@article{Schmidt1993, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, volume = {11}, journal = {IEEE Journal of Lightwave Technology}, number = {9}, pages = {1425 -- 1435}, year = {1993}, language = {en} } @inproceedings{ZschiedrichBurgerKettneretal.2006, author = {Zschiedrich, Lin and Burger, Sven and Kettner, Benjamin and Schmidt, Frank}, title = {Advanced Finite Element Method for Nano-Resonators}, volume = {6115}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/physics/0601025}, doi = {10.1117/12.646252}, pages = {611515}, year = {2006}, 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{ZschiedrichBurgerPomplunetal.2007, author = {Zschiedrich, Lin and Burger, Sven and Pomplun, Jan and Schmidt, Frank}, title = {Goal oriented adaptive finite element method for precise simulation of optical components}, volume = {6475}, booktitle = {Proc. SPIE, Integrated Optics}, editor = {Sidorin, Y. and Waechter, Ch.}, pages = {64750H}, year = {2007}, 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} } @inproceedings{ZschiedrichBurgerSchaedleetal.2005, author = {Zschiedrich, Lin and Burger, Sven and Sch{\"a}dle, Achim and Schmidt, Frank}, title = {Domain decomposition method for electromagnetic scattering problems: application to EUV lithography}, booktitle = {Proceedings of the 5th International Conference on Numerical Simulation of Optoelectronic devices}, doi = {10.1109/NUSOD.2005.1518132}, pages = {55 -- 56}, year = {2005}, language = {en} } @inproceedings{ZschiedrichGreinerPomplunetal.2012, author = {Zschiedrich, Lin and Greiner, Horst and Pomplun, Jan and Hammerschmidt, Martin and Burger, Sven and Schmidt, Frank}, title = {FEM simulations of light extraction from nanostructured organic light-emitting diodes}, booktitle = {Renewable Energy and the Environment Optics and Photonics Congress}, publisher = {Optical Society of America}, doi = {10.1364/SOLED.2012.LT2B.5}, pages = {LT2B.5}, year = {2012}, language = {en} } @article{ZschiedrichKloseSchaedleetal.2006, 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}, volume = {188}, journal = {J. Comput. Appl. Math.}, doi = {10.1016/j.cam.2005.03.047}, pages = {12 -- 32}, year = {2006}, language = {en} } @inproceedings{ZschiedrichSchmidt2008, author = {Zschiedrich, Lin and Schmidt, Frank}, title = {Finite element simulation of light propagation in non-periodic mask patterns}, volume = {7028}, booktitle = {Photomask and Next-Generation Lithography Mask Technology XV}, editor = {Horiuchi, Toshiyuki}, publisher = {SPIE}, year = {2008}, language = {en} } @article{YevickFrieseSchmidt2001, author = {Yevick, David and Friese, T. and Schmidt, Frank}, title = {A Comparison of Transparent Boundary Conditions for the Fresnel Equation}, volume = {168}, journal = {J. Comput. Phys.}, number = {2}, pages = {433 -- 444}, year = {2001}, language = {en} } @article{YevickYuSchmidt1997, author = {Yevick, David and Yu, J. and Schmidt, Frank}, title = {Analytic Studies of Absorbing and Impedance-Matched Boundary Layers}, volume = {9}, journal = {IEEE Photonics Technology Letters}, doi = {10.1109/68.554499}, pages = {73 -- 75}, year = {1997}, language = {en} } @article{ArellanoMingaleevKoltchanovetal.2013, author = {Arellano, Cristina and Mingaleev, Sergei F. and Koltchanov, Igor and Richter, Andre and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Efficient design of photonic integrated circuits (PICs) by combining device- and circuit- level simulation tools}, volume = {8627}, journal = {Proc. SPIE}, doi = {10.1117/12.2004378}, pages = {862711}, year = {2013}, language = {en} } @article{BurgerZschiedrichPomplunetal.2013, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Blome, Mark