TY - JOUR A1 - Lopez-Fernandez, Maria A1 - Lubich, Christian A1 - Schädle, Achim T1 - Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory JF - SIAM J. Sci. Comput. Y1 - 2008 U6 - https://doi.org//10.1137/060674168 VL - 30 IS - 2 SP - 1015 EP - 1037 ER - TY - JOUR A1 - Lopez-Fernandez, Maria A1 - Palencia, Cesar A1 - Schädle, Achim T1 - A spectral order method for inverting sectorial Laplace transforms JF - SIAM J. Numer. Anal. Y1 - 2006 U6 - https://doi.org//10.1137/050629653 VL - 44 IS - 3 SP - 1332 EP - 1350 ER - TY - JOUR A1 - Kalkbrenner, T. A1 - Hakanson, U. A1 - Schädle, Achim A1 - Burger, Sven A1 - Henkel, C. A1 - Sandoghdar, V. T1 - Optical microscopy using the spectral modifications of a nano-antenna JF - Phys. Rev. Lett. Y1 - 2005 U6 - https://doi.org/10.1103/PhysRevLett.95.200801 VL - 95 SP - 200801 ER - TY - CHAP A1 - Schädle, Achim A1 - Zschiedrich, Lin ED - Widlund, Olof ED - Keyes, David T1 - Additive Schwarz method for scattering problems using the PML method at interfaces T2 - Domain Decomposition Methods in Science and Engineering XVI Y1 - 2007 VL - 55 SP - 205 EP - 212 PB - Springer ER - TY - JOUR A1 - Schädle, Achim A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Klose, Roland A1 - Schmidt, Frank T1 - Domain Decomposition Method for Maxwell’s Equations JF - J. Comput. Phys. Y1 - 2007 U6 - https://doi.org/10.1016/j.jcp.2007.04.017 VL - 226 SP - 477 EP - 493 ER - TY - JOUR A1 - Schmidt, Frank A1 - Hohage, Thorsten A1 - Klose, Roland A1 - Schädle, Achim A1 - Zschiedrich, Lin T1 - Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain JF - J. Comput. Appl. Math. Y1 - 2008 U6 - https://doi.org/10.1016/j.cam.2007.04.046 VL - 218 IS - 1 SP - 61 EP - 69 ER - TY - JOUR A1 - Ruprecht, Daniel A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Transparent boundary conditions for time-dependent problems JF - SIAM J. Sci. Comput. Y1 - 2008 U6 - https://doi.org/10.1137/070692637 VL - 30 IS - 5 SP - 2358 EP - 2385 ER - TY - JOUR A1 - Schädle, Achim A1 - López-Fernández, María A1 - Lubich, Christian T1 - Fast and oblivious convolution quadrature JF - SIAM J. Sci. Comput. Y1 - 2006 U6 - https://doi.org/http://dx.doi.org/10.1137/050623139 VL - 28 IS - 2 SP - 421 EP - 438 ER - TY - CHAP A1 - Schädle, Achim A1 - Ruprecht, Daniel A1 - Schmidt, Frank ED - et.al., N. Biggs T1 - Transparent boundary conditions - the pole condition approach T2 - Proceedings of Waves 2007 Y1 - 2007 SP - 301 EP - 303 ER - TY - CHAP A1 - Schmidt, Frank A1 - Burger, Sven A1 - Schädle, Achim A1 - Klose, Roland T1 - Finite element methods for optical device design T2 - Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices Y1 - 2005 U6 - https://doi.org/10.1109/NUSOD.2005.1518133 SP - 57 EP - 58 ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank ED - Sidorin, Y. ED - Wächter, Christoph T1 - JCMmode: an adaptive finite element solver for the computation of leaky modes T2 - Integrated Optics: Devices, Materials, and Technologies IX Y1 - 2005 U6 - https://doi.org/10.1117/12.590372 VL - 5728 SP - 192 EP - 202 PB - Proc. SPIE ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schädle, Achim A1 - Schmidt, Frank ED - Levinson, Harry ED - Dusa, Mircea T1 - A rigorous finite-element domain decomposition method for electromagnetic near field simulations T2 - Optical Microlithography XXI Y1 - 2008 U6 - https://doi.org/10.1117/12.771989 VL - 6924 PB - SPIE ER - TY - CHAP A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schädle, Achim A1 - Schmidt, Frank T1 - Domain decomposition method for electromagnetic scattering problems: application to EUV lithography T2 - Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices Y1 - 2005 U6 - https://doi.org/10.1109/NUSOD.2005.1518132 SP - 55 EP - 56 ER - TY - JOUR A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank T1 - A new finite element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D JF - J. Comput. Appl. Math. Y1 - 2006 U6 - https://doi.org/10.1016/j.cam.2005.03.047 VL - 188 SP - 12 EP - 32 ER - TY - GEN A1 - Burger, Sven A1 - Klose, Roland A1 - Schädle, Achim A1 - Zschiedrich, Lin T1 - HelmPole - A finite element solver for scattering problems on unbounded domains: Implementation based on PML N2 - 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. T3 - ZIB-Report - 03-38 KW - Helmholtz equation KW - finite element method KW - perfectly matched layer Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7609 ER - TY - GEN A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank T1 - A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D N2 - 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. T3 - ZIB-Report - 03-44 KW - transparent boundary conditions KW - perfectly matched layer KW - pole condition Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-7662 ER - TY - GEN A1 - Schädle, Achim A1 - Lopez-Fernandez, Maria A1 - Lubich, Christian T1 - Fast and oblivious convolution quadrature N2 - 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. T3 - ZIB-Report - 05-09 KW - convolution KW - numerical integration KW - Runge-Kutta methods KW - Volterra integral equation KW - anomalous diffusion Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8437 ER - TY - GEN A1 - Lopez-Fernandez, Maria A1 - Lubich, Christian A1 - Palencia, Cesar A1 - Schädle, Achim T1 - Fast Runge-Kutta approximation of inhomogeneous parabolic equations N2 - The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\varepsilon$, by solving only $$O\Big(\log N\, \log \frac1\varepsilon \Big) $$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm. T3 - ZIB-Report - 05-10 KW - parabolic equation KW - Runge-Kutta methods Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8443 ER - TY - JOUR A1 - Antoine, Xavier A1 - Arnold, Anton A1 - Besse, Christophe A1 - Ehrhardt, Matthias A1 - Schädle, Achim T1 - A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations JF - Commun. Comput. Phys. Y1 - 2008 UR - http://www.global-sci.com/openaccess/v4_729.pdf VL - 4 SP - 729 EP - 796 ER - TY - CHAP A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Klose, Roland A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Enkrich, Christian A1 - Linden, S. A1 - Wegener, M. A1 - Soukoulis, C. ED - Szoplik, T. ED - Özbay, E. ED - Soukoulis, C. ED - Zheludev, N. T1 - Numerical Investigation of Light Scattering off Split-Ring Resonators T2 - Metamaterials Y1 - 2005 U6 - https://doi.org/10.1117/12.622184 VL - 5955 SP - 18 EP - 26 PB - Proc. SPIE ER -