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A MULTIGRID SEMISMOOTH NEWTON METHOD FOR SEMILINEAR CONTACT PROBLEMS

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Journal of Computational Mathematics 2017年第4期35卷 486-528页

作者： Michael Ulbrich Stefan Ulbrich Daniela Bratzke technische universitat Miinchen Department of Mathematics Garching b. Munchen Germany technische Universitiit darmstadt Department of Mathematics Darmstadt Germany technische universitat darmstadt Department of Mathematics Darmstadt Germany

This paper develops and analyzes multigrid semismooth Newton methods for a class of inequality-constrained optimization problems in function space which are motivated by and include linear elastic contact problems of Signorini type. We show that after a suitable Moreau-Yosida type regularization of the problem superlinear local convergence is obtained for a class of semismooth Newton methods. In addition, estimates for the order of tile error introduced by the regularization are derived. The main part of the paper is devoted to the analysis of a multilevel preconditioner for the semismooth Newton system. We prove a rigorous bound for the contraction rate of the multigrid cycle which is robust with respect to sufficiently small regularization parameters and the number of grid levels. Moreover, it applies to adaptively refined grids. The paper concludes with numerical results.

关键词： Contact problems Semismooth Newton methods Multigrid methods Errorestimates.

Surface area-volume ratios in insects

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Insect Science 2017年第5期24卷 829-841页

作者： Sara Kuhsel Adrian Bruckner Sebastian Schmelzle Michael Heethoff Nico Bluthgen Department of Biology Technische Universitat Darmstadt Schnittspahnstrasse 3 D-64287 Darmstadt Germany

Body mass, volume and surface area are important for many aspects of the physiology and performance of species. Whereas body mass scaling received a lot of attention in the literature, surface areas of animals have not been measured explicitly in this context. We quantified surface area-volume （SA/V） ratios for the first time using 3D surface models based on a structured light scanning method for 126 species of pollinating insects from 4 orders （Diptera, Hymenoptera, Lepidoptera, and Coleoptera）. Water loss of 67 species was measured gravimetrically at very dry conditions for 2 h at 15 and 30 ℃ to demonstrate the applicability of the new 3D surface measurements and relevance for predicting the performance of insects. Quantified SA/V ratios significantly explained the variation in water loss across species, both directly or after accounting for isometric scaling （residuals of the SA/V - mass2/3 relationship）. Small insects with a proportionally larger surface area had the highest water loss rates. Surface scans of insects to quantify allometric SA/Vratios thus provide a promising method to predict physiological responses, improving the potential of body mass isometry alone that assume geometric similarity.

关键词： body size body shape 3D surface imaging sphericity structured light water loss

ADAPTIVITY IN SPACE AND TIME FOR MAGNETOQUASISTATICS

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Journal of Computational Mathematics 2009年第5期27卷 642-656页

作者： Markus Clemens Jens Lang Delia Teleaga Georg Wimmer Helmut-Schmidt-universitat Hamburg Holstenhofweg 8522043 HamburgGermany technische universitat darmstadt Schlossgartenstraβe 764289 DarmstadtGermany

This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell＇s equations on unstructured 3D tetrahedral grids. Spatial mesh re- finement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H（curl）-conforming edge elements in space with linearly implicit Rosenbrock methods in time. An embedding technique is applied to get efficiency in time through variable time steps. Finally, we present numerical results for the magnetic recording write head benchmark problem proposed by the Storage Research Consortium in Japan.

关键词： Magnetoquasistatics Space-time adaptivity Edge elements Rosenbrock meth-ods Hierarchical error estimator SRC benchmark problem.

