@article{GutschePoulikakosHammerschmidtetal.2016, author = {Gutsche, Philipp and Poulikakos, Lisa and Hammerschmidt, Martin and Burger, Sven and Schmidt, Frank}, title = {Time-harmonic optical chirality in inhomogeneous space}, volume = {9756}, journal = {Proc. SPIE}, arxiv = {http://arxiv.org/abs/1603.05011}, doi = {10.1117/12.2209551}, pages = {97560X}, year = {2016}, language = {en} } @article{DjurdjevacConradWeberSchuette2016, author = {Djurdjevac Conrad, Natasa and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Finding dominant structures of nonreversible Markov processes}, volume = {14}, journal = {Multiscale Modeling and Simulation}, number = {4}, doi = {10.1137/15M1032272}, pages = {1319 -- 1340}, year = {2016}, language = {en} } @article{HammerschmidtBarthPomplunetal.2016, author = {Hammerschmidt, Martin and Barth, Carlo and Pomplun, Jan and Burger, Sven and Becker, Christiane and Schmidt, Frank}, title = {Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs}, volume = {9756}, journal = {Proc. SPIE}, doi = {10.1117/12.2212482}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58187}, pages = {97561R}, year = {2016}, abstract = {Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters.}, language = {en} } @article{HammerschmidtHerrmannPomplunetal.2016, author = {Hammerschmidt, Martin and Herrmann, Sven and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Model order reduction for the time-harmonic Maxwell equation applied to complex nanostructures}, volume = {9742}, journal = {Proc. SPIE}, doi = {10.1117/12.2212367}, pages = {97420M}, year = {2016}, abstract = {Fields such as optical metrology and computational lithography require fast and efficient methods for solving the time-harmonic Maxwell's equation. Highly accurate geometrical modelling and numerical accuracy at low computational costs are a prerequisite for any simulation study of complex nano-structured photonic devices. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem based on the hp-adaptive finite element solver JCMsuite capable of handling geometric and non-geometric parameter dependencies allowing for online evaluations in milliseconds. We apply the RBM to compute light-scattering at optical wavelengths of periodic arrays of fin field-effect transistors (FinFETs) where geometrical properties such as the width and height of the fin and gate can vary in a large range.}, language = {en} } @misc{GutscheLaeuterSchmidt2016, author = {Gutsche, Philipp and L{\"a}uter, Matthias and Schmidt, Frank}, title = {Parameter-dependent Parallel Block Sparse Arnoldi and D{\"o}hler Algorithms on Distributed Systems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58202}, year = {2016}, abstract = {We summarize the basics and first results of the analyses within our ZIB Bridge Project and give an outlook on further studies broadening the usage of hardware acceleration within the Finite Element Method (FEM) based solution of Maxwell's equations.}, language = {en} } @article{HammerschmidtHerrmannPomplunetal.2016, author = {Hammerschmidt, Martin and Herrmann, Sven and Pomplun, Jan and Burger, Sven and Schmidt, Frank}, title = {Reduced basis method for electromagnetic scattering problem: a case study for FinFETs}, volume = {48}, journal = {Optical and Quantum Electronics}, doi = {10.1007/s11082-016-0530-1}, pages = {250}, year = {2016}, abstract = {Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parametrized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occurring e. g. in optical metrology. The reduced basis method pre- sented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources.}, language = {en} } @phdthesis{Nielsen2016, author = {Nielsen, Adam}, title = {Computation Schemes for Transfer Operators}, year = {2016}, language = {en} } @masterthesis{Sikorski2015, type = {Bachelor Thesis}, author = {Sikorski, Alexander}, title = {PCCA+ and Its Application to Spatial Time Series Clustering}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58769}, year = {2015}, language = {en} } @misc{BojarovskiHegeLieetal.2015, author = {Bojarovski, Stefan and Hege, Hans-Christian and Lie, Han Cheng and Weber, Marcus}, title = {Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales}, journal = {Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany}, year = {2015}, abstract = {Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects. The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function. The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models.}, language = {en} } @book{Weiser2016, author = {Weiser, Martin}, title = {Inside Finite Elements}, publisher = {De Gruyter}, year = {2016}, abstract = {All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms.Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.}, language = {en} }