A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions

In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with a wide class of polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight into implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.

[1]  Anne-Sophie Bonnet-Ben Dhia,et al.  Perfectly Matched Layers for the Convected Helmholtz Equation , 2004, SIAM J. Numer. Anal..

[2]  Peter Monk,et al.  The Perfectly Matched Layer in Curvilinear Coordinates , 1998, SIAM J. Sci. Comput..

[3]  Frank Schmidt,et al.  Solving Time-Harmonic Scattering Problems Based on the Pole Condition II: Convergence of the PML Method , 2003, SIAM J. Math. Anal..

[4]  Matti Lassas,et al.  Analysis of the PML equations in general convex geometry , 2001, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[5]  Jian-Ming Jin,et al.  Complex coordinate stretching as a generalized absorbing boundary condition , 1997 .

[6]  Raj Mittra,et al.  Investigation of nonplanar perfectly matched absorbers for finite-element mesh truncation , 1997 .

[7]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[8]  Frank Schmidt,et al.  A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms , 2002 .

[9]  Matti Lassas,et al.  Complex Riemannian metric and absorbing boundary conditions , 2001 .

[10]  Matti Lassas,et al.  On the existence and convergence of the solution of PML equations , 1998, Computing.

[11]  F. Ihlenburg.  Finite Element Analysis of Acoustic Scattering , 1998 .

[12]  Frank Schmidt,et al.  Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory , 2003, SIAM J. Math. Anal..

[13]  Weng Cho Chew,et al.  A 3D perfectly matched medium from modified maxwell's equations with stretched coordinates , 1994 .