Analysis of pneumatic atomizer spray profiles

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Particuology 2016年第6期14卷 80-85页

作者： Walter Schafer Simon Rosenkranz Felix Brinckmann Cameron Tropea AOM-Systems GmbH Flughafenstrasse 15 64347 Griesheim Germany LacTec GmbH Otto-Hahn-Strasse 6-8 63110 Rodgau Germany Institute of Fluid Mechanics and Aerodynamics Technische Universitat Darmstadt Alarich-Weiss-Strasse 10 64287 Darmstadt Germany Graduate School of Computational Engineering Technische Universitat Darmstadt Dolivostrasse 15 64287 Darmstadt Germany

Our objective is to analyze the atomization processes of a pneumatic atomizer by measuring the size and velocity distributions of droplets in a liquid paint spray. The droplet size and velocity distributions have been determined at different axial positions in the spray; a mathematical description of how these quan- tities vary throughout the spray is then proposed. Additionally, the relative number density of droplets and the relative local mass flux are estimated.

关键词： Pneumatic atomizer Spray Measurement Droplet size profile Droplet velocity profile Time-shift

A High-Order Discontinuous Galerkin Solver for Helically Symmetric Flows

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Communications in Computational Physics 2021年第6期30卷 288-320页

作者： Dominik Dierkes Florian Kummer Dominik Plumacher Department of Mechanical Engineering Technische Universitat DarmstadtOtto-Berndt-Straße 264287 DarmstadtGermany

We present a high-order discontinuous Galerkin(DG)scheme to solve the system of helically symmetric Navier-Stokes equations which are discussed in[28].In particular,we discretize the helically reduced Navier-Stokes equations emerging from a reduction of the independent variables such that the remaining variables are:t,r,ξwithξ=az+bϕ,where r,ϕ,z are common cylindrical coordinates and t the *** this,all three velocity components are kept non-zero.A new non-singular coordinateηis introduced which ensures that a mapping of helical solutions into the three-dimensional space is well *** that,periodicity conditions for the helical frame aswell as uniqueness conditions at the centerline axis r=0 are *** the sector near the axis of the computational domain a change of the polynomial basis is implemented such that all physical quantities are uniquely defined at the *** the temporal integration,we present a semi-explicit scheme of third order where the full spatial operator is splitted into a Stokes operator which is discretized implicitly and an operator for the nonlinear terms which is treated *** are conducted for a cylindrical shell,excluding the centerline axis,and for the full cylindrical domain,where the centerline is *** all cases we obtain the convergence rates of order O(hk+1)that are expected from DG *** addition to the first DG discretization of the system of helically invariant Navier-Stokes equations,the treatment of the central axis,the resulting reduction of the DG space,and the simultaneous use of a semi-explicit time stepper are of particular novelty.

关键词： Discontinuous Galerkin(DG) helical flows

Constrained crystals deep convolutional generative adversarial network for the inverse design of crystal structures

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npj Computational Materials 2021年第1期7卷 588-594页

作者： Teng Long Nuno M.Fortunato Ingo Opahle Yixuan Zhang Ilias Samathrakis Chen Shen Oliver Gutfleisch Hongbin Zhang Institute of Materials Science Technische Universität DarmstadtDarmstadtGermany

Autonomous materials discovery with desired properties is one of the ultimate goals for materials science,and the current studies have been focusing mostly on high-throughput screening based on density functional theory calculations and forward modeling of physical properties using machine *** the deep learning techniques,we have developed a generative model,which can predict distinct stable crystal structures by optimizing the formation energy in the latent *** is demonstrated that the optimization of physical properties can be integrated into the generative model as on-top screening or backward propagator,both with their own *** the generative models on the binary Bi-Se system reveals that distinct crystal structures can be obtained covering the whole composition range,and the phases on the convex hull can be reproduced after the generated structures are fully relaxed to the *** method can be extended to multicomponent systems for multi-objective optimization,which paves the way to achieve the inverse design of materials with optimal properties.

