@phdthesis{Zschiedrich2009, author = {Zschiedrich, Lin}, title = {Transparent boundary conditions for Maxwell's equations: Numerical concepts beyond the PML method}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000013994-8}, year = {2009}, abstract = {Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term "multiply structured exterior domain" is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.}, language = {en} } @phdthesis{Roeblitz2009, author = {R{\"o}blitz, Susanna}, title = {Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000008079-9}, year = {2009}, abstract = {The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.}, language = {en} } @phdthesis{Ruprecht2010, author = {Ruprecht, Daniel}, title = {Analysis of a multi-scale asymptotic model for internal gravity waves in a moist atmosphere}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000018355-1}, year = {2010}, abstract = {The thesis presents the analysis of a reduced model for modulation of internal gravity waves by deep convective clouds. The starting point for the derivation are conservation laws for mass, momentum and energy coupled with a bulk micro-physics model describing the evolution of mixing ratios of water vapor, cloud water and rain water. A reduced model for the identified scales of the regime is derived, using multi-scale asymptotics. The closure of the model employs conditional averaging over the horizontal scale of the convective clouds. The resulting reduced model is an extension of the anelastic equations, linearized around a constant background state, which are well-known from meteorology. The closure of the model is achieved purely by analytical means and involves no additional physically motivated assumptions. The essential new parameter arising from the coupling to a micro-physics model is the area fraction of saturated regions on the horizontal scale of the convective clouds. It turns out that this parameter is constant on the employed short timescale. Hence the clouds constitute a constant background, modulating the characteristics of propagation of internal waves. The model is then investigated by analytical as well as numerical means. Important results are, among others, that in the model moisture (i) inhibits propagation of internal waves by reducing the modulus of the group velocity, (ii) reduces the angle between the propagation direction of a wave-packet and the horizontal, (iii) causes critical layers and (iv) introduces a maximum horizontal wavelength beyond which waves are no longer propagating but become evanescent. The investigated examples of orographically generated gravity waves also feature a significant reduction of vertical momentum flux by moisture. The model is extended by assuming systematically small under-saturation, that is saturation at leading order. The closure is similar to the original case but requires additional assumptions. The saturated area fraction in the obtained model is no longer constant but now depends nonlinearly on vertical displacement and thus on vertical velocity.}, language = {en} } @phdthesis{Friese1998, author = {Friese, Tilmann}, title = {Eine Mehrgitter-Methode zur L{\"o}sung des Eigenwertproblems der komplexen Helmholtzgleichung}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-1999000133}, year = {1998}, language = {en} } @phdthesis{Weber2006, author = {Weber, Marcus}, title = {Meshless Methods in Confirmation Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10232}, year = {2006}, language = {en} } @phdthesis{Galliat2002, author = {Galliat, Tobias}, title = {Adaptive Multilevel Cluster Analysis by Self-Organizing Box Maps}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-2002001258}, year = {2002}, abstract = {Als Cluster Analyse bezeichnet man den Prozess der Suche und Beschreibung von Gruppen (Clustern) von Objekten, so daß die Objekte innerhalb eines Clusters bez{\"u}glich eines gegebenen Maßes maximal homogen sind. Die Homogenit{\"a}t der Objekte h{\"a}ngt dabei direkt oder indirekt von den Auspr{\"a}gungen ab, die sie f{\"u}r eine Anzahl festgelegter Attribute besitzen. Die Suche nach Clustern l{\"a}ßt sich somit als Optimierungsproblem auffassen, wobei die Anzahl der Cluster vorher bekannt sein muß. Wenn die Anzahl der Objekte und der Attribute groß ist, spricht man von komplexen, hoch-dimensionalen Cluster Problemen. In diesem Fall ist eine direkte Optimierung zu aufwendig, und man ben{\"o}tigt entweder heuristische Optimierungsverfahren oder Methoden zur Reduktion der Komplexit{\"a}t. In der Vergangenheit wurden in der Forschung fast ausschließlich Verfahren f{\"u}r geometrisch basierte Clusterprobleme entwickelt. Bei diesen Problemen lassen