and Schmidt, Frank}, title = {Advanced finite-element methods for design and analysis of nano-optical structures: Applications}, volume = {8642}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1304.4356}, doi = {10.1117/12.2001094}, pages = {864205}, year = {2013}, language = {en} } @article{HammerschmidtLockauBurgeretal.2013, author = {Hammerschmidt, Martin and Lockau, Daniel and Burger, Sven and Schmidt, Frank and Schwanke, Christoph and Kirner, Simon and Calnan, Sonya and Stannowski, Bernd and Rech, Bernd}, title = {FEM-based optical modeling of silicon thin-film tandem solar cells with randomly textured interfaces in 3D}, volume = {8620}, journal = {Proc. SPIE}, doi = {10.1117/12.2001789}, pages = {86201H}, year = {2013}, language = {en} } @article{BurgerZschiedrichPomplunetal.2013, author = {Burger, Sven and Zschiedrich, Lin and Pomplun, Jan and Schmidt, Frank and Bodermann, Bernd}, title = {Fast simulation method for parameter reconstruction in optical metrology}, volume = {8681}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1304.4367}, doi = {10.1117/12.2011154}, pages = {868119}, year = {2013}, language = {en} } @article{ZschiedrichGreinerBurgeretal.2013, author = {Zschiedrich, Lin and Greiner, Horst and Burger, Sven and Schmidt, Frank}, title = {Numerical analysis of nanostructures for enhanced light extraction from OLEDs}, volume = {8641}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1304.4380}, doi = {10.1117/12.2001132}, pages = {86410B}, year = {2013}, language = {en} } @article{BeckerLockauSontheimeretal.2012, author = {Becker, Christiane and Lockau, Daniel and Sontheimer, Tobias and Schubert-Bischoff, Peter and Rudigier-Voigt, Eveline and Bockmeyer, Matthias and Schmidt, Frank and Rech, Bernd}, title = {Large-area 2D periodic crystalline silicon nanodome arrays on nanoimprinted glass exhibiting photonic band structure effects}, volume = {23}, journal = {Nanotechnology}, number = {13}, doi = {10.1088/0957-4484/23/13/135302}, pages = {135302}, year = {2012}, language = {en} } @article{LockauSontheimerBeckeretal.2013, author = {Lockau, Daniel and Sontheimer, Tobias and Becker, Christiane and Rudigier-Voigt, Eveline and Schmidt, Frank and Rech, Bernd}, title = {Nanophotonic light trapping in 3-dimensional thin-film silicon architectures}, volume = {21}, journal = {Opt. Express}, doi = {10.1364/OE.21.000A42}, pages = {A42}, year = {2013}, language = {en} } @article{LockauSontheimerPreideletal.2013, author = {Lockau, Daniel and Sontheimer, Tobias and Preidel, Veit and Becker, Christiane and Ruske, Florian and Schmidt, Frank and Rech, Bernd}, title = {Optical properties and Limits of a Large-Area Periodic Nanophotonic Light Trapping Design for Polycrystalline Silicon Thin Film Solar Cells}, volume = {1493}, journal = {MRS Proceedings}, doi = {10.1557/opl.2013.28}, pages = {59 -- 64}, year = {2013}, language = {en} } @inproceedings{WohlfeilBurgerStamatiadisetal.2014, author = {Wohlfeil, Benjamin and Burger, Sven and Stamatiadis, Christos and Pomplun, Jan and Schmidt, Frank and Zimmermann, Lars and Petermann, Klaus}, title = {Numerical Simulation of Grating Couplers for Mode Multiplexed Systems}, volume = {8988}, booktitle = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1403.2288}, doi = {10.1117/12.2044461}, pages = {89880K}, year = {2014}, language = {en} } @inproceedings{ZschiedrichMaerzBurgeretal.2006, author = {Zschiedrich, Lin and M{\"a}rz, Reinhard and Burger, Sven and Schmidt, Frank}, title = {Efficient 3D Finite Element Simulation of Fiber-Chip Coupling}, booktitle = {Integrated Photonics Research and Applications/Nanophotonics}, doi = {10.1364/IPRA.2006.ITuF1}, pages = {ITuF1}, year = {2006}, language = {en} } @incollection{PomplunZschiedrichKloseetal.2008, author = {Pomplun, Jan and Zschiedrich, Lin and Klose, Roland and Schmidt, Frank and Burger, Sven}, title = {Finite Element Simulation of Radiation Losses in Photonic Crystal Fibers}, booktitle = {Nanophotonic Materials: Photonic Crystals, Plasmonics, and Metamaterials}, publisher = {Wiley-VCH}, doi = {10.1002/9783527621880.ch17}, pages = {313 -- 331}, year = {2008}, language = {en} } @inproceedings{WenzelCrumpEkhteraeietal.2011, author = {Wenzel, Hans and Crump, Paul and Ekhteraei, Hossein and Schultz, Christoph M. and Pomplun, Jan and Burger, Sven and Zschiedrich, Lin and Schmidt, Frank and Erbert, G{\"o}tz}, title = {Theoretical and experimental analysis of the lateral modes of high-power broad-area lasers}, booktitle = {Numerical Simulation of Optoelectronic Devices}, doi = {10.1109/NUSOD.2011.6041183}, pages = {143 -- 144}, year = {2011}, language = {en} } @article{SontheimerPreidelLockauetal.2013, author = {Sontheimer, Tobias and Preidel, Veit and Lockau, Daniel and Back, Franziska and Rudigier-Voigt, Eveline and L{\"o}chel, Bernd and Erko, Alexei and Schmidt, Frank and Schnegg, Alexander and Lips, Klaus and Becker, Christiane and Rech, Bernd}, title = {Correlation between structural and opto-electronic characteristics of crystalline Si microhole arrays for photonic light management}, volume = {114}, journal = {Journal of Applied Physics}, number = {17}, publisher = {AIP Publishing}, doi = {10.1063/1.4829008}, pages = {173513}, year = {2013}, language = {en} } @article{LockauSontheimerPreideletal.2014, author = {Lockau, Daniel and Sontheimer, Tobias and Preidel, Veit and Ruske, Florian and Hammerschmidt, Martin and Becker, Christiane and Schmidt, Frank and Rech, Bernd}, title = {Advanced microhole arrays for light trapping in thin film silicon solar cells}, volume = {125}, journal = {Solar Energy Materials and Solar Cells}, doi = {10.1016/j.solmat.2013.11.024}, pages = {298 -- 304}, year = {2014}, language = {en} } @article{KirnerHammerschmidtSchwankeetal.2014, author = {Kirner, Simon and Hammerschmidt, Martin and Schwanke, Christoph and Lockau, Daniel and Calnan, Sonya and Frijnts, Tim and Neubert, Sebastian and Sch{\"o}pke, Andreas and Schmidt, Frank and Zollondz, Jens-Hendrik and Heidelberg, Andreas and Stannowski, Bernd and Rech, Bernd and Schlatmann, Rutger}, title = {Implications of TCO Topography on Intermediate Reflector Design for a-Si/μc-Si Tandem Solar Cells — Experiments and Rigorous Optical Simulations}, volume = {4}, journal = {IEEE Journal of Photovoltaics}, number = {1}, doi = {10.1109/JPHOTOV.2013.2279204}, pages = {10 -- 15}, year = {2014}, language = {en} } @inproceedings{HammerschmidtPomplunBurgeretal.2014, author = {Hammerschmidt, Martin and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Adaptive sampling strategies for effcient parameter scans in nano-photonic device simulations}, volume = {8980}, booktitle = {Proc. SPIE}, publisher = {SPIE}, doi = {10.1117/12.2036363}, pages = {89801O}, year = {2014}, language = {en} } @inproceedings{HammerschmidtLockauZschiedrichetal.2014, author = {Hammerschmidt, Martin and Lockau, Daniel and Zschiedrich, Lin and Schmidt, Frank}, title = {Optical modelling of incoherent substrate light-trapping in silicon thin film multi-junction solar cells with finite elements and domain decomposition}, volume = {8980}, booktitle = {Proc. SPIE: Physics and Simulation of Optoelectronic Devices XXII}, publisher = {SPIE}, doi = {10.1117/12.2036346}, pages = {898007}, year = {2014}, language = {en} } @inproceedings{JaegerBarthHammerschmidtetal.2016, author = {J{\"a}ger, Klaus and Barth, Carlo and