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Exact Boundary Conditions for PeriodicWaveguides Containing a Local Perturbation

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Communications in Computational Physics 2006年第6期1卷 945-973页

作者： Patrick Joly Jing-Rebecca Li Sonia Fliss Domaine de Voluceau-Rocquencourt-B.P.105 78153 Le Chesnay CedexFrance

We consider the solution of the Helmholtz equation−u(x)−n(x)2ω2u(x)=f(x),x=(x,y),in a domain which is infinite in x and bounded in *** assume that f(x)is supported in 0:={x∈|a− 详细信息

We consider the solution of the Helmholtz equation−u(x)−n(x)2ω2u(x)=f(x),x=(x,y),in a domain which is infinite in x and bounded in *** assume that f(x)is supported in 0:={x∈|a−le us to find the solution on 0∪􀀀+∪􀀀−.Then the solution can be extended in in a straightforward manner from the values on􀀀−and􀀀+.The exact boundary conditions as well as the extension operators are computed by solving local problems on a single periodicity cell.

关键词： Exact boundary conditions periodic media Dirichlet to Neumann maps

PerfectlyMatched Layer withMixed Spectral Elements for the Propagation of LinearizedWaterWaves

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Communications in Computational Physics 2012年第2期11卷 285-302页

作者： Gary Cohen Sebastien Imperiale INRIA Domaine de VoluceauRocquencourt-BP 10578153 Le Chesnay CedexFrance

After setting a mixed formulation for the propagation of linearized water waves problem,we define its spectral element ***,in order to take into account unbounded domains,we construct absorbing perfectly matched layer for the *** approximate these perfectly matched layer by mixed spectral elements and show their stability using the“frozen coefficient”***,numerical results will prove the efficiency of the perfectly matched layer compared to classical absorbing boundary conditions.

关键词： Linearized water waves perfectly matched layer mixed finite elements

Operator Factorization forMultiple-Scattering Problems and an Application to Periodic Media

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Communications in Computational Physics 2012年第2期11卷 303-318页

作者： J.Coatleven P.Joly POems Project Team UMR ENSTA/CNRS/INRIAInria Rocquencourt78153 Le Chesnay CedexFrance

This work concerns multiple-scattering problems for time-harmonic equations in a reference *** consider scatterers that can be sources,obstacles or compact perturbations of the reference *** aim is to restrict the computational domain to small compact domains containing the *** use Robin-to-Robin(RtR)operators(in the most general case)to express boundary conditions for the interior *** show that one can always factorize the RtR map using only operators defined using single-scatterer *** factorization is based on a decomposition of the diffracted field,on thewhole domainwhere it is *** that there exists a good method for solving single-scatterer problems,it then gives a convenient way to compute RtR maps for a random number of scatterers.

关键词： Multiple-scattering harmonic wave equation exact boundary conditions periodic media

A COMPACT UPWIND SECOND ORDER SCHEME FOR THE EIKONAL EQUATION

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Journal of Computational Mathematics 2010年第4期28卷 489-516页

作者： J.-D. Benamou Songting Luo Hongkai Zhao INRIA INRIA B.P. 105 78153 Le Chesnay Cedex France Department of Mathematics Michigan State University East Lansing MI 48824 USA Department of Mathematics University of California Irvine CA 92697 USA

We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on： 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.

关键词： Eikonal equation Upwind scheme Hamilton-Jacobi Viscosity Solution Sweeping method.

A Reduced Basis Approach for Some Weakly Stochastic Multiscale Problems

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Chinese Annals of Mathematics,Series B 2012年第5期33卷 657-672页

作者： Claude le BRIS Florian THOMINES CERMICS Ecole Nationale des Ponts et Chaussees6 et 8 Avenue Blaise PascalCite DescartesChamps-sur-Marne77455 Marne-La-Vallée Cedex 2France INRIA Rocquencourt MICMAC teamprojectDomaine de VoluceauBP10578153 Le Chesnay CedexFrance. INRIA Rocquencourt MICMAC team-projectDomaine de VoluceauBP10578153 Le Chesnay CedexFrance Laboratoire Navier Ecole Nationale des Ponts et Chaussees6 et 8 Avenue Blaise PascalCite DescartesChamps-Sur-Marne77455 Marne-La-Vallée Cedex 2France.

