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A Penalty-Regularization-Operator Splitting Method for the Numerical Solution of a Scalar Eikonal Equation

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Chinese Annals of Mathematics,Series B 2015年第5期36卷 659-688页

作者： Alexandre CABOUSSAT roland GLOWINSKI Haute Ecole de Gestion de Genève HES-SO//University of Applied Sciences Department of Mathematics University of Houston

In this article, we discuss a numerical method for the computation of the minimal and maximal solutions of a steady scalar Eikonal equation. This method relies on a penalty treatment of the nonlinearity, a biharmonic regularization of the resulting variational problem, and the time discretization by operator-splitting of an initial value problem associated with the Euler-Lagrange equations of the regularized variational problem. A low-order finite element discretization is advocated since it is well-suited to the low regularity of the solutions. Numerical experiments show that the method sketched above can capture efficiently the extremal solutions of various two-dimensional test problems and that it has also the ability of handling easily domains with curved boundaries.

关键词： Eikonal equation Minimal and maximal solutions Regularization methods Penalization of equality constraints Dynamical flow Operator splitting Finite element methods

On the Numerical Solution to a Nonlinear Wave Equation Associated with the First Painlev Equation:an Operator-Splitting Approach

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Chinese Annals of Mathematics,Series B 2013年第2期34卷 237-254页

作者： roland GLOWINSKI Annalisa QUAINI Department of Mathematics University of Houston4800 Calhoun RdHouston(TX) 77204USA Laboratoire Jacques-Louis Lions Universit Pierre et Marie Curie4Place Jussieu75252 Paris CEDEX 05France

The main goal of this article is to discuss the numerical solution to a nonlinear wave equation associated with the first of the celebrated Painlevd transcendent ordinary differential equations. In order to solve numerically the above equation, whose solutions blow up in finite time, the authors advocate a numerical methodology based on the Strang＇s symmetrized operator-splitting scheme. With this approach, one can decouple nonlinearity and differential operators, leading to the alternate solution at every time step of the equation as follows：（i） The first Painlevd ordinary differential equation, （ii） a linear wave equation with a constant coefficient. Assuming that the space dimension is two, the authors consider a fully discrete variant of the above scheme, where the space-time discretization of the linear wave equation sub-steps is achieved via a Galerkin/finite element space approximation combined with a second order accurate centered time discretization scheme. To handle the nonlinear sub-steps, a second order accurate centered explicit time discretization scheme with adaptively variable time step is used, in order to follow accurately the fast dynamic of the solution before it blows up. The results of numerical experiments are presented for different coefficients and boundary conditions. They show that the above methodology is robust and describes fairly accurately the evolution of a rather ＂violent＂ phenomenon.

关键词： Painlevd equation Nonlinear wave equation Blow-up solution Operator-SDlitting

Conserved host-pathogen interactions identify novel treatment options in betacoronavirus infections

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Signal Transduction and Targeted Therapy 2021年第3期6卷 557-559页

作者： Soeren Lukassen roland Eils Charity-Universitatsmedizin Berlin corporate member of Freie Umversitat BerlinHumboldt-Universitat zu Berlinand Berlin Institute of HealthBerlinGermany Center for Digital Health Berlin Institute of Health(BIH)BerlinGermany Health Data Science Unit Heidelberg University Hospital and BioQuantHeidelbergGermany

In a recent study published in Science,1 Gordon et *** the host-pathogen interactome of the coronaviruses SARS-CoV-1,SARS-CoV-2,and MERS-CoV,all of which caused lethal outbreaks in the past two *** functionally characterize a number of these interactions,leveraging the information to identify promising candidate molecules for drug-repurposing.

关键词： identif interactions treatment

REGULARIZATION METHODS FOR THE NUMERICAL SOLUTION OF THE DIVERGENCE EQUATION △. u = f＊

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Journal of Computational Mathematics 2012年第4期30卷 354-380页

作者： Alexandre Caboussat roland Glowinski University of Houston Department of Mathematics Houston Texas USA

The problem of finding a L^∞-bounded two-dimensional vector field whose divergence is given in L2 is discussed from the numerical viewpoint. A systematic way to find such a vector field is to introduce a non-smooth variational problem involving a L^∞-norm. To solve this problem from calculus of variations, we use a method relying on a well- chosen augmented Lagrangian functional and on a mixed finite element approximation. An Uzawa algorithm allows to decouple the differential operators from the nonlinearities introduced by the L^∞-norm, and leads to the solution of a sequence of Stokes-like systems and of an infinite family of local nonlinear problems. A simpler method, based on a L2- regularization is also considered. Numerical experiments are performed, making use of appropriate numerical integration techniques when non-smooth data are considered; they allow to compare the merits of the two approaches discussed in this article and to show the ability of the related methods at capturing L^∞bounded solutions.

关键词： Divergence equation Bounded solutions Regularization methods AugmentedLagrangian Uzawa algorithm Nonlinear variational problems.

