List of publications. L. Halpern

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1. Laurence Halpern, Jeffrey Rauch. Bérenger's PML on Cubic Domains for Pauli's Equations. AFST. Tome XXXIII, no 2, pp. 361–403. 2024
2. Gabriele Ciaramella, Laurence Halpern, Luca Mechelli, Convergence analysis and optimization of a Robin Schwarz waveform relaxation method for time-periodic parabolic optimal control problems. Journal of Computational Physics. vol 496. 112572 (2023).
3. Martin Gander, Laurence Halpern, Florence Hubert, Stella Krell. Discrete Optimization of Robin Transmission Conditions for Anisotropic Diffusion with Discrete Duality Finite Volume Methods. Vietnam Journal of Mathematics  Vol 49, pp 1349–1378. (2021)
4. Bérangère Delourme, Laurence Halpern. A  complex homographic best approximation problem. Application to Optimized Robin-Schwarz algorithms, and optimal control problems. SIAM Journal on Numerical Analysis, 59(3), pp 1769-1810 (2021).
5. Martin Gander, Laurence Halpern, Florence Hubert, Stella Krell. Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations. Moroccan J. of Pure and Appl. Anal. (MJPAA)Volume 7(2),  pp 182–214, 2021.
6. L. Halpern, L. Métivier, J. Rauch and J. Ryan, Nobody's perfect; matched layers for heterogeneous media. SIAM J. Sci. Comput. 41(1),  pp A1--A25, 2019.
7. M. Gander, L. Halpern, J. Rannou and J. Ryan, A direct time parallel solver by diagonalization for the wave equation. SIAM J. Sci. Comput. 41(1),  pp A220--A245, 2019.
8. G. Ciaramella, M. J. Gander, L. Halpern and J. Salomon, Methods of Reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning. SMAI Journal of Computational Mathematics, Vol. 5, pp. 161--193, 2019.
   
9. M. Gander, L. Halpern and V. Martin, Multiscale analysis of heterogeneous domain decomposition methods for time-dependent advection–reaction–diffusion, JCAM 344, pp 904-924, 2018.
10. L. Halpern and J. Rauch, Hyperbolic boundary value problems with trihedral corners,  DCDS-A,  AIMS 38 (8), pp. 4403-4450, 2016.
11. M. Gander, L. Halpern  and V. Martin, A new algorithm based on factorization for heterogeneous domain decomposition, Numer. Algorithms,  73(1), pp 167-195, 2016.
12. D. Bennequin, M. Gander, L. Gouarin and L. Halpern, Optimized Schwarz Waveform Relaxation for Advection Reaction Diffusion Equations in Two Dimensions, Numer. Math. (2016) 134, pp 513--567. 
13. M. Gander, L. Halpern  and K.  Santugini, Continuous analysis of the additive Schwarz method: a stable decomposition in H1 with explicit constants. ESAIM, Math. Model. Numer. Anal. 49, No. 3, pp. 713-740, 2015.
14. L. Halpern & F. Hubert, A finite volume Ventcell-Schwarz algorithm  for advection-diffusion equations. SIAM Journal on Numerical Analysis Vol. 52, No 3, pp 1103–1465, 2014.
15. Thi Bach Tuyet Dang, Laurence Halpern & Jean-Jacques Marigo, Asymptotic analysis of small defects near a singular point in antiplane elasticity, with an application to the nucleation of a crack at a notch. Math. and Mechanics of complex systems, vol 2, n°2, pp 141-179,  2014.
    
