20,896 research outputs found
Wavelet-Based High-Order Adaptive Modeling of Lossy Interconnects
Abstract—This paper presents a numerical-modeling strategy for simulation of fast transients in lossy electrical interconnects. The proposed algorithm makes use of wavelet representations of voltages and currents along the structure, with the aim of reducing the computational complexity of standard time-domain solvers. A special weak procedure for the implementation of possibly dynamic and nonlinear boundary conditions allows to preserve stability as well as a high approximation order, thus leading to very accurate schemes. On the other hand, the wavelet expansion allows the computation of the solution by using few significant coefficients which are automatically determined at each time step. A dynamically refinable mesh is then used to perform a sparse time-stepping. Several numerical results illustrate the high efficiency of the proposed algorithm, which has been tuned and optimized for best performance in fast digital applications typically found on modern PCB structures. Index Terms—Finite difference methods, time-domain analysis, transmission lines, wavelet transforms. I
Rigorous Simulations of 3D Patterns on Extreme Ultraviolet Lithography Masks
Simulations of light scattering off an extreme ultraviolet lithography mask
with a 2D-periodic absorber pattern are presented. In a detailed convergence
study it is shown that accurate results can be attained for relatively large 3D
computational domains and in the presence of sidewall-angles and
corner-roundings.Comment: SPIE Europe Optical Metrology, Conference Proceeding
Efficient hierarchical approximation of high-dimensional option pricing problems
A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to show how an efficient discretisation can be achieved by hierarchical approximation as well as asymptotic expansions of the underlying continuous problem. The relation to a number of state-of-the-art methods is highlighted
Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures
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.Comment: 24 page
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