TY - JOUR A1 - Le, Thi Thai T1 - Kelvin-Helmholtz instability in a shallow-water flow with a finite width JF - Journal of Mathematical Physics N2 - We examine an effect of side walls on the linear stability of an interface of tangential-velocity discontinuity in shallow-water flow. The flow is pure horizontal in the plane xy, and the fluid is bounded in a finite width 2d in the y− direction. In region 0 < y < d, the fluid is moving with uniform velocity U but is at rest for −d < y < 0. Without side walls, the flow is unstable for a velocity difference U<√8c U < √8 c, with c being the velocity of gravity waves. In this work, we show that if the velocity difference U is smaller than 2c, the interface is always destabilized, also known as the flow is unstable. The unstable region of an infinite width model is shrunken by the effects of side walls in the case of narrow width, while there is no range for the Froude number for stabilization in the case of large width. These results play an important role in predicting the wave propagations and have a wide application in the fields of industry. As a result of the interaction of waves and the mean flow boundary, the flow is unstable, which is caused by a decrease in the kinetic energy of disturbance. Y1 - 2019 U6 - https://doi.org/10.1063/1.5126321 VL - 60 IS - 1 SP - 123101 PB - AIP Publishing ER - TY - JOUR A1 - Jin, Liangbing A1 - Le, Thi Thai A1 - Fukumoto, Yasuhide T1 - Frictional effect on stability of discontinuity interface in tangential velocity of a shallow-water flow JF - Physics Letters A N2 - We examine a frictional effect on the linear stability of an interface of discontinuity in tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the other, and the bottom surface is assumed to exert drag force, quadratic in velocity, on the thin fluid layer. In the absence of the drag, the instability of the Kelvin-Helmholtz type is suppressed for U>√8 c, with c being the propagating speed of the gravity wave. We find by asymptotic analyses for both small and large values of the drag strength that the drag, regardless of its strength, makes the flow unstable for the whole range of the Froude number U/c. Y1 - 2019 U6 - https://doi.org/10.1016/j.physleta.2019.125839 VL - 383 IS - 26 SP - 125839 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Weiser, Martin A1 - Santiago, Xavier Garcia A1 - Zschiedrich, Lin A1 - Bodermann, Bernd A1 - Burger, Sven T1 - Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion N2 - We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstruction result. T3 - ZIB-Report - 17-37 KW - computational metrology KW - optical metrology KW - computational lithography KW - nanolithography KW - finite- element methods KW - nanooptics Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64704 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Adaptive sampling strategies for efficient parameter scans in nano-photonic device simulations N2 - Rigorous optical simulations are an important tool in optimizing scattering properties of nano-photonic devices and are used, for example, in solar cell optimization. The finite element method (FEM) yields rigorous, time-harmonic, high accuracy solutions of the full 3D vectorial Maxwell's equations [1] and furthermore allows for great flexibility and accuracy in the geometrical modeling of these often complex shaped 3D nano-structures. A major drawback of frequency domain methods is the limitation of single frequency evaluations. For example the accurate computation of the short circuit current density of an amorphous silicon / micro-crystalline multi-junction thin film solar cell may require the solution of Maxwell's equations for over a hundred different wavelengths if an equidistant sampling strategy is employed. Also in optical metrology, wavelength scans are frequently used to reconstruct unknown geometrical and material properties of optical systems numerically from measured scatterometric data. In our contribution we present several adaptive numerical integration and sampling routines and study their efficiency in the context of the determination of generation rate profiles of solar cells. We show that these strategies lead to a reduction in the computational effort without loss of accuracy. We discuss the employment of tangential information in a Hermite interpolation scheme to achieve similar accuracy on coarser grids. We explore the usability of these strategies for scatterometry and solar cell simulations. T3 - ZIB-Report - 14-20 KW - finite element method KW - optical simulations KW - adaptive sampling KW - optical metrology KW - parameter scans KW - solar cells Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50395 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Lockau, Daniel A1 - Zschiedrich, Lin A1 - Schmidt, Frank T1 - Optical modelling of incoherent substrate light-trapping in silicon thin film multi-junction solar cells with finite elements and domain decomposition N2 - In many experimentally realized applications, e.g. photonic crystals, solar cells and light-emitting diodes, nano-photonic systems are coupled to a thick substrate layer, which in certain cases has to be included as a part of the optical system. The finite element method (FEM) yields rigorous, high