@misc{SchaedleZschiedrich2005, author = {Sch{\"a}dle, Achim and Zschiedrich, Lin}, title = {Additive Schwarz method for scattering problems using the PML method at interfaces}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8613}, number = {05-27}, year = {2005}, abstract = {Scattering problems in integrated optics can be modeled in simple cases by the Helmholtz equation. The computational domain is truncated by a non-reflecting boundary condition. We investigate Schwarz algorithms with a sort of DtN operator, realized by the PML-method, at the interfaces of the sub-domains as an iterative solver.}, language = {en} } @misc{LopezFernandezLubichSchaedle2006, author = {Lopez-Fernandez, Maria and Lubich, Christian and Sch{\"a}dle, Achim}, title = {Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory}, doi = {10.1137/060674168}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-9399}, number = {06-45}, year = {2006}, abstract = {To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing \$N\$ steps requires only \$O(N\log N)\$ operations and \$O(\log N)\$ active memory, in place of \$O(N^2)\$ operations and \$O(N)\$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schr{\"o}dinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.}, language = {en} } @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{LopezFernandezPalenciaSchaedle2005, author = {Lopez-Fernandez, Maria and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {A spectral order method for inverting sectorial Laplace transforms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8607}, number = {05-26}, year = {2005}, abstract = {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.}, language = {en} } @article{HiptmairSchaedle2003, author = {Hiptmair, Ralf and Sch{\"a}dle, Achim}, title = {Non-reflecting boundary conditions for Maxwell's equations}, volume = {71}, journal = {Computing}, number = {3}, year = {2003}, language = {en} } @article{DollingKleinWegeneretal.2007, author = {Dolling, G. and Klein, M. and Wegener, M. and Sch{\"a}dle, Achim and Burger, Sven and Linden, S.}, title = {Negative beam displacement for negative-index photonic metamaterials}, volume = {15}, journal = {Optics Express}, number = {21}, doi = {10.1364/OE.15.014219}, pages = {14219 -- 14227}, year = {2007}, language = {en} } @article{DollingWegenerSchaedleetal.2006, author = {Dolling, G. and Wegener, M. and Sch{\"a}dle, Achim and Burger, Sven and Linden, S.}, title = {Observation of magnetization waves in negative-index photonic metamaterials}, volume = {89}, journal = {Appl. Phys. Lett.}, doi = {10.1063/1.2403905}, pages = {231118}, year = {2006}, language = {en} } @article{LopezFernandezLubichPalenciaetal.2005, author = {L{\´o}pez-Fern{\´a}ndez, Maria and Lubich, Christian and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {Fast Runge-Kutta approximation of inhomogeneous parabolic equations}, volume = {102}, journal = {Numer. Math.}, doi = {http://dx.doi.org/10.1007/s00211-005-0624-3}, pages = {277 -- 291}, year = {2005}, language = {en} } @article{LopezFernandezLubichSchaedle2008, author = {Lopez-Fernandez, Maria and Lubich, Christian and Sch{\"a}dle, Achim}, title = {Adaptive, Fast and Oblivious Convolution in Evolution Equations with Memory}, volume = {30}, journal = {SIAM J. Sci. Comput.}, number = {2}, doi = {/10.1137/060674168}, pages = {1015 -- 1037}, year = {2008}, language = {en} } @article{LopezFernandezPalenciaSchaedle2006, author = {Lopez-Fernandez, Maria and Palencia, Cesar and Sch{\"a}dle, Achim}, title = {A spectral order method for inverting sectorial Laplace transforms}, volume = {44}, journal = {SIAM J. Numer. Anal.