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A matrix basis formulation is introduced to represent the 3 x 3 dyadic Greens functions in the frequency domain for the Maxwells equations and the elastic wave equation in layered media. The formulation can be used to decompose the Maxwells Greens functions into independent TE and TM components, each satisfying a Helmholtz equation, and decompose the elastic wave Greens function into the S-wave and the P-wave components. In addition, a derived vector basis formulation is applied to the case for acoustic wave sources from a non-viscous fluid layer.
The well-known Greens function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Greens function solutions of nonlinear differential equations of higher order. We show
We propose a controllability method for the numerical solution of time-harmonic Maxwells equations in their first-order formulation. By minimizing a quadratic cost functional, which measures the deviation from periodicity, the controllability method
This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly v
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwells equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level modified equation
The contraction of the Poincare group with respect to the space trans- lations subgroup gives rise to a group that bears a certain duality relation to the Galilei group, that is, the contraction limit of the Poincare group with respect to the time tr