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A Residual Distribution Method Using Discontinuous Elements for the Computation of Possibly Non Smooth Flows

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Advances in Applied Mathematics and Mechanics 2010年第1期2卷 32-44页

作者： Remi Abgrall Team Bacchus INRIA Bordeaux Sud-Ouest and Institut de Mathematiques de BordeauxUniversite Bordeaux I341 cours de la Liberation 33405 Talence CedexFrance

In this paper,we describe a residual distribution(RD)method where,contrarily to“standard”this type schemes,the mesh is not necessarily *** also allows to use discontinuous elements,contrarily to the“standard”case where continuous elements are ***,if continuity is forced,the scheme is similar to the standard RD ***,the situation becomes comparable with the Discontinuous Galerkin(DG)method,but it is simpler to implement than DG and has guaranteed L^(∞)*** focus on the second-order case,but the method can be easily generalized to higher degree polynomials.

关键词： Discontinuous finite element methods residual distribution schemes hyperbolic problems nonlinear stabilisation

Improving the utility of locally differentially private protocols for longitudinal and multidimensional frequency estimates

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Digital Communications and Networks 2024年第2期10卷 369-379页

作者： Héber H.Arcolezi Jean-François Couchot Bechara Al Bouna Xiaokui Xiao inria andÉcole Polytechnique(IPP) PalaiseauFrance Femto-ST Institute Univ.Bourg.Franche-ComtéUBFCCNRSBelfortFrance TICKET Lab. Antonine University Hadat-BaabdaBaabdaLebanon School of Computing National University of SingaporeSingaporeSingapore

This paper investigates the problem of collecting multidimensional data throughout time(i.e.,longitudinal studies)for the fundamental task of frequency estimation under Local Differential Privacy(LDP)*** to frequency estimation of a single attribute,the multidimensional aspect demands particular attention to the privacy ***,when collecting user statistics longitudinally,privacy progressively ***,the“multiple”settings in combination(i.e.,many attributes and several collections throughout time)impose several challenges,for which this paper proposes the first solution for frequency estimates under *** tackle these issues,we extend the analysis of three state-of-the-art LDP protocols(Generalized Randomized Response–GRR,Optimized Unary Encoding–OUE,and Symmetric Unary Encoding–SUE)for both longitudinal and multidimensional data *** the known literature uses OUE and SUE for two rounds of sanitization(***),i.e.,L-OUE and L-SUE,respectively,we analytically and experimentally show that starting with OUE and then with SUE provides higher data utility(i.e.,L-OSUE).Also,for attributes with small domain sizes,we propose Longitudinal GRR(L-GRR),which provides higher utility than the other protocols based on unary ***,we also propose a new solution named Adaptive LDP for LOngitudinal and Multidimensional FREquency Estimates(ALLOMFREE),which randomly samples a single attribute to be sent with the whole privacy budget and adaptively selects the optimal protocol,i.e.,either L-GRR or *** shown in the results,ALLOMFREE consistently and considerably outperforms the state-of-the-art L-SUE and L-OUE protocols in the quality of the frequency estimates.

关键词： Local differential privacy Discrete distribution estimation Frequency estimation Multidimensional data Longitudinal studies

FullApertureReconstruction of theAcoustic Far-Field Pattern from Few Measurements

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Communications in Computational Physics 2012年第2期11卷 647-659页

作者： Helene Barucq Chokri Bekkey Rabia Djellouli inria bordeaux sud-ouest research center Team Project Magique-3D&LMA/CNRS UMR 5142Universite de Pau et des Pays de l’AdourFrance Faculte des Sciences de Monastir Tunisia Department of Mathematics California State University Northridge&Interdisciplinary Research Institute for the SciencesIRISUSA

We propose a numerical procedure to extend to full aperture the acoustic farfield pattern(FFP)when measured in only few observation *** reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized *** proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton *** present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.

关键词： Acoustic scattering problem limited aperture inverse obstacle problem ill-posed problem total variation Tikhonov regularization Newton method

Effect of wind stress forcing on ocean dynamics at air-sea interface

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Frontiers of Information Technology & Electronic Engineering 2018年第8期19卷 1056-1062页

作者： Hussein YAHIA Veronique GARCON Joel sudRE Christophe MAES research center inria bordeaux-South West Talence 33405France CNRS LEGOS LaboratoryToulouse 31400France Brest University CNRSIRDIFREMERLOPSIUEMBrest 29238France

We evidence and study the differences in turbulence statistics in ocean dynamics carried by wind forcing at the air-sea interface. Surface currents at the air-sea interaction are of crucial importance because they transport heat from low to high latitudes. At first order, oceanic currents are generated by the balance of the Coriolis and pressure gradient forces(geostrophic current) and the balance of the Coriolis and the frictional forces dominated by wind stress(Ekman current) in the surface ocean layers. The study was conducted by computing statistical moments on the shapes of spectra computed within the framework of microcanonical multi-fractal formalism. Remotely sensed daily datasets derived from one year of altimetry and wind data were used in this study, allowing for the computation of two kinds of vector fields: geostrophy with and geostrophy without wind stress forcing. We explore the statistical properties of singularity spectra computed from velocity norms and vorticity data, notably in relation with kurtosis information to underline the differences in the turbulent regimes associated with both kinds of velocity fields.

