PAPER:

A New Formalism for Time Dependent Electromagnetic Scattering from a Bounded Obstacle

Maria Cristina Recchioni

Istituto di Matematica e Statistica

Università di Ancona

Piazza Martelli, 60121 Ancona, Italy

e-mail : recchioni@posta.econ.unian.it

Francesco Zirilli

Dipartimento di Matematica "G. Castelnuovo"

Università di Roma "La Sapienza"

00185 Roma, Italy

e-mail : f.zirilli@caspur.it

Abstract

We consider a time dependent three dimensional electromagnetic scattering problem. Let R³ be the three dimensional real Euclidean space filled with a medium of electric permittivity e, magnetic permeability m and zero electric conductivity. The quantities e, m are positive constants and there are no free charges in the space. Let W Ì R³ be a bounded simply connected obstacle with a locally Lipschitz boundary ¶W, that is assumed to have a nonzero constant boundary electromagnetic impedance. The limit cases of perfectly conducting and perfectly insulating obstacles are studied. We consider an incoming electromagnetic wave packet that hits W. We present a method to compute the scattered electromagnetic field as a superposition of time harmonic electromagnetic waves. These time harmonic electromagnetic waves are the solutions of exterior boundary value problems for the vector Helmholtz equation with the divergence free condition and they are computed with an "operator expansion" method that generalizes the methods presented in [1] and [2]. The "operator expansion" method for time harmonic acoustic scattering from an unbounded surface was introduced for the first time by Milder [3]. The method proposed is computationally very efficient. In fact it is highly parallelizable with respect to time and space variables. Several numerical experiments obtained with a parallel implementation of the method are shown. The numerical results obtained are discussed from the numerical and the physical point of view. The quantitative character of the numerical experience shown is established. The website: http://www.econ.unian.it/recchioni/w4/ shows some animations relative to the numerical experiments.

[1]

L. Fatone, C. Pignotti, M.C. Recchioni, F. Zirilli: "Time harmonic electromagnetic scattering from a bounded obstacle: An existence theorem and a computational method", J. Math. Phys., 40, 1999, 4859-4887.

[2]

E. Mecocci, L. Misici, M.C. Recchioni, F. Zirilli: "A new formalism for time dependent wave scattering from a bounded obstacle", to appear in J. Acoust. Soc. Am. .

[3]

D.M. Milder: "An improved formalism for wave scattering from rough surface", J. Acoust. Soc. Am., 89, 1991, 529-541.

ANIMATION 1: Cube Eⁱ = (1,1,0) ^Te^-i(z+t)

• Animation 1 ( File GIF - 753K )

ANIMATION 2: Cube Eⁱ = (1,0,0) ^Te^-i(z+t)

• Animation 2 ( File GIF - 753K )

ANIMATION 3: Double Cone Eⁱ = (1,0,0) ^Te^-(z+t)2

• Animation 3 ( File GIF - 753K )

ANIMATION 4: Double Cone Eⁱ = (1,0,0) ^Te^-16(z+t)2

• Animation 4 ( File GIF - 753K )

ANIMATION 5: Holed Sphere Eⁱ = (1,0,0) ^Te^-(z+t)2/4

• Animation 5 ( File GIF - 753K )