Hammerschmidt, Martin and Herrmann, Sven and Burger, Sven and Schmidt, Frank and Becker, Christiane}, title = {Sinusoidal Nanotextures for Enhanced Light Management in Thin-Film Solar Cells}, booktitle = {28th Workshop on Quantum Solar Energy Conversion - (QUANTSOL)}, editor = {European Society for Quantum Solar Energy Conversion,}, year = {2016}, language = {en} } @article{JaegerKoeppelBarthetal.2016, author = {J{\"a}ger, Klaus and K{\"o}ppel, Grit and Barth, Carlo and Hammerschmidt, Martin and Herrmann, Sven and Burger, Sven and Schmidt, Frank and Becker, Christiane}, title = {Sinusoidal gratings for optimized light management in c-Si thin-film solar cells}, volume = {9898}, journal = {Proc. SPIE}, doi = {10.1117/12.2225459}, pages = {989808}, year = {2016}, language = {en} } @incollection{KantnerHoehneKopruckietal.2020, author = {Kantner, Markus and H{\"o}hne, Theresa and Koprucki, Thomas and Burger, Sven and W{\"u}nsche, Hans-J{\"u}rgen and Schmidt, Frank and Mielke, Alexander and Bandelow, Uwe}, title = {Multi-dimensional modeling and simulation of semiconductor nanophotonic devices}, volume = {194}, booktitle = {Semiconductor Nanophotonics}, editor = {Kneissl, Michael and Knorr, Andreas and Reitzenstein, Stephan and Hoffmann, Axel}, publisher = {Springer}, address = {Cham}, doi = {10.1007/978-3-030-35656-9_7}, pages = {241 -- 283}, year = {2020}, language = {en} } @inproceedings{HiremathZschiedrichBurgeretal.2014, author = {Hiremath, Kirankumar and Zschiedrich, Lin and Burger, Sven and Schmidt, Frank}, title = {Finite elements based numerical solution of nonlocal hydrodynamic Drude model of nano-plasmonic scatterers}, booktitle = {12th International Conference on Fiber Optics and Photonics}, doi = {10.1364/PHOTONICS.2014.M3D.4}, pages = {M3D.4}, year = {2014}, language = {en} } @misc{DeuflhardFrieseSchmidtetal.1996, author = {Deuflhard, Peter and Friese, Tilmann and Schmidt, Frank and M{\"a}rz, Reinhard and Nolting, Hans-Peter}, title = {Effiziente Eigenmodenberechnung f{\"u}r den Entwurf integriert-optischer Chips}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2131}, number = {SC-96-02}, year = {1996}, abstract = {{\bf Efficient eigenmode computation for the design of integrated optical chips.}The paper deals with adaptive multigrid methods for 2D Helmholtz eigenvalue problems arising in the design of integrated optical chips. Typical features of the technological problem are its geometric complexity, its multiscale structure, the possible occurrence of eigenvalue clusters, and the necessity of quite stringent required relative error tolerances. For reasons of sheer computational complexity, multigrid methods must be used to solve the discretized eigenvalue problems and adaptive grids must be automatically constructed to avoid an undesirable blow-up of the required number of nodes for these accuracies. In view of the problem specifications, an adaptive multigrid method based on Rayleigh quotient minimization, simultaneous eigenspace iteration, and conjugate gradient method as smoother is carefully selected. Its performance in the numerical simulation of a component of a rather recent optical chip (heterodyne receiver of HHI) is documented.}, language = {de} } @misc{SchmidtYevick1996, author = {Schmidt, Frank and Yevick, David}, title = {Discrete Transparent Boundary Conditions for Schr{\"o}dinger-Type Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-2289}, number = {SC-96-17}, year = {1996}, abstract = {We present a general technique for constructing nonlocal transparent boundary conditions for one-dimensional Schr{\"o}dinger-type equations. Our method supplies boundary conditions for the \$\theta\$-family of implicit one-step discretizations of Schr{\"o}dinger's equation in time. The use of Mikusi\'nski's operator approach in time avoids direct and inverse transforms between time and frequency domains and thus implements the boundary conditions in a direct manner.