A spectral order method for inverting sectorial Laplace transforms

Laplace transforms which admit a holomorphic extension to some sector strictly containing the right half plane and exhibiting a potential behavior are considered. A spectral order, parallelizable method for their numerical inversion is proposed. The method takes into account the available information about the errors arising in the evaluations. Several numerical illustrations are provided.Comment: 17 pages 11 figure

Fast and oblivious convolution quadrature

We give an algorithm to compute $N$ steps of a convolution quadrature approximation to a continuous temporal convolution using only $O(N \log N)$ multiplications and $O(\log N)$ active memory. The method does not require evaluations of the convolution kernel, but instead $O(\log N)$ evaluations of its Laplace transform, which is assumed sectorial. The algorithm can be used for the stable numerical solution with quasi-optimal complexity of linear and nonlinear integral and integro-differential equations of convolution type. In a numerical example we apply it to solve a subdiffusion equation with transparent boundary conditions

A Rigorous Finite-Element Domain Decomposition Method for Electromagnetic Near Field Simulations

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an accurate modeling of complicated geometrical features. However, from a numerical point of view solving the arising system of linear equations is very demanding even for medium sized 3D domains. In numerics, a domain decomposition method is a commonly used strategy to overcome this problem. Within this approach the overall computational domain is split up into smaller domains and interface conditions are used to assure continuity of the electromagnetic field. Unfortunately, standard implementations of the domain decomposition method as developed for electrostatic problems are not appropriate for wave propagation problems. In an earlier paper we therefore proposed a domain decomposition method adapted to electromagnetic field wave propagation problems. In this paper we apply this method to 3D mask simulation.Comment: 9 pages, 7 figures, SPIE conference Advanced Lithography / Optical Microlithography XXI (2008

Non-Reflecting Boundary Conditions for Maxwell's Equations

A new discrete non-reflecting boundary condition for the time-dependent Maxwell equations describing the propagation of an electromagnetic wave in an infinite homogenous lossless rectangular waveguide with perfectly conducting walls is presented. It is derived from a virtual spatial finite difference discretization of the problem on the unbounded domain. Fourier transforms are used to decouple transversal modes. A judicious combination of edge based nodal values permits us to recover a simple structure in the Laplace domain. Using this, it is possible to approximate the convolution in time by a similar fast convolution algorithm as for the standard wave equatio

Open Boundaries for the Nonlinear Schrodinger Equation

We present a new algorithm, the Time Dependent Phase Space Filter (TDPSF) which is used to solve time dependent Nonlinear Schrodinger Equations (NLS). The algorithm consists of solving the NLS on a box with periodic boundary conditions (by any algorithm). Periodically in time we decompose the solution into a family of coherent states. Coherent states which are outgoing are deleted, while those which are not are kept, reducing the problem of reflected (wrapped) waves. Numerical results are given, and rigorous error estimates are described. The TDPSF is compatible with spectral methods for solving the interior problem. The TDPSF also fails gracefully, in the sense that the algorithm notifies the user when the result is incorrect. We are aware of no other method with this capability.Comment: 21 pages, 4 figure

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

Innovative Wandbausysteme aus Holz unter Erdbebeneinwirkungen

Neben der bekannten Holztafel- und Holzskelettbauweise entwickelten sich in den letzten Jahren verschiedene innovative Wandbausysteme aus Holz, von denen zwei im Rahmen dieser Arbeit hinsichtlich ihrer Eigenschaften unter Erdbeben untersucht wurden. In experimentellen Untersuchungen wurden einzelne Verbindungen und auch ganze Wandscheiben der Bauweisen untersucht. Das Verhalten von Verbindungen und Wandscheiben kann mit den erstellten numerischen Modellen berechnet werden