Scientific Computing Seminar
Abstract:
We propose a new numerical approach for the approximation of the scattered
radiation by objects of uncertain shape. We model the uncertainty by
representing it in terms of a known random variable, and employ the polynomial
chaos expansion method.
This later method has proved, in the majority of cases, to be computationally
superior to the conventional Monte-Carlo sampling method.
We consider the scattering phenomenon from a macroscopic point of view which
is governed by Maxwell's equations, and accordingly use the approximation to
solve Maxwell's Equations numerically. We show that the discontinuous nature
of the problem's domain causes a dramatic reduction in accuracy when the
standard polynomial chaos expansion is employed. In order to obtain spectral
convergence, we introduce a new implicit approach in which the approximation
is obtained indirectly by expanding the interface fields at all possible
states of the object's shape.
The presented new variant of the polynomial chaos expansion not only handles
the discontinuity more accurately then the standard method, but also proves to
be beneficiary in other aspects. First, the original problem in the unbounded
domain is transformed to evaluation of one-dimensional integrals over a finite
interval, thus efficiently reducing the computational domain. Furthermore, the
approximation automatically satisfies the far-field radiation conditions and
therefore its accuracy is not jeopardized by the reduction of the
computational domain.
Joined work with Yuval Harness
PDE Seminar