@misc{Schmidt1998, author = {Schmidt, Frank}, title = {An Alternative Derivation of the Exact DtN-Map on a Circle}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3752}, number = {SC-98-32}, year = {1998}, abstract = {The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of time-harmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace transformation techniques, where the asymptotic Sommerfeld radiation condition is reformulated accordingly.}, language = {en} } @book{AbbinkBaermannBešinovicetal.2018, author = {Abbink, Erwin and B{\"a}rmann, Andreas and Bešinovic, Nikola and Bohlin, Markus and Cacchiani, Valentina and Caimi, Gabrio and de Fabris, Stefano and Dollevoet, Twan and Fischer, Frank and F{\"u}genschuh, Armin and Galli, Laura and Goverde, Rob M.P. and Hansmann, Ronny and Homfeld, Henning and Huisman, Dennis and Johann, Marc and Klug, Torsten and T{\"o}rnquist Krasemann, Johanna and Kroon, Leo and Lamorgese, Leonardo and Liers, Frauke and Mannino, Carlo and Medeossi, Giorgio and Pacciarelli, Dario and Reuther, Markus and Schlechte, Thomas and Schmidt, Marie and Sch{\"o}bel, Anita and Sch{\"u}lldorf, Hanno and Stieber, Anke and Stiller, Sebastian and Toth, Paolo and Zimmermann, Uwe}, title = {Handbook of Optimization in the Railway Industry}, volume = {268}, editor = {Bornd{\"o}rfer, Ralf and Klug, Torsten and Lamorgese, Leonardo and Mannino, Carlo and Reuther, Markus and Schlechte, Thomas}, publisher = {Springer Verlag}, isbn = {978-3-319-72152-1}, doi = {10.1007/978-3-319-72153-8}, year = {2018}, abstract = {This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation}, language = {en} } @phdthesis{Schmidt2002, author = {Schmidt, Frank}, title = {A New Approach to Coupled Interior-Exterior Helmholtz-Type Problems: Theory and Algorithms}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7128}, number = {02-45}, year = {2002}, abstract = {The work presents a new approach to the numerical solution of time-harmonic and time-dependent scattering problems. We replace Sommerfeld's radiation condition valid for the Helmholtz equation by a more general concept called pole condition. The pole condition is based on the Laplace transform of the exterior solution and allows a characterization of outgoing waves. Both new insight into the analysis of scattering problems as well as new numerical algorithms are obtained.}, language = {en} } @misc{CordesWeberSchmidtEhrenberg2002, author = {Cordes, Frank and Weber, Marcus and Schmidt-Ehrenberg, Johannes}, title = {Metastable Conformations via successive Perron-Cluster Cluster Analysis of dihedrals}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7074}, number = {02-40}, year = {2002}, abstract = {Decomposition of the high dimensional conformational space of bio-molecules into metastable subsets is used for data reduction of long molecular trajectories in order to facilitate chemical analysis and to improve convergence of simulations within these subsets. The metastability is identified by the Perron-cluster cluster analysis of a Markov process that generates the thermodynamic distribution. A necessary prerequisite of this analysis is the discretization of the conformational space. A combinatorial approach via discretization of each degree of freedom will end in the so called ''curse of dimension''. In the following paper we analyze Hybrid Monte Carlo simulations of small, drug-like biomolecules and focus on the dihedral degrees of freedom as indicators of conformational changes. To avoid the ''curse of dimension'', the projection of the underlying Markov operator on each dihedral is analyzed according to its metastability. In each decomposition step of a recursive procedure, those significant dihedrals, which indicate high metastability, are used for further decomposition. The procedure is introduced as part of a hierarchical protocol of simulations at different temperatures. The convergence of simulations within metastable subsets is used as an ''a posteriori'' criterion for a successful identification of metastability. All results are presented with the visualization program AmiraMol.}, language = {en} } @misc{ZschiedrichKloseSchaedleetal.2003, author = {Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2D}, doi = {10.1016/j.cam.2005.03.047}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7662}, number = {03-44}, year = {2003}, abstract = {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.