38 research outputs found
On representations of the Helmholtz Green's function
We consider the free space Helmholtz Green's function and split it into the
sum of oscillatory and non-oscillatory (singular) components. The goal is to
separate the impact of the singularity of the real part at the origin from the
oscillatory behavior controlled by the wave number k. The oscillatory component
can be chosen to have any finite number of continuous derivatives at the origin
and can be applied to a function in the Fourier space in
operations. The non-oscillatory component
has a multiresolution representation via a linear combination of Gaussians and
is applied efficiently in space.Comment: 10 pages, 3 figure