Transparent absorbing boundary (TAB) for the truncation of the computational domain

Abstract

A new approach to domain truncation without reflection is proposed for finite methods. The open-space Maxwell's equations, along with boundary conditions, are transformed to an equivalent system with a homogeneous closed boundary; the latter is then solved numerically. Like the popular perfectly matched layer (PML), the new method is independent of frequency and incident angle. Its uniqueness is that it does not need the extra absorption region, since the field attenuation takes place in the domain of the subject.Index Terms-Absorbing boundary, computational domain, truncation method, equivalent system.

A systematic approach to the derivation of constitutive parameters of a perfectly matched absorber

“…For this choice, it is evident that the TAB medium is terminated by a perfectly conducting wall at (i.e., ). Without any loss of generality, however, we can assume that the field satisfies (6) in the half-space , and this allows the function to be defined over the entire positive half-space. For instance, we can define , where is a positive constant.…”

“…We stipulate that, in the region , be given by (6) where the function satisfies the following conditions:…”

“…It is evident that condition a) assures the continuity of at the interface , and b) is a statement of the fact that should decay in the region . In [6], the function is chosen to be (7) where is the length of the attenuation path and and are integers such that . For this choice, it is evident that the TAB medium is terminated by a perfectly conducting wall at (i.e., ).…”

“…Another approach to mesh truncation in finite methods is the transparent absorbing boundary (TAB) method [6], where the open-space Maxwell's equations are transformed into an equivalent system with a closed homogeneous boundary. This is achieved by modulating the amplitudes of the fields in the computational domain to obtain reflection-free truncation of this domain.…”

Extended Electromagnetic Continuity Condition and Generalized Huygens' Principle

“…The TAB is a recently suggested technique for the truncation of the computational ( ) domains in finite methods Peng & Balanis, 1997, 1998 . In the original formulation, the numerical solution is built for``auxiliary'' fields E and H, which are connected to the physical fields E and H by the relations…”