16. M. Gander, L. Halpern,  Méthodes de décomposition de domaines - Notions de base. Encyclopédie des techniques de l'ingénieur,  méthodes numériques, AF1375.
17. M. Gander, L. Halpern,  Méthodes de décomposition de domaines - Extensions. Encyclopédie des techniques de l'ingénieur,  méthodes numériques, AF1376.
18. L. Halpern, C. Japhet. and J. Szeftel.  Optimized Schwarz Waveform Relaxation and Discontinuous Galerkin Time Stepping for Heterogeneous Problem. SIAM Journal on Numerical Analysis Vol. 50, No 5, pp 2588–2611, 2012.
19. L. Métivier, P. Lailly, F. Delprat-Jannaud, L. Halpern. A 2D nonlinear inversion of well-seismic data.Inverse Problems, vol 27, n°5,  2011.
20. L. Halpern, Sabrina Petit-Bergez and J. Rauch, The Analysis of Matched Layers.Confluentes Mathematici, vol 3, n° 2, pp 159-236, 2011.
21. L. Halpern and J. Szeftel. Optimized and Quasi-Optimal Schwarz Waveform Relaxation for the One Dimensional Schrödinger equation. Mathematical Models & Methods In Applied Sciences, vol 20, n°12, pp 2167-2199, 2010.
22. F. Caetano, M. Gander, L. Halpern and J. Szeftel. Schwarz waveform relaxation algorithms for semilinear reaction-diffusion. Networks and heterogeneous media Volume 5, Number 3, pp 487--505, September 2010.
    
23. M. Gander, L. Halpern, C. Japhet and V. Martin. Viscous Problems with Inviscid Approximations in Subregions: a New Approach Based on Operator Factorization. CANUM 2008,  272--288, ESAIM Proc., 27, EDP Sci. 2009.
    
