###
Efficient numerical solution of acoustic and electromagnetic
scattering from periodic structures.

* *Larry (Yuxiang) Liu

Physics Department,
Dartmouth College

A lot of modern micro-devices, sensors and solar cells involve the
scattering problem from a periodic structure. The scattered wave is governed
by Helmholtz for acoustic waves or Maxwell equation for electromagnetic
waves. The method of fundamental solution (MFS) is an efficient way to solve
those kind of partial differential equations (PDEs). It has exponential
convergence and computationally efficient. We have developed algorithms to
solve the acoustic and electromagnetic scattering problems over various
types of objects. For a 3D acoustic wave scattering from a single
axisymmetric object with a generic smooth boundary, an accuracy of O(1e-12)
can be achieved in around 60 seconds even with high wavenumber k = 75 (31
wavelengths in diameter). New incident wave evaluation can be done in 2
seconds once the matrix is factorized. For the 3D electromagnetic wave
scattering from a single axisymmetric object, an accuracy of O(1e-6) can be
achieved in 20 minutes with high wavenumber k0 = 50 in the vacuum and k =
158 (50 wavelengths in diameter) in the dielectric. The computation time
could be dramatically reduced if we implement fast multipole method (FMM)
for electric and magnetic field evaluations, which we will do soon. We also
solved the 2D acoustic scattering from a periodic structure and get an
accuracy of O(1e-12) in less than 1 second. We will continue our research on
3D acoustic scattering and 3D electromagnetic scattering problems.

Back to ACMS schedule