}, language = {en} } @misc{MayEisenhardtSchmidtEhrenbergetal.2003, author = {May, Andreas and Eisenhardt, Steffen and Schmidt-Ehrenberg, Johannes and Cordes, Frank}, title = {Rigid body docking for Virtual Screening}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-7690}, number = {03-47}, year = {2003}, abstract = {A recently developed algorithm allows Rigid Body Docking of ligands to proteins, regardless of the accessibility and location of the binding site. The Docking procedure is divided into three subsequent optimization phases, two of which utilize rigid body dynamics. The last one is applied with the ligand already positioned inside the binding pocket and accounts for full flexibility. Initially, a combination of geometrical and force-field based methods is used as a Coarse Docking strategy, considering only Lennard-Jones interactions between the target and pharmaceutically relevant atoms or functional groups. The protein is subjected to a Hot Spot Analysis, which reveals points of high affinity in the protein environment towards these groups. The hot spots are distributed into different subsets according to their group affiliation. The ligand is described as a complementary point set, consisting of the same subsets. Both sets are matched in \$\mathrm{I\!R}^{3}\$, by superimposing members of the same subsets. In the first instance, steric inhibition is nearly neglected, preventing the system's trajectory from trapping in local minima and thus from finding false positive solutions. Hence the exact location of the binding site can be determined fast and reliably without any additional information. Subsequently, errors resulting from approximations are minimized via finetuning, this time considering both Lennard-Jones and Coulomb forces. Finally, the potential energy of the whole complex is minimized. In a first evaluation, results are rated by a reduced scoring function considering only noncovalent interaction energies. Exemplary Screening results will be given for specific ligands.}, language = {en} } @misc{YevickFrieseSchmidt2000, author = {Yevick, David and Friese, Tilmann and Schmidt, Frank}, title = {A Comparison of Transparent Boundary Conditions for the Fresnel Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5738}, number = {00-05}, year = {2000}, abstract = {We establish the relationship between the transparent boundary condition (BPP) of Baskakov and Popov [Wave Motion 14 (1991) 121-128] and Pakpadakis et. al. [J. Acoust. Soc. Am. 92 (1992) 2030-2038] and a second boundary condition (SDY) introduced by Schmidt and Deuflhard [Comp. Math. Appl. 29 (1995) 53-76] and Schmidt and Yevick [J. Compu. Phys. 134 (1997) 96-107], that is explicitly tailored to the form of the underlying numerical propagation scheme. Our analysis demonstrates that if the domain is first discretized in the propagation direction, the SDY expression can be obtained by applying the exact sequence of steps used to derive the BPP procedure. The BPP method is thus an approximate realization of the computationally far simpler and unconditionally stable SDY boundary condition.}, language = {en} } @misc{Schmidt2000, author = {Schmidt, Frank}, title = {Discrete Nonreflecting Boundary Conditions for the Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5744}, number = {00-06}, year = {2000}, abstract = {We derive exact discrete nonreflecting boundary conditions for time-harmonic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior problem as an initial value problem with initial data given on the boundary of the computational domain. The solution of the exterior problem is obtained via Laplace transformation techniques which supply the boundary conditions in terms of discrete Dirichlet-to-Neumann operators.}, language = {en} } @misc{Schmidt1995, author = {Schmidt, Frank}, title = {Simultaneous Computation of the Lowest Eigenvalue and Eigenvectors of the Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-5281}, number = {TR-95-13}, year = {1995}, abstract = {This report collects a number of proposals to determine the lowest eigensolutions of the scalar Helmholtz equation. The basic routine of all discussed algorithms is the standard Rayleigh quotient minimization process. The minimization is performed in a direct multilevel manner, and a subspace iteration is used to determine simultaneously a couple of eigensolutions. As smoother the nonlinear Gauß-Seidel, the nonlinear conjugate gradient method and a preconditioned version of this method are compared with respect to their efficiency. The numerical examples are based on realistic 1D and 2D models of integrated optics components.}, language = {en} } @misc{FrieseSchmidtYevick1999, author = {Friese, Tilman and Schmidt, Frank and Yevick, David}, title = {Transparent Boundary Conditions for a Wide-Angle Approximation of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4345}, number = {SC-99-45}, year = {1999}, abstract = {We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach.}, language = {en} } @misc{SchmidtFrieseYevick1999, author = {Schmidt, Frank and Friese, Tilmann and Yevick, David}, title = {Transparent Boundary Conditions for Split-Step Pade Approximations of the One-Way Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4353}, number = {SC-99-46}, year = {1999}, abstract = {In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by Schmidt and Deuflhard {[}Comp. Math. Appl. 29 (1995) 53-76{]} and Schmidt and Yevick {[}J. Comput. Phys. 134 (1997) 96-107{]} to propagation methods based on arbitrary Pad\'e approximations to the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method.