Deposition of nano-crystalline tungsten carbide powders from gaseous WO_(2)(OH)_(2)

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Tungsten 2023年第1期5卷 136-144页

作者： Markus Ostermann roland Haubner TU Wien Institute of Chemical Technologies and AnalyticsGetreidemarkt 9/164-031060 ViennaAustria

Lower WC grain sizes in the nanometer range have positive effects on the properties of hardmetals(e.g.,hardness),but the established production processes of WC are limited to grain sizes of about 150 *** produce WC powder with grain sizes in the lower nanometer range,an alternative WC production process based on the chemical vapor transport(CVT) reaction of WO_(3) and H_(2)O forming gaseous WO_(2)(OH)_(2) at about 1100 ℃,followed by a carburation reaction with H_(2)/CH_(4)-gas mixtures was *** influences of different process parameters such as furnace temperature,humidity and gas flows were investigated to improve the *** the right set of parameters the produced powder consisted mainly of agglomerated WC grains with a size of about 5 *** the common hexagonal WC phase,the cubic WC1-xphase was stabilized due to the small crystallite *** addition,a thin layer of amorphous carbon was present on the powder surface due to the catalytic methane decomposition on the WC *** amount of oxidic and metallic residues in the product powder was minimized with the parameter optimization and the powder yield was increased up to about 50%.With further optimization of the process parameters and usage of improved flow breakers,the purity and yield of the product powder can be further *** an application in the hardmetal section is not realistic at the moment,applications in the catalysis sector could be considered due to the small grain size and good catalytic activity of the cubic WC1-xphase.

关键词： Tungsten carbide CVT-mechanism WO2(OH)2 Carburation Nano-sized powder Transmission electron microscopy(TEM)

Exploring Content Popularity in Information-Centric Networks

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China Communications 2015年第7期12卷 13-22页

作者： Andriana Ioannou Stefan weber School of Computer Science and Statistics Trinity College

Information-Centric Networking(ICN), an alternative architecture to the current Internet infrastructure, focuses on the distribution and retrieval of content by employing caches in a network to reduce network traffic. The employment of caches may be accomplished using graph-based and content-based criteria such as the position of a node in a network and content popularity. The contribution of this paper lies on the characterization of content popularity for on-path in-network caching. To this end, four dynamic approaches for identifying content popularity are evaluated via simulations. Content popularity may be determined per chunk or per object, calculated by the number of requests for a content against the sum of requests or the maximum number of requests. Based on the results, chunk-based approaches provide 23% more accurate content popularity calculations than object-based approaches. In addition, approaches that are based on the comparison of a content against the maximum number of requests have been shown to be more accurate than the alternatives.

关键词： network distributed architectures future internet information-centric networks caching technologies on-path caching content popularity

Correction to:Preface:Special Issue on Modeling,Simulation,and Optimization in Operational Research

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Journal of the Operations Research Society of China 2024年第2期12卷 548-548页

作者： Gerhard-Wilhelm weber J.Joshua Thomas Jose Antonio Marmolejo Saucedo Ugo Fiore Igor Litvinchev Pandian Vasant Poznan University of Technology PoznanPoland Institute of Applied Mathematics Middle East Technical UniversityAnkaraTurkey UOW Malaysia KDU Penang University CollegePetaling JayaMalaysia Facultad de Ingenieria Universidad PanamericanaMexico CityMexico Parthenope University and at Federico II University NaplesItaly Nuevo Leon State University San Nicolas de los GarzaMexico MERLIN Research Centre Ton Duc Thang UniversityHo Chi Minh CityVietnam

Towards social behavior in virtual-agent navigation

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Science China(Information Sciences) 2016年第11期59卷 16-32页

作者： Angelos KREMYZAS Norman JAKLIN roland GERAERTS Department of Information and Computing Sciences Utrecht University

We present Social Groups and Navigation(SGN), a method to simulate the walking behavior of small pedestrian groups in virtual environments. SGN is the first method to simulate group behavior on both global and local levels of an underlying planning hierarchy. We define quantitative metrics to measure the coherence and the sociality of a group based on existing empirical data of real crowds. SGN does not explicitly model coherent and social formations, but it lets such formations emerge from simple geometric rules. In addition to a previous version, SGN also handles group-splitting to smaller groups throughout navigation as well as social sub-group behavior whenever a group has to temporarily split up to re-establish its coherence. For groups of four, SGN generates between 13% and 53% more socially-friendly behavior than previous methods, measured over the lifetime of a group in the simulation. For groups of three, the gain is between 15% and 31%, and for groups of two, the gain is between 1% and 4%. SGN is designed in a flexible way, and it can be integrated into any crowd-simulation framework that handles global path planning and any path following as separate *** show that SGN enables the simulation of thousands of agents in real time.

关键词： virtual humans social-group behavior autonomous agent navigation crowd simulation

A NEW APPROACH AND ERROR ANALYSIS FOR RECONSTRUCTING THE SCATTERED WAVE BY THE POINT SOURCE METHOD

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Journal of Computational Mathematics 2007年第2期25卷 113-130页

作者： Jijun Liu Gen Nakamura roland Potthast Department of Mathematics Southeast University Nanjing 210096 China Department of Mathematics Graduate School of Science Hokkaido University Sapporo 060-0810 Japan Institute for Numerical and Applied Mathematics University of Gottingen Lotzestr 16-1837085 Gottingen Germany

Consider an inverse scattering problem by an obstacle D belong to R^2 with impedance boundary. We investigate the reconstruction of the scattered field u^s from its far field pattern u^∞ using the point source method. First, by applying the boundary integral equation method, we provide a new approach to the point-source method of Potthast by classical potential theory. This extends the range of the point source method from plane waves to scattering of arbitrary waves. Second, by analyzing the behavior of the Hankel function, we obtain an improved strategy for the choice of the regularizing parameter from which an improved convergence rate （compared to the result of [15]） is achieved for the reconstruc- tion of the scattered wave. Third, numerical implementations are given to test the validity and stability of the inversion method for the impedance obstacle.

关键词： Inverse scattering Regularization Error estimate Numerics