24. L. Halpern and J. Szeftel.  Nonlinear Schwarz Waveform  Relaxation for Semilinear Wave Propagation. Math. Comp. 78, pp 865-889, 2009.
25. D. Bennequin, M. Gander and L. Halpern. A Homographic Best Approximation Problem with Application to Optimized Schwarz Waveform Relaxation. Math. Comp. 78, no. 265, pp 185--223, 2009.
26. M. Gander, L. Halpern, F. Magoules, F.X. Roux. Analysis of  patch substructuring methods. Int. J. Appl. Math. Comput. Sci.  vol 17, n°3, 395-402, 2007.
27. M. Gander, L. Halpern, F. Magoules. An Optimized Schwarz Method with Two-Sided Robin Transmission Conditions for the Helmholtz Equation, Int. J. for Num. Meth. in Fluids, Vol. 55, No. 2, pp. 163-175, 2007.
28. L. Halpern and O. Lafitte.  Dirichlet to Neumann map for domains with corners and approximate boundary conditions. Journal of Computational and Applied Mathematics. Volume 204, Issue 2, pp 505-514, 15 July 2007.
29. M. Gander and L. Halpern. Optimized Schwarz Waveform Relaxation for Advection Reaction Diffusion Problems.  SIAM Journal on Numerical Analysis Vol.45, # 2, pp 666--697, 2007.
30. L. Halpern. Absorbing Boundary Conditions and Optimized Schwarz Waveform Relaxation. BIT, Volume 46,  pp 21-34, November 2006.
31. L. Halpern . Local space-time refinement for the one dimensional wave equation. Journal of Computational Acoustics, vol.13, no.3, pp 153-176, september 2005.
32. M. Gander and L. Halpern. Absorbing Boundary Conditions for the Wave Equation and Parallel Computing . Math. Comp. 74 , pp 153-176, 2005.
33. L. Halpern. Non conforming space-time  grids for the wave equation : a new approach. VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques, prensas Universitarias de Zaragoza, pp 479-496, 2004.
34. M. Gander and L. Halpern. Méthodes de relaxation d'ondes (SWR) pour l'équation de la chaleur en dimension 1. C. R. Acad. Sci. Paris Ser.I, Math. vol 336, # 6, pp 519--524, 2003.
35. M. Gander, L. Halpern and  F. Nataf. Optimal Schwarz Waveform Relaxation for the one dimensional Wave Equation. SIAM Journal on Numerical Analysis Vol. 41, No 5, pp 1643-1681, 2003.
36. P. D'Anfray , L. Halpern and  J. Ryan. New trends in coupled simulations featuring domain decomposition and metacomputing. M2AN Vol. 36, # 5, pp  953-970, September/October 2002.
37. L. Halpern and  A. Rahmouni. One-way operators, absorbing boundary conditions and domain decomposition for wave propagation. Modern methods in Scientific Computing and Applications, pp 155-209. A. Bourlioux et M.J. Gander editeurs. Kluver Academic Publishers, 2002.
38. M. Gander  and L. Halpern. Un algorithme discret de décomposition de domaines pour l'équation des ondes en dimension 1. C. R. Acad. Sci. Paris Ser.I, Math.  vol 333, # 7, pp 699-702, 2001. 
39. L. Halpern   S. Labbé. La théorie du micromagnétisme. Modélisation et simulation du comportement des matériaux magnétiques. Matapli septembre 2001.
40. L. Halpern. A Spectral method for the Stokes problem in three dimensional unbounded domains. Math. Comp. 70 # 236, pp 1417-1436, 2001.
41. M. Gander  and L. Halpern. Méthodes de décomposition de domaines pour l'équation des ondes en dimension 1. C. R. Acad. Sci. Paris Ser.I, Math. vol 333,  # 6, pp 589-592, 2001.
42. H. Ammari, L. Halpern  K. Hamdache. Asymptotic behaviour of thin ferromagnetic films. Asymptot. Anal. 24, # 3-4,  pp 277-294, 2000.
43. L. Halpern. Spectral methods in polar coordinates for the Stokes problem. Application to computations in unbounded domains. Math. Comp. 65 # 214, pp 507-531, 1996.
44. L. Halpern and  J. Rauch.  Artificial boundary conditions for general parabolic equations. Numer. Math vol 71, pp 185-224, 1995.
45. C. Bardos, L. Halpern, G. Lebeau, J. Rauch, E. Zuazua.  Stabilisation de l'équation des ondes au moyen d'un feed-back portant sur la condition aux limites de Dirichlet. Asymptotic Anal. vol 4, # 4, pp 285-291, 1991.
46. L. Halpern. Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems. SIAM Journal on Math. Anal. vol 22, # 5, pp 1256-1283, 1991.
47. C. Bernardi, V. Girault  and L. Halpern. Variational formulation for a non linear elliptic equation in a three-dimensional exterior domain. Nonlinear Anal. vol 15, # 11, pp 1017-1029, 1990.
48. B. Engquist and L. Halpern. Long-time behavior of absorbing boundary conditions. Math. Meth.  Appl. Sci. vol 13, # 3, pp 189-203, 1990.
49. L. Halpern  and  H. Vandeven. Condition aux limites transparente et méthode spectrale pour le problème de Stokes dans un domaine extérieur. C. R. Acad. Sci. Paris Ser.I, Math. vol 311, pp 701-706, 1990.
50. L. Halpern  and M. Schatzmann. Artificial boundary conditions for incompressible flows. SIAM Journal on Math. Anal. vol 20, # 2, pp 308-353, 1989.
51. B. Engquist and L. Halpern. Open boundary conditions for long time computations. Computational acoustics vol 3 (Princeton), 1989.
52. A. Bamberger, B. Engquist, L. Halpern and P. Joly. Parabolic wave equation approximation in heterogenous media. SIAM Journal on Appl. Math vol 48, # 1, pp 99-128, 1988.
53. A. Bamberger, B. Engquist, L. Halpern and P. Joly. Higher order wave equation approximation in heterogenous media. SIAM Journal on Appl. Math vol 48, # 1, pp 129-154, 1988.
54. L. Halpern and L.N Trefethen. Wide-angle one-way wave equations. J. Acoust. Soc. Amer. vol 84, # 4, pp 1397-1404 , 1988.
55. L. Halpern. Conditions aux limites artificielles pour un système incomplètement parabolique. C. R. Acad. Sci. Paris Ser.I, Math. vol 307, # 8, pp 413-416, 1988.
56. A. Bendali  and L. Halpern. Conditions aux limites absorbantes pour le système de Maxwell dans le vide en dimension 3. C. R. Acad. Sci. Paris Ser.I, Math. vol 307, # 20, pp 1011-1013, 1988.  
57. A. Bamberger and L. Halpern. Study of steady-states for a non linear Schrödinger equation with a non autonomous term.  SIAM Journal on Math. Anal. vol 18, # 1, pp 97-126, 1987.
58. L. Halpern  and J. Rauch. Error analysis for absorbing boundary conditions. Numer. Math. vol 51, # 4, pp 459-467, 1987.
59. L. Halpern and M. Schatzmann. Conditions aux limites artificielles pour les équations de Navier-Stokes incompressibles. C. R. Acad. Sci. Paris Ser.I, Math. vol 304, # 3, pp 83-86, 1987.
60. L. Halpern. Artificial boundary conditions for the linear advection diffusion equation. Math. of Comp vol 46,# 174, pp 425-438, 1986.
61. L.N Trefethen  and L. Halpern.  Well-posedness of one-way wave equations and absorbing boundary conditions. Math. of Comp. vol 47,# 176, pp 421-435, 1986.
62. A. Bendali  and L. Halpern. Approximation par troncature de domaine de la solution du problème aux limites extérieur en régime sinusoïdal. C. R. Acad. Sci. Paris Ser.I, Math. vol 294, #16, pp 557-560, 1982.
63. L. Halpern. Absorbing boundary conditions for the discretization schemes of the one dimensional wave equation. Math. of Comp. vol 38, # 158, pp 415-429, 1982.