sich die Objekte als Punkte in einem von den Attributen aufgespannten metrischen Raum modellieren; das verwendete Homogenit{\"a}tsmaß basiert auf der geometrischen Distanz der den Objekten zugeordneten Punkte. Insbesondere zur Bestimmung sogenannter metastabiler Cluster sind solche Verfahren aber offensichtlich nicht geeignet, da metastabile Cluster, die z.B. in der Konformationsanalyse von Biomolek{\"u}len von zentraler Bedeutung sind, nicht auf einer geometrischen, sondern einer dynamischen {\"A}hnlichkeit beruhen. In der vorliegenden Arbeit wird ein allgemeines Clustermodell vorgeschlagen, das zur Modellierung geometrischer, wie auch dynamischer Clusterprobleme geeignet ist. Es wird eine Methode zur Komplexit{\"a}tsreduktion von Clusterproblemen vorgestellt, die auf einer zuvor generierten Komprimierung der Objekte innerhalb des Datenraumes basiert. Dabei wird bewiesen, daß eine solche Reduktion die Clusterstruktur nicht zerst{\"o}rt, wenn die Komprimierung fein genug ist. Mittels selbstorganisierter neuronaler Netze lassen sich geeignete Komprimierungen berechnen. Um eine signifikante Komplexit{\"a}tsreduktion ohne Zerst{\"o}rung der Clusterstruktur zu erzielen, werden die genannten Methoden in ein mehrstufiges Verfahren eingebettet. Da neben der Identifizierung der Cluster auch deren effiziente Beschreibung notwendig ist, wird ferner eine spezielle Art der Komprimierung vorgestellt, der eine Boxdiskretisierung des Datenraumes zugrunde liegt. Diese erm{\"o}glicht die einfache Generierung von regelbasierten Clusterbeschreibungen. F{\"u}r einen speziellen Typ von Homogenit{\"a}tsfunktionen, die eine stochastische Eigenschaft besitzen, wird das mehrstufige Clusterverfahren um eine Perroncluster Analyse erweitert. Dadurch wird die Anzahl der Cluster, im Gegensatz zu herk{\"o}mmlichen Verfahren, nicht mehr als Eingabeparameter ben{\"o}tigt. Mit dem entwickelten Clusterverfahren kann erstmalig eine computergest{\"u}tzte Konformationsanalyse großer, f{\"u}r die Praxis relevanter Biomolek{\"u}le durchgef{\"u}hrt werden. Am Beispiel des HIV Protease Inhibitors VX-478 wird dies detailliert beschrieben.}, language = {en} } @phdthesis{MoualeuNgangue2013, author = {Moualeu-Ngangue, Dany Pascal}, title = {A Mathematical Tuberculosis Model in Cameroon}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000095327-7}, school = {Freie Universit{\"a}t Berlin}, pages = {154}, year = {2013}, abstract = {This thesis firstly presents a nonlinear extended deterministic model for the transmission dynamics of tuberculosis, based on realistic assumptions and data collected from the WHO. This model enables a comprehensive qualitative analysis of various aspects in the outbreak and control of tuberculosis in Sub-Saharan Africa countries and successfully reproduces the epidemiology of tuberculosis in Cameroon for the past (from 1994-2010). Some particular properties of the model and its solution have been presented using the comparison theorem applied to the theory of differential equations. The existence and the stability of a disease free equilibrium has been discussed using the Perron-Frobenius theorem and Metzler stable matrices. Furthermore, we computed the basic reproduction number, i.e. the number of cases that one case generates on average over the course of its infectious period. Rigorous qualitative analysis of the model reveals that, in contrast to the model without reinfections, the full model with reinfection exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the basic reproduction ratio (R0), is less than unity. The global stability of the disease-free equilibrium has been discussed using the concepts of Lyapunov stability and bifurcation theory. With the help of a sensitivity analysis using data of Cameroon, we identified the relevant parameters which play a key role for the transmission and the control of the disease. This was possible applying sophisticated numerical methods (POEM) developed at ZIB. Using advanced approaches for optimal control considering the costs for chemoprophylaxis, treatment and educational campaigns should provide a framework for designing realistic cost effective strategies with different intervention methods. The forward-backward sweep method has been used to solve the numerical optimal control problem. The numerical result of the optimal control problem reveals that combined effort in education and chemoprophylaxis may lead to a reduction of 80\\% in the number of infected people in 10 years. The mathematical and numerical approaches developed in this thesis could be similarly applied in many other Sub-Saharan countries where TB is a public health problem.