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.

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