A tensor product finite element method for the diffraction grating problem with transparent boundary conditions

作者：Xia, Zhi; Du, Kui^*

来源：Computers & Mathematics with Applications, 2017, 73(4): 628-639.

DOI：10.1016/j.camwa.2017.01.002

• Helmholtz equation
• Transparent boundary condition
• Tensor product finite element method
• FFT

We consider the diffraction grating problem in optics, which has been modeled by a boundary value problem governed by a Helmholtz equation with transparent boundary conditions. A tensor-product finite element method is proposed to numerically solve the problem. An FFT-based matrix decomposition algorithm is developed to solve the linear system arising in the vertically layered medium case, which can be used as a preconditioning technique for the general case. Numerical examples are presented to illustrate the accuracy and efficiency of the method.

• 出版日期2017-2-15
• 单位厦门大学