}, language = {en} } @phdthesis{Reuter2018, author = {Reuter, Bernhard}, title = {Generalisierte Markov-Modellierung von Nichtgleichgewichtssystemen - Simulation und Modellierung der Amyloid-beta(1-40)-Konformationsdynamik unter Mikrowelleneinfluss}, year = {2018}, language = {de} } @phdthesis{Quer2018, author = {Quer, Jannes}, title = {Importance Sampling for metastable dynamical systems in molecular dynamics}, year = {2018}, language = {en} } @phdthesis{Klimm2018, author = {Klimm, Martina}, title = {New Strategies in Conformation Dynamics}, year = {2018}, language = {en} } @phdthesis{Villatoro2018, author = {Villatoro, Jos{\´e}}, title = {A combined approach for the analysis of biomolecules using IR-MALDI ion mobility spectrometry and molecular dynamics simulations of peptide ions in the gas phase}, year = {2018}, language = {en} } @phdthesis{Barth2018, author = {Barth, Carlo}, title = {Analysis of photonic crystals for interaction with near-surface emitters}, doi = {10.14279/depositonce-6880}, year = {2018}, language = {en} } @phdthesis{Fackeldey2009, author = {Fackeldey, Konstantin}, title = {The Weak Coupling Method for Coupling Continuum Mechanics with Molecular Dynamics}, year = {2009}, language = {en} } @phdthesis{Gladilin2003, author = {Gladilin, Evgeny}, title = {Biomechanical Modeling of Soft Tissue and Facial Expressions for Craniofacial Surgery Planning}, address = {Germany}, year = {2003}, language = {en} } @phdthesis{Klapproth2012, author = {Klapproth, Corinna}, title = {Adaptive numerical integration for dynamical contact problems}, year = {2012}, language = {en} } @phdthesis{Schmidt2002, author = {Schmidt, Frank}, title = {Solution of Interior-Exterior Helmholtz-Type Problems Based on the Pole Condition Concept}, year = {2002}, language = {en} } @phdthesis{Reinecke2009, author = {Reinecke, Isabel}, title = {Mathematical modeling and simulation of the female menstrual cycle}, year = {2009}, language = {en} } @phdthesis{Weber2006, author = {Weber, Marcus}, title = {Meshless Methods in Conformation Dynamics}, year = {2006}, language = {en} } @phdthesis{Schiela2006, author = {Schiela, Anton}, title = {The Control Reduced Interior Point Method. A Function Space Oriented Algorithmic Approach}, address = {Fachbereich Mathematik}, year = {2006}, language = {en} } @phdthesis{Pomplun2010, author = {Pomplun, Jan}, title = {Reduced basis method for electromagnetic scattering problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000017571-3}, year = {2010}, language = {en} } @phdthesis{Kettner2012, author = {Kettner, Benjamin}, title = {Detection of spurious modes in resonance mode computations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000038256-7}, year = {2012}, language = {en} } @phdthesis{Lockau2013, author = {Lockau, Daniel}, title = {Optical modeling of thin film silicon solar cells with random and periodic light management textures}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:83-opus-38759}, year = {2013}, language = {en} } @phdthesis{Hammerschmidt2016, author = {Hammerschmidt, Martin}, title = {Optical simulation of complex nanostructured solar cells with a reduced basis method}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000102429-1}, pages = {XX, 169}, year = {2016}, abstract = {Simulations of optical processes and complex nanostructured devices have become omnipresent in recent years in several fields of current research and industrial applications, not limited to the field of photovoltaics. Devices or processes are optimized with respect to a certain objective where the underlying physical processes are described by partial differential equations. In photovoltaics and photonics electromagnetic fields are investigated which are governed by Maxwell's equations. In this thesis a reduced basis method for the solution of the parameter dependent electromagnetic scattering problem with arbitrary parameters is developed. The method is developed with the specific challenges arising in optical simulations of thin-film silicon solar cells in mind. These are large in domain size and have a complex three-dimensional structure, making optimization tasks infeasible if high-accuracy of the electromagnetic field solution is required. The application of the empirical interpolation methods allows to expand an arbitrary parameter dependence affinely. Thus not only geometries, but also material tensors and source fields can be parameterized. Additionally, the required non-linear post-processing steps of the electromagnetic field to derive energy fluxes or volume absorption are addressed. The reduced basis method allows to reduce the computational costs by orders of magnitude compared to efficient finite element solvers. In