Finite element methods; iterative techniques; multiple electromagnetic scattering; short wave problem
Abstract :
[en] We present a multiple-scattering solver for nonconvex geometries obtained as the union of a finite number of convex obstacles. The algorithm is a finite element reformulation of a high-frequency integral equation technique proposed previously. It is based on an iterative solution of the scattering problem, where each iteration leads to the resolution of a single scattering problem in terms of a slowly oscillatory amplitude.
Disciplines :
Electrical & electronics engineering
Author, co-author :
Geuzaine, Christophe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Vion, Alexandre ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Gaignaire, Roman ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Dular, Patrick ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
V Sabariego, Ruth ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Language :
English
Title :
An Amplitude Finite Element Formulation for Multiple-Scattering by a Collection of Convex Obstacles
C. Geuzaine, O. Bruno, and F. Reitich, "On the solution of multiple-scattering problems," IEEE Trans. Magn., vol.41, no.5, pp. 1488-1491, May 2005.
O. Bruno, C. Geuzaine, J. Monro, Jr., and F. Reitich, "Prescribed error tolerances within fixed computational times for scattering problems of arbitrarily high frequency: The convex case," Philosoph. Trans. Roy Soc. Ser. A, Math., Phys., Eng., Sci., vol.362, no.1816, pp. 629-645, 2004.
M. Balabane, "Boundary decomposition for helmholtz and maxwell equations I: Disjoint sub-scatterers," Asymptotic Anal., vol.38, no.1, pp. 1-10, 2004.
C. T. Tai, "An iterative method of solving a system of linear equations and its physical interpretation from the point of view of scattering theory," IEEE Trans. Antennas Propagat., pp. 713-714, Sep. 1970.
X. Antoine and C. Geuzaine, "Phase reduction models for improving the accuracy of the finite element solution of time-harmonic scattering problems I: General approach and low-order models," J. Comput. Phys., available online.
C. Geuzaine, J. Bedrossian, and X. Antoine, "An amplitude formulation to reduce the pollution error in the finite element solution of time-harmonic scattering problems," IEEE Trans. Magn., vol.44, no.6, pp. 782-785, Jun. 2008.
G. A. Kriegsmann, A. Taflove, and K. Umashankar, "A new formulation of electromagnetic wave scattering using the on-surface radiation condition method," IEEE Trans. Antennas Propagat., vol.35, pp. 153-161, 1987.
A. Bayliss, M. Gunzburger, and E. Turkel, "Boundary conditions for the numerical solution of elliptic equations in exterior regions," SIAM J. Appl. Math., vol.42, pp. 430-451, 1982.
C. Geuzaine, B. Meys, P. Dular, F. Henrotte, and W. Legros, "A Galerkin projection method for mixed finite elements," IEEE Trans. Magn., vol.35, no.3, pp. 1438-1441, Mar. 1999.