (BPM). Different models are presented and compared. It appears that the approach is able to correctly model the propagation of the propagative modes of the wave field while inaccuracies still remain for the evanescent and transition modes.
ThompsonL.L.. A review of finite element methods for time-harmonic acoustics. J. Acoust. Soc. Amer., 119(3): 1315–1330, 2006.
2.
BurtonA. J. and MillerG. F.. The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc. R. Soc. Lond., pages 323–201, 1971.
3.
ChenG. and ZhouJ.. Boundary Element Methods.Academic Press, Cambridge, 1992.
4.
ColtonD. and KressR.. Integral Equation Methods in Scattering Theory.John Wiley and Sons Inc., New York, 1983.
5.
SaadY.. Iterative Methods for Sparse Linear Systems.PWS Pub. Co., Boston, 1996.
6.
RokhlinV.. Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys., 86(2):414–439, 1990.
LuY. Y.. A complex coefficient rational Padé approximaton of √1+x. Appl. Numer Math., 27, 1998.
9.
ZalaC.MilinazzoF. and BrookeG. H.. Rational square-root approximations for parabolic equation algorithms. J. Acoust. Soc. Amer., 101, 1997.
10.
LuY. Y. and HoP. L.. Beam propagation method using a [(p-1)/p] Padé approximant of the propagator. Opt. Lett., 27(9):683–685, 2002.
11.
YevickD.. The application of complex Padé approximants to vector field propagation. IEEE Photon. Technol. Lett., 12, 2000.
12.
CollinsM. D.. An energy-conserving parabolic equation for elastic media. J. Acoust. Soc. Amer., 94, 1993.
13.
GodinO. A.. Reciprocity and energy conservation within the parabolic approximation. Wave Motion, 29, 1999.
14.
VassalloC.. Difficulty with vectorial BPM. Electron. Lett., 33, 1997.
15.
ChuiS. L. and LuY. Y.. A propagator-θ beam propagation method. IEEE Photon. Technol. Lett., 26, 2004.
16.
BedrossianJ.GeuzaineC. and AntoineX.. An amplitude formulation to reduce the pollution error in the finite element solution of time-harmonic scattering problems. IEEE Transactions on Magnetics, 44(6):782–785, 2008.
17.
AntoineX. and GeuzaineC., Phase Reduction Models for Improving the Accuracy of the Finite Element Solution of Time-Harmonic Scattering Problems I: General Theory and Low-Order Models. Journal of Computational Physics, 228(8): 3114–3136, 2009.