关键词： Ocean dynamics Remote sensing Turbulence Signal processing Multi-fractal formalism

A Modified Discontinuous GalerkinMethod for Solving Efficiently Helmholtz Problems

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Communications in Computational Physics 2012年第2期11卷 335-350页

作者： Magdalena Grigoroscuta-Strugaru Mohamed Amara Henri Calandra Rabia Djellouli inria bordeaux sud-ouest research center Team Project Magique-3D and LMA/CNRS UMR 5142Universit´e de Pau et des Pays de l’AdourFrance BCAM Basque Center for Applied MathematicsBilbaoSpain. TOTAL Avenue LarribauPauFrance Department of Mathematics California State University Northridge and Interdisciplinary Research Institute for the SciencesIRISUSA

A new solution methodology is proposed for solving efficiently Helmholtz *** proposed method falls in the category of the discontinuous Galerkin ***,unlike the existing solution methodologies,this method requires solving(a)well-posed local problems to determine the primal variable,and(b)a global positive semi-definite Hermitian system to evaluate the Lagrange multiplier needed to restore the continuity across the element *** numerical results obtained for two-dimensional interior Helmholtz problems are presented to assess the accuracy and the stability of the proposed solution methodology.

关键词： Helmholtz equation discontinuous Galerkin plane waves Lagrange multipliers inf-sup condition waveguide problems

Reasoning about Software Trustworthiness with Derivation Trees

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Journal of Shanghai Jiaotong university(Science) 2024年第3期29卷 579-587页

作者：邓玉欣陈泽众汪洋杜文杰毛碧飞梁智章林秋诗李静辉 Shanghai Key Laboratory of Trustworthy Computing East China Normal UniversityShanghai 200062China Shanghai Normal University Shanghai 200233China Trustworthiness Theory research center Huawei Technologies Co.Ltd.Shenzhen 518129GuangdongChina

In order to analyze the trustworthiness of complex software systems,we propose a model of evidence-based software trustworthiness called trustworthiness derivation tree(TDT).The basic idea of constructing a TDT is to refine main properties into key ingredients and continue the refinement until basic facts such as evidences are *** skeleton of a TDT can be specified by a set of rules,which are convenient for automated reasoning in *** develop a visualization tool that can construct the skeleton of a TDT by taking the rules as input,and allow a user to edit the TDT in a graphical user *** a software development life cycle,TDTs can serve as a communication means for different stakeholders to agree on the properties about a system in the requirement analysis phase,and they can be used for deductive reasoning so as to verify whether the system achieves trustworthiness in the product validation *** have piloted the approach of using TDTs in more than a dozen real scenarios of software ***,using TDTs helped us to discover and then resolve some subtle problems.

关键词： trustworthiness refinement evidence visualization

High-Order Schemes Combining the Modified Equation Approach and Discontinuous Galerkin Approximations for the Wave Equation

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Communications in Computational Physics 2012年第2期11卷 691-708页

作者： Cyril Agut Julien Diaz Abdelaaziz Ezziani LMA CNRS UMR 5142Universite de PauFrance inria bordeaux research center Project Team Magique3DFrance

We present a new high ordermethod in space and time for solving the wave equation,based on a newinterpretation of the“Modified Equation”***,contrary to most of the works,we consider the time discretization before the space *** the time discretization,an additional biharmonic operator appears,which can not be discretized by classical finite *** propose a new Discontinuous Galerkinmethod for the discretization of this operator,andwe provide numerical experiments proving that the new method is more accurate than the classicalModified Equation technique with a lower computational burden.

关键词： High order schemes discontinuous Galerkin method acoustic wave equation

A Review of Residual Distribution Schemes for Hyperbolic and Parabolic Problems:The July 2010 State of the Art

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Communications in Computational Physics 2012年第4期11卷 1043-1080页

作者： Remi Abgrall Team Bacchus Institut de Mathematiques de BordeauxINRIA and University of Bordeaux33405 Talence cedexFrance

We describe and review non oscillatory residual distribution schemes that are rather natural extension of high order finite volume schemes when a special emphasis is put on the structure of the computational *** provide their connections with standard stabilized finite element and discontinuous Galerkin schemes,show that their are really non *** also discuss the extension to these methods to parabolic *** also draw some research perspectives.

关键词： Hyperbolic problems Navier Stokes equations unstructuredmeshes residual distribution methods

Phase-field modeling of fracture for quasi-brittle materials

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Underground Space 2019年第1期4卷 10-21页

作者： Jacinto Ulloa Patricio Rodríguez Cristóbal Samaniego Esteban Samaniego Department of Civil Engineering Katholieke Universiteit LeuvenB-3001 LeuvenBelgium Departamento de Recursos Hídricos y Ciencias Ambientales Universidad de CuencaCuenca 010151Ecuador Universidad de Cuenca Cuenca 010151Ecuador Institut für Kontinuumsmechanik Leibniz Universität HannoverHannover 30167Germany inria bordeaux-sud-ouest research center 200 Avenue de la Vieille TourTalence 33405France Facultad de Ingeniería Universidad de CuencaEcuador

This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack *** the computational mechanics community,several studies have treated the issue of modeling fracture using phase *** of these studies have used an approach that implies the lack of a damage *** herein explore an alternative model that includes a damage threshold and study how it compares with the most popular *** formulation is systematically explained within a rigorous variational ***,we present the corresponding three-dimensional finite element discretization that leads to a straightforward numerical *** simulations in two dimensions and three dimensions are then *** results show that while an elastic stage and a damage threshold are ensured by the present model,good agreement with the results reported in the literature can be obtained,where such features are generally absent.

关键词： Quasi-brittle materials Fracture Variational formulation Phase fields Gradient damage