In this paper,a multiscale problem arising in material science is *** problem involves a random coefficient which is assumed to be a perturbation of a deterministic coefficient,in a sense made precisely in the body of the *** homogenized limit is then computed by using a perturbation *** computation requires repeatedly solving a corrector-like equation for various configurations of the *** this purpose,the reduced basis approach is employed and adapted to the specific *** authors perform numerical tests that demonstrate the efficiency of the approach.

关键词：多尺度问题随机基础材料科学校正方程数值试验摄动法上下文

HIGH-ORDER EXPLICIT TIME-INTEGRATORS FOR DISCONTINUOUS GAleRKIN DISCRETIZATIONS OF THE MAXWELL EQUATIONS

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International Journal of Modeling, Simulation, and Scientific Computing 2013年第1期4卷 132-153页

作者： H.FAHS M.SAFA LAMA Laboratory University Paris-Est Marne-la-Vallee UMR CNRS 80505 boulevard Descartes 77454 Marne-la-Vall´ee Cedex 2France INRIA Paris-Rocquencourt Domaine de Voluceau BP.10578153 Le Chesnay CedexFrance

We investigate the practical implementation of a high-order explicit time-stepping method based on polynomial approximations,for possible application to large-scale problems in *** the spatial discretization by a high-order discontinuous Galerkin method,we obtain a linear system of differential equations of the form,∂tY(t)=HY(t)+S(t),where H is a matrix containing the spatial derivatives and t is the time *** formal solution can be written in terms of the matrix exponential,exp(tH),acting on some *** introduce a general family of time-integrators based on the approximation of exp(tH)by Jacobi polynomial *** discuss the efficient implementation of this technique,and based on some test problems,we compare the virtues and shortcomings of the *** also demonstrate how these schemes provide an efficient alternative to standard explicit integrators for computing solutions over long time intervals.

关键词： Maxwell’s equations discontinuous Galerkin method time-stepping schemes

ALowFrequencyModel for Acoustic Propagation in a 2D Flow Duct:Numerical Computation

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Communications in Computational Physics 2012年第2期11卷 508-524页

作者： Lauris Joubert Patrick Joly POEMS CNRS-INRIA-ENSTA UMR 270632 Boulevard Victor75015 ParisFrance POEMS CNRS-INRIA-ENSTAUMR 2706INRIA RocquencourtBP 10578153 Le Chesnay CedexFrance

In this paper we study a low frequency model for acoustic propagation in a 2D flow *** some Mach profile flow,we are able to give a well-posedness *** proof relies on a quasi-explicit expression of the solution which provides us an efficient numerical *** give and comment numerical results for particular linear,tangent and quadratic ***,we give a numerical validation of our asymptotic model.

关键词： Acoustics in flow Galbrun’s equations asymptotic analysis Laplace transform

OPTIMIZED IMPleMENTATION OF REAL-TIME IMAGE PROCESSING ALGORITHMS ON FIELD PROGRAMMABle GATE ARRAYS

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OPTIMIZED IMPLEMENTATION OF REAL-TIME IMAGE PROCESSING ALGOR...

Complete Radiation Boundary Conditions for Convective Waves

1998 Fourth International Conference Signal Processing

作者： AILTON F.DIAS CHRISTOPHE LAVARENNE MOHAMED AKIL YVES SOREL INRIA-Rocquencourt-Projet SOSSO B.P.10578153 Le Chesnay CedexFrance

＜正＞We present the Algorithm Architecture "Adequation" methodology for the optimized implementation of real-time image processing algorithms on field programmable gate *** methodology is based on a single factorized graphs model,used from the algorithm specification down to the architecture implementation,through optimizations expressed in terms of defactorization transformations. A simple image processing example is presented to illustrate the methodology.

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Communications in Computational Physics 2012年第2期11卷 610-628页

作者： Thomas Hagstrom Eliane Becache Dan Givoli Kurt Stein Dept.of Mathematics Southern Methodist UniversityDallasTX 75275USA. Propagation des Ondes Etude Mathematique et Simulation(POEMS)INRIADomaine de Voluceau-RocquencourtBP 10578153 Le Chesnay CedexFrance Dept.of Aerospace Engineering TechnionHaifa 32000Israel

Local approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated,analyzed,and *** results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in[4].

关键词： Radiation boundary conditions convective waves