A tensor product finite element method for the diffraction grating problem with transparent boundary conditions. (15th February 2017)

• Record Type: Journal Article
• Authors: Xia, Zhi; Du, Kui
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 4(2017)
• Page Start: 628
• Page End: 639
• Publication Date: 2017-02-15
• Subjects: Helmholtz equation -- Transparent boundary condition -- Tensor product finite element method -- FFT; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.01.002
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.