Publications in conferences (Proceedings of DD-publications to be found on www.ddm.org)

1. L. Halpern &  J. Rauch,  Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss.
   Séminaire Laurent Schwartz — EDP et applications  2012-2013, Exp. No. 10. http://slsedp.cedram.org/item?id=SLSEDP_2012-2013_A10_0.pdf
2. M. Borrel, L. Halpern , J. Ryan, Euler - Navier-Stokes coupling for multiscale aeroacoustics problems. 20^th AIAA computational fluid dynamics conference, june 2011, Hawai.
3. M. Borrel, L. Halpern , J. Ryan, Euler - Navier-Stokes coupling for aeroacoustics problems. Computational Fluid Dynamics 2010: Proceedings of the Sixth International Conference on Computational Fluid Dynamics, ICCFD6, St Petersburg, Russia.
4. F. Caetano, M. Gander, L. Halpern, J. Szeftel Schwarz waveform relaxation algorithms for semilinear reaction-diffusion. Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2010.
5. M. Gander, L. Gouarin and L. Halpern. Optimized Schwarz Waveform Relaxation Methods: A Large Scale Numerical Study. Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2010.
6. M.J. Gander, L. Halpern and V. Martin. How close to the fully viscous solution can one get when inviscid approximations are used in subregions?. Domain Decomposition Methods in Science and Engineering XIX, Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2010.
7. L. Halpern, C. Japhet & J. Szeftel. Discontinuous Galerkin and nonconforming in time optimized Schwarz waveform relaxation. Domain decomposition methods in science and engineering XVIII, Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2010.
   
8. L. Halpern, C. Japhet. and J. Szeftel. Discontinuous Galerkin and nonconforming in time optimized Schwarz waveform relaxation for  heterogeneous problems. idem.
9. M. Gander, L. Halpern, C. Japhet and V. Martin. Viscous problems with inviscid approximations in subregions: a new approach based on operator factorization. CANUM 2008,  272--288, ESAIM Proc., 27, EDP Sci., Les Ulis, 2009.
10. L. Halpern and J. Szeftel. Optimized and Quasi-Optimal Schwarz Waveform Relaxation for the One Dimensional Schrödinger  equation. idem.
11. M. Gander,  L. Halpern, S. Labbé and K. Santugini.  Optimized Schwarz Waveform Relaxation for Micro-Magnetics. idem.
    