}, language = {en} } @misc{SchmidtMaerz1995, author = {Schmidt, Frank and M{\"a}rz, Reinhard}, title = {On the Reference Wave Vector pf Paraxial Helmholtz Equations}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1660}, number = {SC-94-38}, year = {1995}, abstract = {The reference wave vector of the paraxial Helmholtz equation is determined using various strategies which result all in similar expressions. The effort for its evaluation is so small that the reference wave vector can be adapted for each propagation step of an arbitrary BPM-algorithm.}, language = {en} } @misc{DeuflhardSchmidt1993, author = {Deuflhard, Peter and Schmidt, Frank}, title = {Discrete Transparent Boundary Conditions for the Numerical Solution of Fresnel's Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-1205}, number = {SC-93-24}, year = {1993}, abstract = {The paper presents a construction scheme of deriving transparent , i. e. reflection-free, boundary conditions for the numerical solution of Fresnel's equation (being formally equivalent to Schr{\"o}dinger's equation). These boundary conditions appear to be of a nonlocal Cauchy type. As it turns out, each kind of linear implicit discretization induces its own discrete transparent boundary conditions.}, language = {en} } @misc{Schmidt1991, author = {Schmidt, Frank}, title = {An Adaptive Approach to the Numerical Solution of Fresnel's Wave Equation.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-628}, number = {SC-91-12}, year = {1991}, abstract = {An adaptive approach to the numerical solution of the wave propagation in integrated optics devices with 1D cross sections is described. First, Fresnel's approximation of the exact wave equation resulting from Maxwell's equations is considered. A criterion to estimate the validity of this approximation is derived. Fresnel's wave equation being formally equivalent to Schroedinger's equation uniquely defines an initial-boundary-value problem, which is solved numerically by a stepwise calculation of the propagating field. Discretization in longitudinal direction first with stepsize control leads to a stationary subproblem for the transversal field distribution, which is then handled by an adaptive finite element method. Thus full adaptivity of the algorithm is realized. The numerical examples are concentrated on taper structures playing an essential role in integrated optics devices for telecommunication systems.}, language = {en} } @misc{Schmidt1997, author = {Schmidt, Frank}, title = {Computation of Discrete Transparent Boundary Conditions for the 2D Helmholtz Equation}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3330}, number = {SC-97-64}, year = {1997}, abstract = {We present a family of nonlocal transparent boundary conditions for the 2D Helmholtz equation. The whole domain, on which the Helmholtz equation is defined, is decomposed into an interior and an exterior domain. The corresponding interior Helmholtz problem is formulated as a variational problem in standard manner, representing a boundary value problem, whereas the exterior problem is posed as an initial value problem in the radial variable. This problem is then solved approximately by means of the Laplace transformation. The derived boundary conditions are asymptotically correct, model inhomogeneous exterior domains and are simple to implement.}, language = {en} } @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} }