@misc{SchaedleZschiedrichBurgeretal.2006, author = {Sch{\"a}dle, Achim and Zschiedrich, Lin and Burger, Sven and Klose, Roland and Schmidt, Frank}, title = {Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures}, doi = {/10.1016/j.jcp.2007.04.017}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8984}, number = {06-04}, year = {2006}, abstract = {We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.}, language = {en} } @misc{BurgerKloseSchaedleetal.2003, author = {Burger, Sven and Klose, Roland and Sch{\"a}dle, Achim and Zschiedrich, Lin}, title = {HelmPole - A finite element solver for scattering problems on unbounded domains: Implementation based on PML}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7609}, number = {03-38}, year = {2003}, abstract = {The solution of scattering problems described by the Helmholtz equation on unbounded domains is of importance for a wide variety of applications, for example in electromagnetics and acoustics. An implementation of a solver for scattering problems based on the programming language Matlab is introduced. The solver relies on the finite-element-method and on the perfectly-matched-layer-method, which allows for the simulation of scattering problems on complex geometries surrounded by inhomogeneous exterior domains. This report gives a number of detailed examples and can be understood as a user manual to the freely accessible code of the solver HelmPole.}, language = {en} } @misc{ZschiedrichKloseSchaedleetal.2003, author = {Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D}, doi = {10.1016/j.cam.2005.03.047}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7662}, number = {03-44}, year = {2003}, abstract = {In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped 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 to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.}, language = {en} }