addition, an efficient tailored domain decomposition algorithm is presented to model incoherent layers or illuminations in optical systems efficiently. This is of particular interest for solar cells in superstrate configuration where the absorber is illuminated through a glass substrate. The developed methods are employed in application examples taken from collaborations with experimentalists active in the joint lab "BerOSE" (Berlin Joint Lab for Optical Simulations for Energy Research). The optical model of a thin-film silicon multi-junction with incoherent light-trapping is characterized in great detail. The computational gains through hybrid, hp adaptive finite elements are studied and the incoherent domain decomposition algorithm is applied to model a more realistic light-trapping by the glass substrate. The numerical examples of a hexagonal nano-hole array and multi-junction silicon solar cell with a tunable intermediate reflector layer show that the reduced basis method is well suited as a forward solver for modeling and optimization tasks arising in photovoltaics and photonics. Reduced models for illumination and geometric parameters are built providing up to five orders of magnitude savings in computational costs. Resonance phenomena present in the nano-hole array example are detected and the model adapts itself automatically.}, language = {en} } @phdthesis{Omari2019, author = {Omari, Mohamed}, title = {A Mathematical Model of Bovine Metabolism and Reproduction: Application to Feeding Strategies, Drug Administration and Experimental Design}, year = {2019}, language = {en} } @phdthesis{Reidelbach2019, author = {Reidelbach, Marco}, title = {Optimal Network Generation for the Simulation of Proton Transfer Processes}, year = {2019}, language = {en} } @phdthesis{Donati2019, author = {Donati, Luca}, title = {Reweighting methods for Molecular Dynamics}, publisher = {Freie Universit{\"a}t Berlin}, doi = {10.17169/refubium-2305}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-refubium-24541-6}, year = {2019}, abstract = {The dynamical response of molecular systems, when the potential energy function is perturbed at a microscopic level, is difficult to predict without a numerical or laboratory experiment. This is due to the non-linearity and high-dimensionality of molecular systems. An efficient investigation of such a behaviour is necessary to better understand the nature of molecules and to improve the predictability of Molecular Dynamics simulations. In this thesis we propose a reweighting scheme for Markov State Models (MSMs), based on the Girsanov theorem, that permits to reduce the computational cost of the analysis when the potential energy function of a molecule is perturbed. The method has been successfully extended and implemented with metadynamics, in order to build the MSM of a molecular system in a significantly shorter computational time compared to a standard unbiased MD simulation. We also propose a new method to discretize the infinitesimal generator into a rate matrix, that could be used to efficiently study Hamiltonian perturbations as well.}, language = {en} } @phdthesis{Wohlfeil2015, author = {Wohlfeil, Benjamin}, title = {Integrated fiber grating couplers in silicon photonics}, doi = {10.14279/depositonce-4521}, year = {2015}, language = {en} } @phdthesis{Durmaz2016, author = {Durmaz, Vedat}, title = {Atomistic Binding Free Energy Estimations for Biological Host-Guest Systems}, publisher = {FU Dissertationen Online}, pages = {216}, year = {2016}, abstract = {Accurate quantifications of protein-ligand binding affinities by means of in silico methods increasingly gain importance in various scientific branches including toxicology and pharmacology. In silico techniques not only are generally less demanding than laboratory experiments regarding time as well as cost, in particular, if binding assays or synthesis protocols need to be developed in advance. At times, they also provide the only access to risk assessments on novel chemical compounds arising from biotic or abiotic degradation of anthropogenic substances. However, despite the continuous technological and algorithmic progress over the past decades, binding free energy estimations through molecular dynamics simulations still pose an enormous computational challenge owed to the mathematical complexity of solvated macromolecular systems often consisting of hundreds of thousands of atoms. The goals of this thesis can roughly be divided into two categories dealing with different aspects of host-guest binding quantification. On the one side algorithmic strategies for a comprehensive exploration and decomposition of conformational space in