}, number = {3}, doi = {/10.1137/050629653}, pages = {1332 -- 1350}, year = {2006}, language = {en} } @article{KalkbrennerHakansonSchaedleetal.2005, author = {Kalkbrenner, T. and Hakanson, U. and Sch{\"a}dle, Achim and Burger, Sven and Henkel, C. and Sandoghdar, V.}, title = {Optical microscopy using the spectral modifications of a nano-antenna}, volume = {95}, journal = {Phys. Rev. Lett.}, doi = {10.1103/PhysRevLett.95.200801}, pages = {200801}, year = {2005}, language = {en} } @inproceedings{SchaedleZschiedrich2007, author = {Sch{\"a}dle, Achim and Zschiedrich, Lin}, title = {Additive Schwarz method for scattering problems using the PML method at interfaces}, volume = {55}, booktitle = {Domain Decomposition Methods in Science and Engineering XVI}, editor = {Widlund, Olof and Keyes, David}, publisher = {Springer}, pages = {205 -- 212}, year = {2007}, language = {en} } @article{SchaedleZschiedrichBurgeretal.2007, 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}, volume = {226}, journal = {J. Comput. Phys.}, doi = {10.1016/j.jcp.2007.04.017}, pages = {477 -- 493}, year = {2007}, language = {en} } @article{SchmidtHohageKloseetal.2008, author = {Schmidt, Frank and Hohage, Thorsten and Klose, Roland and Sch{\"a}dle, Achim and Zschiedrich, Lin}, title = {Pole condition: A numerical method for Helmholtz-type scattering problems with inhomogeneous exterior domain}, volume = {218}, journal = {J. Comput. Appl. Math.}, number = {1}, doi = {10.1016/j.cam.2007.04.046}, pages = {61 -- 69}, year = {2008}, language = {en} } @article{RuprechtSchaedleSchmidtetal.2008, author = {Ruprecht, Daniel and Sch{\"a}dle, Achim and Schmidt, Frank and Zschiedrich, Lin}, title = {Transparent boundary conditions for time-dependent problems}, volume = {30}, journal = {SIAM J. Sci. Comput.}, number = {5}, doi = {10.1137/070692637}, pages = {2358 -- 2385}, year = {2008}, language = {en} } @article{SchaedleLopezFernandezLubich2006, author = {Sch{\"a}dle, Achim and L{\´o}pez-Fern{\´a}ndez, Mar{\´i}a and Lubich, Christian}, title = {Fast and oblivious convolution quadrature}, volume = {28}, journal = {SIAM J. Sci. Comput.}, number = {2}, doi = {http://dx.doi.org/10.1137/050623139}, pages = {421 -- 438}, year = {2006}, language = {en} } @inproceedings{SchaedleRuprechtSchmidt2007, author = {Sch{\"a}dle, Achim and Ruprecht, Daniel and Schmidt, Frank}, title = {Transparent boundary conditions - the pole condition approach}, booktitle = {Proceedings of Waves 2007}, editor = {et.al., N. Biggs}, pages = {301 -- 303}, year = {2007}, language = {en} } @inproceedings{SchmidtBurgerSchaedleetal.2005, author = {Schmidt, Frank and Burger, Sven and Sch{\"a}dle, Achim and Klose, Roland}, title = {Finite element methods for optical device design}, booktitle = {Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices}, doi = {10.1109/NUSOD.2005.1518133}, pages = {57 -- 58}, year = {2005}, language = {en} } @inproceedings{ZschiedrichBurgerKloseetal.2005, author = {Zschiedrich, Lin and Burger, Sven and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {JCMmode: an adaptive finite element solver for the computation of leaky modes}, volume = {5728}, booktitle = {Integrated Optics: Devices, Materials, and Technologies IX}, editor = {Sidorin, Y. and W{\"a}chter, Christoph}, publisher = {Proc. SPIE}, doi = {10.1117/12.590372}, pages = {192 -- 202}, year = {2005}, language = {en} } @inproceedings{ZschiedrichBurgerSchaedleetal.2008, author = {Zschiedrich, Lin and Burger, Sven and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A rigorous finite-element domain decomposition method for electromagnetic near field simulations}, volume = {6924}, booktitle = {Optical Microlithography XXI}, editor = {Levinson, Harry and Dusa, Mircea}, publisher = {SPIE}, doi = {10.1117/12.771989}, year = {2008}, language = {en} }