accuracy solutions of full 3D vectorial Maxwell's equations [1] and allows for great flexibility and accuracy in the geometrical modelling. Time-harmonic FEM solvers have been combined with Fourier methods in domain decomposition algorithms to compute coherent solutions of these coupled system. [2,3] The basic idea of a domain decomposition approach lies in a decomposition of the domain into smaller subdomains, separate calculations of the solutions and coupling of these solutions on adjacent subdomains. In experiments light sources are often not perfectly monochromatic and hence a comparision to simulation results might only be justified if the simulation results, which include interference patterns in the substrate, are spectrally averaged. In this contribution we present a scattering matrix domain decomposition algorithm for Maxwell's equations based on FEM. We study its convergence and advantages in the context of optical simulations of silicon thin film multi-junction solar cells. This allows for substrate light-trapping to be included in optical simulations and leads to a more realistic estimation of light path enhancement factors in thin-film devices near the band edge. T3 - ZIB-Report - 14-21 KW - finite element method KW - rigorous optical modeling KW - domain decomposition KW - multi-junction solar cells KW - thin-film silicon solar cells KW - incoherent layers KW - incoherent light-trapping Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-50410 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Reduced basis method for Maxwell's equations with resonance phenomena T2 - Proc. SPIE N2 - Rigorous optical simulations of 3-dimensional nano-photonic structures are an important tool in the analysis and optimization of scattering properties of nano-photonic devices or parameter reconstruction. To construct geometrically accurate models of complex structured nano-photonic devices the finite element method (FEM) is ideally suited due to its flexibility in the geometrical modeling and superior convergence properties. Reduced order models such as the reduced basis method (RBM) allow to construct self-adaptive, error-controlled, very low dimensional approximations for input-output relationships which can be evaluated orders of magnitude faster than the full model. This is advantageous in applications requiring the solution of Maxwell's equations for multiple parameters or a single parameter but in real time. We present a reduced basis method for 3D Maxwell's equations based on the finite element method which allows variations of geometric as well as material and frequency parameters. We demonstrate accuracy and efficiency of the method for a light scattering problem exhibiting a resonance in the electric field. T3 - ZIB-Report - 15-37 KW - reduced basis method KW - finite element method KW - maxwell equation KW - photonic crystal KW - nano-photonics Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-55687 SN - 1438-0064 VL - 9630 SP - 96300R ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Model order reduction for the time-harmonic Maxwell equation applied to complex nanostructures T2 - Proc. SPIE N2 - Fields such as optical metrology and computational lithography require fast and efficient methods for solving the time-harmonic Maxwell’s equation. Highly accurate geometrical modeling and numerical accuracy atcomputational 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-scatteringoptical wavelengths off 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. T3 - ZIB-Report - 16-05 KW - reduced basis method KW - finite element method KW - rigorous optical modeling KW - reduced order models KW - electromagnetic field solver Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57239 SN - 1438-0064 VL - 9742 SP - 97420M ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank T1 - Reduced basis method for the optimization of nano-photonic devices N2 - 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 occuring e. g. in optical metrology. The reduced basis method presented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources. T3 - ZIB-Report - 16-10 KW - reduced basis method KW - model reduction KW - optical critical dimension metrology KW - electromagnetic field solver Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57556 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Barth, Carlo A1 - Pomplun, Jan A1 - Burger, Sven A1 - Becker, Christiane A1 - Schmidt, Frank T1 - Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs N2 - 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. T3 - ZIB-Report - 16-06 KW - finite element method KW - rigorous optical modeling KW - photonic crystals KW - reduced basis method KW - parameter estimation KW - optical metrology Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57249 SN - 1438-0064 ER - TY - GEN A1 - Gutsche, Philipp A1 - Läuter, Matthias A1 - Schmidt, Frank T1 - Parameter-dependent Parallel Block Sparse Arnoldi and Döhler Algorithms on Distributed Systems N2 - 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. T3 - ZIB-Report - 16-15 KW - Generalized Eigenvalue Problem KW - Many Integrated Core Coprocessor (MIC) KW - Finite Element Method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58202 SN - 1438-0064 ER -