conjunction with an automated selection of representative molecular geometries and binding poses have been elaborated providing initial structures for free energy calculations. In light of the dreaded trapping problem typically associated with molecular dynamics simulations, the focus was laid on a particularly systematic generation of representatives covering a broad range of physically accessible molecular conformations and interaction modes. On the other side and ensuing from these input geometries, binding affinity models based on the linear interaction energy (LIE) method have been developed for a couple of (bio)molecular systems. The applications included a successful prediction of the liquid-chromatographic elution order as well as retention times of highly similar hexabromocyclododecane (HBCD) stereoisomers, a novel empirical LIE-QSAR hybrid binding affinity model related to the human estrogen receptor α (ERα), and, finally, the (eco)toxicological prioritization of transformation products originating from the antibiotic sulfamethoxazole with respect to their binding affinities to the bacterial enzyme dihydropteroate synthase. Altogether, a fully automated approach to binding mode and affinity estimation has been presented that is content with an arbitrary geometry of a small molecule under observation and a spatial vector specifying the binding site of a potential target molecule. According to our studies, it is superior to conventional docking and thermodynamic average methods and primarily suggesting binding free energy calculation on the basis of several heavily distinct complex geometries. Both chromatographic retention times of HBCD and binding affinities to ERα yielded squared coefficients of correlation with experimental results significantly higher than 0.8. Approximately 85 \% (100 \%) of predicted receptor-ligand binding modes deviated less than 1.53 {\AA} (2.05 {\AA}) from available crystallographic structures.}, language = {en} } @phdthesis{Mangalgiri2019, author = {Mangalgiri, Gauri}, title = {Development of Titanium Dioxide Metasurfaces and Nanosoupbowls for Optically Enhancing Silicon Photocathodes}, doi = {10.18452/20160}, year = {2019}, language = {en} } @phdthesis{Stoetzel2014, author = {St{\"o}tzel, Claudia}, title = {Numerical and Discrete Modeling of Reproductive Endocrinological Networks}, year = {2014}, abstract = {This thesis deals with the mathematical modeling of endocrinological networks that are underlying the female hormone cycle. These networks consist of a variety of biological mechanisms in different parts of the organism. Their interaction leads to periodic changes of various substances that are necessary for reproduction. In every cycle, hormones are secreted from the hypothalamic-pituitary-gonadal axis into the bloodstream, where they distribute and influence several functions in the body. Their most important task in reproduction is to regulate processes in the ovaries, where follicles and corpus luteum develop. These produce steroids that are released into the blood and from therein regulate the processes in the hypothalamic-pituitary-gonadal axis. The hormonal cycle is thus a result of a large feedback loop, whose self-regulation is a complex interplay of multiple components. For the modeling of these processes, a high abstraction level is required, which can be realized by various modeling approaches. In this work, some of these approaches are implemented. The first step in all approaches is the representation of the most important mechanisms in a flowchart. In the next step, this can be implemented as a system of ordinary differential equations using Hill functions, as a piecewise defined affine differential equation model, or directly as a purely regulatory model. Using this approach, a differential equation model for the hormonal cycle of cows is developed. This is compared with a more advanced model of the menstrual cycle in humans. Both models are validated by comparing simulations with measured values, and by studying external influences such as drug administration. For the example of the bovine estrous cycle, continuous analysis methods are used to investigate stability, follicular wave patterns, and robustness with respect to parameter perturbations. Furthermore, the model is substantially reduced while preserving the main simulation results. To take a look at alternative modeling approaches, corresponding discrete models are derived, exemplified for the bovine model. For a piecewise affine version of the model, parameter constraints for the continuous model are calculated. Stability is analyzed globally for a purely discrete model. In addition, core discrete models are derived, which retain the dynamic properties of the original model.