No Access

FAST ITERATION ALGORITHM FOR INTEGRAL EQUATIONS OF THE FIRST KIND ARISING IN 2D DIFFRACTION BY SOFT OBSTACLES

A. SCALIA

D.M.I., University of Catania, Catania, 95125 Viale A. Doria 6 (CT), Italy

Search for more papers by this author

V. POPUZIN

D.M.I., University of Catania, Catania, 95125 Viale A. Doria 6 (CT), Italy

Search for more papers by this author

, and

M. PENNISI

D.M.I., University of Catania, Catania, 95125 Viale A. Doria 6 (CT), Italy

Search for more papers by this author

https://doi.org/10.1142/S0218396X13500070Cited by:0 (Source: Crossref)

Abstract

We propose a new iteration numerical algorithm to solve boundary integral equations of the first kind arising in the 2D scattering by soft obstacles. The main idea is to operate on each iteration step with an integral equation, which has a convolution kernel, by changing the full kernel with a special averaging procedure. The practical convergence of the algorithm is demonstrated by some examples for three different geometries. If M is the number of iterations then the computational cost of the algorithm is MNlog(N).

Keywords:

References

L. Greengard and V. Rokhlin , J. Comput. Phys. 73 , 325 ( 1987 ) . Crossref, Web of Science, Google Scholar
V. Rokhlin , J. Comput. Phys. 86 , 414 ( 1990 ) . Crossref, Web of Science, Google Scholar
D. Colton and R. Kress , Integral Equation Methods in Scattering Theory ( John Wiley , New York , 1983 ) . Google Scholar
S. Borm , L. Grasedyck and W. Huckbusch , Eng. Anal. Bound. Elem. 27 , 405 ( 2003 ) . Crossref, Web of Science, Google Scholar
F. Q. Hu , J. Comp. Phys. 120 , 340 ( 1995 ) . Crossref, Web of Science, Google Scholar
J. Liu and Q. H. Liu, IEEE Microwave Wireless Compon. Lett. 14(3), 97 (2004). Crossref, Web of Science, Google Scholar
M. A. Sumbatyan and A. Scalia , Equations of Mathematical Diffraction Theory ( CRC Press , Boca Raton, Florida , 2005 ) . Google Scholar
M. Abramowitz and I. Stegun , Handbook of Mathematical Functions ( Dover , New York , 1965 ) . Google Scholar
L. V. Kantorovich and G. P. Akilov , Functional Analysis ( Pergamon Press , New York , 1982 ) . Google Scholar
R. H. Chan and M. K. Ng , SIAM Rev. 38 , 427 ( 1996 ) . Crossref, Web of Science, Google Scholar
E. C. Ifeachor and B. W. Jervis , Digital Signal Processing: A Practical Approach , 2nd edn. ( Prentice Hall , Upper Saddle River, New Jersey , 2002 ) . Google Scholar
G. H. Golub and C. F. Van Loan , Matrix Computations , 3rd edn. ( John Hopkins University Press , Baltimor, Maryland , 1996 ) . Google Scholar
I. K. Lifanov , L. N. Poltavskii and G. M. Vainikko , Hypersingular Integral Equations and Their Applications ( CRC Press , Boca Raton, Florida , 2004 ) . Google Scholar