12. E. Blayo, L. Halpern and C. Japhet. Optimized Schwarz waveform relaxation algorithms with nonconforming time discretization for coupling convection-diffusion problems with discontinuous coefficients. Domain Decomposition Methods in Science and Engineering XVI; Series: Lecture Notes in Computational Science and Engineering, Vol. 55 Widlund,   Olof B.; Keyes, David E. (Eds.), Springer, 2007.
13. L. Halpern. Optimized Schwarz Waveform Relaxation Algorithms for  Convection-diffusion Problems and Best Approximation. Domain Decomposition Methods in Science and Engineering XVI. Series: Lecture Notes in Computational Science and Engineering, Vol. 55  Widlund, Olof B.; Keyes, David E. (Eds.), Springer, 2007.
14. M. Gander, L. Halpern and M.  Kern. A Schwarz Waveform Relaxation Method for  Advection--Diffusion--Reaction Problems with Discontinuous  Coefficients and non-Matching Grids. Domain Decomposition Methods in Science and Engineering XVI.  Series: Lecture Notes in Computational Science and Engineering, Vol. 55 Widlund, Olof B.; Keyes, David E. (Eds.), Springer, 2007.
15. M. Gander, L. Halpern, C. Japhet and V. Martin. Advection Diffusion Problems with Pure Advection Approximation in Subregions. Domain Decomposition Methods in Science and Engineering XVI. Series: Lecture Notes in Computational Science and Engineering,  Vol. 55 Widlund, Olof B.; Keyes, David E. (Eds.), Springer, 2007.
16. M. Gander, L. Halpern and C. Japhet. Optimized Schwarz Algorithms for Coupling Convection and Convection-Diffusion Problems.  Domain decomposition methods in science and engineering (Lyon, 2000), 255--262, Theory Eng. Appl. Comput. Methods, Internat. Center Numer. Methods Eng. (CIMNE), Barcelona, 2002.
17. M. Gander, L. Halpern and  F. Nataf.  Optimized Schwarz methods. Domain decomposition methods in sciences and engineering (Chiba, 1999), pp 15-27, DDM.org, Augsburg, 2001.
18. M. Gander, L. Halpern and  F. Nataf.  Domain decomposition methods for wave propagation. Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000), pp 807--811, SIAM, Philadelphia, PA, 2000.
19. L. Halpern and  S. Labbé. From the Quasi-static to the Dynamic Maxwell's Model in Micromagnetism. Mathematical and numerical aspects of wave propagation (Santiago de Compostela, 2000), pp 310-314, SIAM, Philadelphia, PA, 2000.
20. M. Gander, L. Halpern and  F. Nataf. Optimal Convergence for Overlapping and Non-Overlapping Schwarz Waveform Relaxation. Eleventh International Conference on Domain Decomposition Methods (London, 1998), pp 27-36, DDM.org, Augsburg, 1999.
21. L. Halpern. Conditions aux limites artificielles pour le système de Navier-Stokes incompressible. Non linear partial differential equations and their applications, Collge de France seminar, Vol X, 1988.
22. L. Halpern.  Far-field boundary conditions for computation over long time.  Appl. Numer. Math., Transactions of IMACS, 1988.
23. L. Halpern. The paraxial approximation for the wave equation : some new results.  Advances in Computer Methods for Partial Differential Equations, Publ IMACS 1984.

Edition

1. Mathematical and numerical aspects of wave propagation phenomena. Proceedings of the first international conference held in Strasbourg. 1991.
2. Absorbing boundaries and layers,domain decomposition methods. Avec Loic Tourrette. Nova Science Publishers, 2001.