Computation of Creeping Waves on Smooth Objects
<br>
<br>

Wave scattering problems have a vast number of applications,
including radar and sonar technology, seismic tomography and medical
imaging. In such problems, the scattering of an incident wave with some
object or inhomogeneity is studied. The underlying equation is usually a
time-independent formulation of the wave equation, known as the Helmholtz
equation. At high frequencies, direct numerical methods for solving the
Helmholtz equation are computationally very expensive. In such cases,
asymptotic methods based on constructing asymptotic expansions of the
solution are used. Most asymptotic techniques are based on geometrical
optics (GO) and geometrical theory of diffraction (GTD).
<br>
<br>

One type of diffracted waves of GTD are creeping waves which can give an
important contribution to the solution of medium to high frequency
scattering problems. They are generated at the light-shadow boundary on
the illuminated scatterer by grazing incident waves and propagate along
geodesics on the scatterer surface, continuously shedding diffracted waves
in their tangential direction.
<br>
<br>

In this talk we show how to efficiently compute the creeping waves. We
consider an application to mono-static radar cross section problems
where creeping waves from all illumination angles must be computed."