}, language = {en} } @phdthesis{Goetschel2015, author = {G{\"o}tschel, Sebastian}, title = {Adaptive Lossy Trajectory Compression for Optimal Control of Parabolic PDEs}, year = {2015}, abstract = {Optimal control problems governed by nonlinear, time-dependent PDEs on three-dimensional spatial domains are an important tool in many fields, ranging from engineering applications to medicine. For the solution of such optimization problems, methods working on the reduced objective functional are often employed to avoid a full spatio-temporal discretization of the problem. The evaluation of the reduced gradient requires one solve of the state equation forward in time, and one backward solve of the adjoint equation. The state enters into the adjoint equation, requiring the storage of a full 4D data set. If Newton-CG methods are used, two additional trajectories have to be stored. To get numerical results that are accurate enough, in many cases very fine discretizations in time and space are necessary, leading to a significant amount of data to be stored and transmitted to mass storage. This thesis deals with the development and analysis of methods for lossy compression of such finite element solutions. The algorithms are based on a change of basis to reduce correlations in the data, combined with quantization. This is achieved by transforming the finite element coefficient vector from the nodal to the hierarchical basis, followed by rounding the coefficients to a prescribed precision. Due to the inexact reconstruction, and thus inexact data for the adjoint equation, the error induced in the reduced gradient, and reduced Hessian, has to be controlled, to not impede convergence of the optimization. Accuracy requirements of different optimization methods are analyzed, and computable error estimates for the influence of lossy trajectory storage are derived. These tools are used to adaptively control the accuracy of the compressed data. The efficiency of the algorithms is demonstrated on several numerical examples, ranging from a simple linear, scalar equation to a semi-linear system of reaction-diffusion equations. In all examples considerable reductions in storage space and bandwidth requirements are achieved, without significantly influencing the convergence behavior of the optimization methods. Finally, to go beyond pointwise error control, the hierarchical basis transform can be replaced by more sophisticated wavelet transforms. Numerical experiments indicate that choosing suitable norms for error control allows higher compression factors.}, language = {en} } @phdthesis{Manley2016, author = {Manley, Phillip}, title = {Simulation of Plasmonic Nanoparticles in Thin Film Solar Cells}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000102531-2}, year = {2016}, language = {en} } @phdthesis{Agarwal2016, author = {Agarwal, Animesh}, title = {Path Integral Techniques in Molecular Dynamics Simulations of Open Boundary Systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000103020-4}, year = {2016}, language = {en} } @phdthesis{Badowski2016, author = {Badowski, Tomasz}, title = {Adaptive importance sampling via minimization of estimators of cross-entropy, mean square and inefficiency constants}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000102823-3}, year = {2016}, language = {en} } @phdthesis{Daragmeh2016, author = {Daragmeh, Adman}, title = {Model Order Reduction of Linear Control Systems: Comparison of Balance Truncation and Singular Perturbation Approximation with Application to Optimal Control}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000102586-2}, year = {2016}, language = {en} } @phdthesis{Gul2016, author = {Gul, Raheem}, title = {Mathematical Modeling and Sensitivity Analysis of Lumped­ Parameter Model of the Human Cardiovascular System}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000101271-2}, year = {2016}, language = {en} } @phdthesis{Lie2016, author = {Lie, Han Cheng}, title = {On a strongly convex approximation of a stochastic optimal control problem for importance sampling of metastable diffusions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000101680-4}, year = {2016}, language = {en} } @phdthesis{Sriwattanaworachai2016, author = {Sriwattanaworachai, Nisara}, title = {Spectral approach to metastability of non-reversible complex processes}, year = {2016}, language = {en} } @phdthesis{Vega2016, author = {Vega, Iliusi}, title = {Reconstruction and analysis of the state space for the identification of dynamical states in real-world time-series}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-fudissthesis000000104520-1}, year = {2016}, language = {en} } @phdthesis{Bujotzek2013, author = {Bujotzek, Alexander}, title = {Molecular Simulation of Multivalent Ligand-Receptor Systems}, year = {2013}, language = {en} } @phdthesis{Gupta2013, author = {Gupta, Pooja}, title = {Integrating high-density marker information into the genetic evaluation of the honey bee}, year = {2013}, language = {en} } @phdthesis{Winkelmann2013, author = {Winkelmann, Stefanie}, title = {Markov Decision Processes with Information Costs}, year = {2013}, language = {en} } @phdthesis{Aiche2013, author = {Aiche, Stephan}, title = {Inferring Proteolytic Processes from Mass Spectrometry Time Series Data}, year = {2013}, language = {en} } @phdthesis{Yousef2013, author = {Yousef, Kaveh}, title = {Stress responses in Escherichia coli and HIV as model systems of adaptation to the environment}, year = {2013}, language = {en} } @phdthesis{Lubkoll2015, author = {Lubkoll, Lars}, title = {An Optimal Control Approach to Implant Shape Design : Modeling, Analysis and Numerics}, pages = {210}, year = {2015}, abstract = {Facial trauma or congenital malformation of bones of the skull may degrade both skeletal integrity as well as the esthetic appearance. For the attending surgeon a prediction of the esthetic outcome of a bone replacement or augmentation implant insertion is challenging. Therefore, it would be advantageous if we were able to compute an implant shape from a given desired outcome. This task presents the main focus of this thesis. Besides the development of a model for the implant shape design problem, this work is concerned with the efficient solution and optimization of realistic models. This includes recent material laws for different soft tissue types as well as complex geometries attained from medical image data. The implant shape design problem can be described as an optimal control problem with constraints given by the necessary optimality conditions in polyconvex hyperelasticity with nonlinear pressure-type boundary conditions. Important theoretical results, such as existence of solutions and higher regularity, are currently not available for such problems. Based on the existence result for polyconvex materials laws, existence of solutions of the nonconvex optimal control problem is proven for the case of a simpler Neumann boundary condition. Due to the "impossible convexity" and the high nonlinearity of hyperelastic material laws the numerical solution of the arising problems is difficult. In this regard, an affine covariant composite step method for nonconvex, equality constrained optimization is presented. The corresponding globalization strategy is based on the affine covariant Newton method for underdetermined systems and cubic regularization methods for unconstrained optimization problems. The linear systems arising from the discretization of constrained optimization problems are described by saddle point matrices. The efficient solution of these equality systems by conjugate gradient methods for convex and nonconvex problems is discussed. Moreover, an error estimator that fits into the affine covariant setting is presented. The presented composite step method was implemented in the C++ finite element library Kaskade 7. The performance of the algorithm is demonstrated on several examples. Next to simple optimization problems, with admissible set given through models of linear and nonlinear heat transfer, we give four examples with nonconvex, hyperelastic constraints.}, language = {en} } @phdthesis{Nielsen2016, author = {Nielsen, Adam}, title = {Computation Schemes for Transfer Operators}, year = {2016}, language = {en} } @phdthesis{Gupta2013, author = {Gupta, Pooja}, title = {Integrating high-density marker information into the genetic evaluation of the honey bee}, year = {2013}, language = {en} } @phdthesis{DjurdjevacConrad2012, author = {Djurdjevac Conrad, Natasa}, title = {Methods for analyzing complex networks using random walker}, year = {2012}, language = {en} } @phdthesis{Pakhomov2021, author = {Pakhomov, Anton}, title = {Efficient modeling and optimization of surface second-harmonic generation from nanophotonic components}, doi = {10.22032/dbt.49369}, year = {2021}, language = {en} } @phdthesis{Binkowski2023, author = {Binkowski, Felix}, title = {Riesz-projection-based methods for the numerical simulation of resonance phenomena in nanophotonics}, doi = {10.17169/refubium-41230}, year = {2023}, language = {en} } @phdthesis{Plock2025, author = {Plock, Matthias}, title = {On Methods for Bayesian Optimization of Least Squares Problems and Optimization of Nanophotonic Devices}, doi = {10.17169/refubium-48179}, year = {2025}, language = {en} }