关键词： properties crystal inverse

Cathodic activated stainless steel mesh as a highly active electrocatalyst for the oxygen evolution reaction with self-healing possibility

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Journal of Energy Chemistry 2020年第10期29卷 153-160页

作者： Gui-Rong Zhang Liu-Liu Shen Patrick Schmatz Konrad Krois Bastian J.M.Etzold Ernst-Berl-Institut für technische und Makromolekulare Chemie Technische Universit鋞Darmstadt64287 DarmstadtGermany

The oxygen evolution reaction(OER)represents one of the major bottlenecks for broad-based applications of many clean energy storage/conversion *** key to solving this problem lies in developing high-performing,cost effective and stable catalysts for the ***,we demonstrate that ubiquitous stainless steel mesh(SSM)materials activated by a facile cathodization treatment can be employed as a high performing OER catalyst,as showcased by the impressively low overpotentials of 275 and 319 mV to reach the benchmark current densities of 10 and 100 mA cm^−2(1.0 M KOH),*** SSM also exhibits excellent performance in a two-electrode water electrolyzer,which requires a low cell voltage of 1.58 at 10 mA cm^−2 and outperforms many of water electrolyzers using earth-abundant OER ***,cathodized SSM with minor performance degradation after the stability test can also be readily healed by subjecting it to an additional cathodization *** is disclosed that the superior performance of cathodized SSMs stems from the surface enrichment of OER active Ni(oxy)hydroxide,facile gas-bubble removal and transportation over the unique mesh-structured surfaces,while the abundant reservoir of nickel in the bulk allows healing of the catalyst by a facile cathodization.

关键词： Oxygen evolution reaction Water splitting Stainless steel mesh Cathodization Mass transfer limitation Self-healing

ClustNails:Visual Analysis of Subspace Clusters

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Tsinghua Science and Technology 2012年第4期17卷 419-428页

作者： Andrada Tatu Leishi Zhang Enrico Bertini Tobias Schreck Daniel Keim Sebastian Bremm Tatiana von Landesbergert Department of Computer and Information Science University of Konstanz Konstanz 78457 Germany Department of Computer Science Technische Universitat Darmstadt Darmstadt 64283 Germany

Subspace clustering addresses an important problem in clustering multi-dimensional data. In sparse multi-dimensional data, many dimensions are irrelevant and obscure the cluster boundaries. Subspace clustering helps by mining the clusters present in only locally relevant subsets of dimensions. However, understanding the result of subspace clustering by analysts is not trivial. In addition to the grouping information, relevant sets of dimensions and overlaps between groups, both in terms of dimensions and records, need to be analyzed. We introduce a visual subspace cluster analysis system called ClustNails. It integrates several novel visualization techniques with various user interaction facilities to support navigating and interpreting the result of subspace clustering. We demonstrate the effectiveness of the proposed system by applying it to the analysis of real world data and comparing it with existing visual subspace cluster analysis systems.

关键词： subspace cluster analysis visualization data exploration pixel-based techniques

Chemo-mechanical coupling effect on high temperature oxidation:A review

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Science China(Technological Sciences) 2019年第8期62卷 1297-1321页

作者： FANG XuFei LI Yan YUE MengKun FENG Xue AML Department of Engineering Mechanics Tsinghua University Beijing 100084 China Center for Mechanics and Materials Tsinghua University Beijing 100084 China Institute of Materials Science Technische Universitat Darmstadt Darmstadt 64287 Germany

The rapid development in the field of chemo-mechanical coupling has drawn increasing attention in recent years. Chemomechanical coupling phenomena exist in many research areas, ranging from development of advanced batteries, biomechanical engineering, hydrogen embrittlement, and high temperature oxidation, etc. In this review, we attempt to provide an overview of the recent advances in chemo-mechanical coupling study on high temperature oxidation. The theoretical frameworks, computational modeling, and experimental studies on this subject are summarized and discussed. The stress-diffusion coupling effect in diffusion-controlled oxidation process, stress-induced evolution of oxide morphology in microscale experiment, and stressoxidation interaction at crack front for intergranular fracture are highlighted. In addition, potential applications and possible methods via surface engineering for improving oxidation-resistance of high temperature structural materials are briefly discussed.

关键词： chemo-mechanical coupling high temperature oxidation microscale experiment fracture