}, language = {en} } @misc{DeuflhardFrieseSchmidt1997, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank}, title = {A Nonlinear Multigrid Eigenproblem Solver for the Complex Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3240}, number = {SC-97-55}, year = {1997}, abstract = {The paper is motivated by the need for a fast robust adaptive multigrid method to solve complex Helmholtz eigenvalue problems arising from the design of optical chips. A nonlinear multigrid method is developed, which can be regarded as an extension of a previous adaptive Rayleigh quotient minimization method for selfadjoint Helmholtz eigenproblems. Since the complex Helmholtz operator is just a compact nonselfadjoint perturbation of a selfadjoint operator, linear algebra techniques like Schur decomposition can be extended from the finite dimensional case. The efficiency of the derived adaptive nonlinear multigrid method is illustrated by computations for a technologically relevant integrated optics component containing Multi Quantum Well Layers.}, language = {en} } @misc{Schmidt1997, author = {Schmidt, Frank}, title = {Construction of Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3292}, number = {SC-97-60}, year = {1997}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for time-discretized one-dimensional Schr{\"o}dinger type equations. The main tool of construction is the discrete counterpart to Mikusi\'nski's continuous algebraic operator approach. Existing techniques are simplified and generalized. Both adaptive time-steps and time-dependent exterior potentials are taken into account.}, language = {en} } @article{BlomeMcPeakBurgeretal.2014, author = {Blome, Mark and McPeak, Kevin and Burger, Sven and Schmidt, Frank and Norris, David}, title = {Back-reflector design in thin-film silicon solar cells by rigorous 3D light propagation modeling}, volume = {33}, journal = {COMPEL: Int. J. Comput. Mathem. Electr. Electron. Eng.}, number = {4}, doi = {10.1108/COMPEL-12-2012-0367}, pages = {1282 -- 1295}, year = {2014}, language = {en} } @inproceedings{BurgerZschiedrichSchmidtetal.2008, author = {Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and Evanschitzky, Peter and Erdmann, Andreas}, title = {Benchmark of rigorous methods for electromagnetic field simulation}, volume = {7122}, booktitle = {Photomask Technology}, editor = {Kawahira, H. and Zurbrick, L. S.}, publisher = {Proc. SPIE}, doi = {10.1117/12.801248}, pages = {71221}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2011, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Rigorous simulations of 3D patterns on extreme ultraviolet lithography masks}, volume = {8083}, booktitle = {Modelling Aspects in Optical Metrology III}, editor = {Bodermann, Bernd}, publisher = {Proc. SPIE}, doi = {10.1117/12.889831}, pages = {80831B}, year = {2011}, language = {en} } @inproceedings{BurgerPomplunSchmidtetal.2011, author = {Burger, Sven and Pomplun, Jan and Schmidt, Frank and Zschiedrich, Lin}, title = {Finite-element method simulations of high-Q nanocavities with 1D photonic bandgap}, volume = {7933}, booktitle = {Physics and Simulation of Optoelectronic Devices XIX}, publisher = {Proc. SPIE}, doi = {10.1117/12.875044}, pages = {79330T}, year = {2011}, language = {en} } @incollection{BurgerZschiedrichKettneretal.2008, author = {Burger, Sven and Zschiedrich, Lin and Kettner, Benjamin and Schmidt, Frank}, title = {FEM simulation of light scattering by nonspherical objects}, booktitle = {Mie Theory 1908 - 2008}, editor = {Hergert, W. and Wriedt, T.}, publisher = {Universit{\"a}t Bremen}, pages = {82 -- 83}, year = {2008}, language = {en} } @inproceedings{BurgerZschiedrichKloseetal.2005, author = {Burger, Sven and Zschiedrich, Lin and Klose, Roland and Sch{\"a}dle, Achim and Schmidt, Frank and Enkrich, Christian and Linden, S. and Wegener, M. and Soukoulis, C.}, title = {Numerical Investigation of Light Scattering off Split-Ring Resonators}, volume = {5955}, booktitle = {Metamaterials}, editor = {Szoplik, T. and {\"O}zbay, E. and Soukoulis, C. and Zheludev, N.}, publisher = {Proc. SPIE}, doi = {10.1117/12.622184}, pages = {18 -- 26}, year = {2005}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2009, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank and Kettner, Benjamin and Lockau, D.}, title = {3D Finite-Element Simulations of Enhanced Light Transmission Through Arrays of Holes in Metal Films}, volume = {7390}, booktitle = {Numerical Methods in Optical Metrology}, publisher = {Proc. SPIE}, doi = {10.1117/12.827543}, pages = {73900H}, year = {2009}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2010, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {Finite element method for accurate 3D simulation of plasmonic waveguides}, volume = {7604}, booktitle = {Integrated Optics: Devices, Materials, and Technologies XIV}, publisher = {Proc. SPIE}, doi = {10.1117/12.841995}, pages = {76040F}, year = {2010}, language = {en} } @inproceedings{BurgerZschiedrichPomplunetal.2008, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank}, title = {JCMsuite: An Adaptive FEM Solver for Precise Simulations in Nano-Optics}, booktitle = {Integrated Photonics and Nanophotonics Research and Applications}, publisher = {Optical Society of America}, doi = {10.1364/IPNRA.2008.ITuE4}, pages = {ITuE4}, year = {2008}, language = {en} }