Abstract: Standard
finite element or boundary element methods for high
frequency scattering problems, with piecewise
polynomial approximation spaces, suffer from the
limitation that the number of degrees of freedom
required to achieve a prescribed level of accuracy
grows at least linearly with respect to the
frequency. Here we present a new boundary element
method for problems of acoustic scattering by convex
polygons for which, by including in the
approximation space the products of plane wave basis
functions with piecewise polynomials supported on a
graded mesh, we can demonstrate a computational cost
that grows only logarithmically with respect to the
frequency.
[LECTURE SLIDES]
