Analysis of Transient Scattering From Conductors Using Laguerre Polynomials as Temporal Basis Functions
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Analysis of Transient Scattering From Conductors Using Laguerre Polynomials as Temporal Basis FunctionsAbstract
In this paper, a new method is presented for analyzing
the transient electromagnetic response from a
three-dimensional (3-D) perfectly electric conducting
body using the time-domain electric field integral
equation (TD-EFIE). Instead of the conventional
marching-on in time (MOT) technique, the solution
method in this paper is based on the Galerkin’s method
that involves separate spatial and temporal testing
procedure. Triangular patch basis functions are used for
spatial expansion and testing functions for arbitrarily
shaped 3-D structures. The time-domain unknown
coefficient is approximated as an orthonormal basis
function set that is derived from the Laguerre functions.
These basis functions are also used as the temporal
testing. With the representation of the derivative of the
time-domain coefficient in an analytic form, the time
derivative of the vector potential in the TD-EFIE can be
handled analytically. We also propose an alternative
formulation to solve the differential form of the
TD-EFIE. Two methods presented in this paper result in
very accurate and stable transient responses from
conducting objects. Detailed mathematical steps are
included and representative numerical results are
presented and compared
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