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.

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The 60-GHz band is proposed for the radio link frequency in broad-band cellular systems. 140-155-Mb/s transmission experiments are reported with optically generated millimeter-waves at frequencies in the 60-GHz band. By applying the sideband injection locking technique, the remotely generated millimeter-wave signals depict quartz accuracy and low phase noise <-100 dBc/Hz at offset frequencies 21 MHz

We propose a new method for fast estimation of error bounds for outputs of interest in the reduced basis context, efficiently applicable to real world 3D problems. Geometric parameterizations of complicated 2D, or even simple 3D, structures easily leads to affine expansions consisting of a high number of terms (∝ 100 − 1000). Application of state-of-the-art techniques for computation of error bounds becomes practically impossible. As a way out we propose a new error estimator, inspired by the subdomain residuum method, which leads to substantial savings (orders of magnitude) regarding online and offline computational times and memory consumption. We apply certified reduced basis techniques with the newly developed error estimator to 3D electromagnetic scattering problems on unbounded domains. A numerical example from computational lithography demonstrates the good performance and effectivity of the proposed estimator. Introduction.Numerical design and optimization, as well as inverse reconstruction and parameter estimation, usually requires the multiple solution of a parameterized model, described by a partial differential equation (PDE). In these many-query or real-time contexts, short online computational times become indispensable.The reduced basis method allows us to split up the solution process of a parameterized problem into an expensive offline and a cheap online phase [1]. In the offline phase the problem is solved rigorously several times. These solutions build the reduced basis. The full problem is projected onto the reduced basis space, which results in a significant reduction of the problem size. In the online phase only the reduced system is solved. Usually the reduced basis method is applied to input-output relationships, where the inputs are parameters to a PDE and the outputs are functionals of the PDE solution. Error estimators assure the reliability of the reduced basis solution and are, therefore, of great importance.For online-offline decomposition in the reduced basis setup, an affine decomposition of the underlying PDE is essential. Geometries with complicated parameter dependencies in two dimensions and already simple geometries in three dimensions can, however, lead to affine decompositions with a very high number of terms (∝ 100− 1000). This results in poor online performance of the reduced model, when state-ofthe-art techniques are applied; see, for example, a discussion in [1]. Also, offline construction of the error estimator becomes orders of magnitude more expensive than construction of the reduced basis system itself. In the following we introduce a novel and much cheaper error estimator for the reduced basis method, inspired by the