# American Institute of Mathematical Sciences

March  2011, 15(2): 401-415. doi: 10.3934/dcdsb.2011.15.401

## Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method

 1 LSEC, Institute of Computational Mathematics, Chinese Academy of Science, Beijing 100190, China 2 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States

Received  November 2009 Revised  March 2010 Published  December 2010

In this paper, we apply a newly developed generalized discontinuous Galerkin (GDG) method for rigorous simulations of 2-D phase shift masks (PSM). The main advantage of the GDG method is its accurate treatment of jumps in solutions using the Dirac $\delta$ generalized functions as source terms of partial differential equations. The scattering problem of the PSM is cast with a total field/scattering field formulation while the GDG method is used to handle the inhomogeneous jump conditions between the total and scattering fields along the physical and perfectly matched layer (PML) interfaces. Numerical results demonstrate the high order accuracy of the GDG method and its capability of handling the non-periodic structures such as optical images near mask edges.
Citation: Xia Ji, Wei Cai. Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 401-415. doi: 10.3934/dcdsb.2011.15.401
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