where L represents the spatially continuous transport operator and S denotes the scattering operator. [psi] and Q are the spatially continuous angular fluxes and fixed source, respectively.

Noting the linearity of the transport operator L and the scattering operator S, we obtain

To circumvent this problem, we use the feature that the

scattering operator characterizes the complete electromagnetic response of the region inside a closed observation contour.

This leads them to a definition of the time-dependent

scattering operator that encodes the far-field behavior (with respect to a stationary observer) in the asymptotic regions of the black hole: the event and cosmological horizons.

Thus

scattering operator is defined from [A.sub.J]X(x) = X(x) * [[PHI].sub.J](x) and U[[lambda]]X(x) = [absolute value of X * [[psi].sub.[lambda]](x)] [12].

where n is the number of the iteration, [??] the real domain

scattering operator, and [??] the modal domain

scattering operator.

For example, the high-order field point sampling scheme [7] and tangential EPA (TEPA) [10] have been proposed to improve the accuracy of

scattering operator. The efficiency of

scattering operator has been improved by hierarchical LU decomposition method [11].

Strauss [1] obtained the

scattering operator in the presence of a moving object.

Firstly, each brick is described through a

scattering operator of equivalent surface current densities defined over a brick's surface.

where A, B [member of] X [right arrow] X are bounded and nonlinear operators, which are derived from the semidiscretised transport and

scattering operators. X [member of] [R.sup.n] is a Banach space and [parallel]x[parallel] is the corresponding norm in X.

where the exponents W and F stand for WCIP and FDTLM, the operator S contains the transmission/reflection conditions on ([summation]), and [([S.sup.W.sub.i]).sub.i=uv,down] are the

scattering operators for homogeneous media in domain i.

Prosvirnin, "Spectral

scattering operators in problems of wave diffraction on flat screens," Nauk.