Publications

Joint publications of ANTipODE

[1] N. Crouseilles, S. Jin and M. Lemou. Nonlinear geometric optics method based multi-scale numerical schemes for highly-oscillatory transport equations. Math. Models Meth-ods Appl. Sci. 27, pp. 2031-2070, 2017.
[4] N. Crouseilles, S. Jin, M. Lemou, F. Méhats, A micro-macro method for a kinetic graphene model in one-space dimension, accepted for publication in SIAM MMS.
[5] N. Crouseilles, S. Jin, M. Lemou and L. Liu. Nonlinear geometric optics based multi-scale stochastic Galerkin methods for highly-oscillatory transport equations with random inputs, under revision for M2AN.
[6] P. Chartier, D. Fang, Lemou, F. Méhats, Asymptotic analysis and numerical methods for a
spin boson problem, in preparation.
[7] P. Chartier, M. Lemou, F. Méhats, A. Nair, Uniformly accurate methods for the multiscale
Landau-Zenner problem, in preparation.
[8] M. Lemou, F. Méhats, Z. Ding, Wellposedness and stability of the gravitational Vlasov-Poisson
system with external potential, to be submitted.
[10] P. Chartier, M. Lemou and M. Tao, Attraction into Resonance for Single Variable Frequency Fast Oscillators, in preparation.

Main publications of the participants relevant to ANTipODE

[2] P. Chartier, M. Lemou, F. Méhats, G. Vilmart, A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations, FOCM 2019
[3] P. Chartier, M. Lemou, F. Méhats, G. Vilmart, Highly-oscillatory problems with time-dependent vanishing frequency, SIAM Journal on Numerical Analysis, 2019

[9] P. Chartier, M. Lemou, F. Méhats, X. Zhao, Uniformly accurate methods for Vlasov equations with non-homogeneous strong magnetic fields, Mathematics of Computation, 2019.

 

  • P. Chartier, J. Makazaga, A. Murua, and G. Vilmart, Multi-revolution composition methods for highly-oscillatory differential equations, Numer. Math. 128, pp. 167-192, 2014.
  • P. Chartier, M. Lemou and F. Méhats, Highly-oscillatory evolution equations with non-resonant frequencies: averaging and numerics, Numer. Math. 136, pp. 907-939, 2017.
  • P. Chartier, F. Méhats and L. Le Treust, Uniformly accurate time-splitting methods for the semiclassical Schrödinger equation, Part I: Construction of the schemes and simulations; Part II: Numerical analysis of the linear case, submitted.
  • P. Chartier, F. Méhats, M. Thalhammer and Y. Zhang, Superconvergence of Strang splitting for NLS in T d, Math. of Comp. 85, pp. 2863-2885, 2016.
  • F. Castella, P. Chartier, F. Méhats and A. Murua, Stroboscopic averaging for the non-linear Schrödinger equation, FOCM 15, pp. 519-559, 2015.
  • P. Chartier, N. Crouseilles, M. Lemou and F. Méhats, Uniformly accurate numerical schemes for highly-oscillatory Klein-Gordon and nonlinear Schrödinger equation, Numer. Math. 129, pp. 211-250, 2015.
  • P. Chartier, A. Murua and J.M. Sanz-Serna, Higher-order averaging, formal series and numerical integration. Part I: B-series, FOCM, 2010, Part II: the quasi-periodic case, FOCM, 2012, Part III: error bounds, FOCM, 2013.
  • P. Chartier, F. Méhats, M. Thalhammer and Y. Zhang, Convergence of multi-revolution composition time-splitting methods for highly-oscillatory differential equa-tions of Schrödinger type, to appear in ESAIM:M2AN.
  • N. Crouseilles, L. Einkemmer and E. Faou, An asymptotic preserving scheme for the relativistic Vlasov-Maxwell equations in the classical limit, Comput. Phys. Comm. 209, pp. 13-26, 2016.
  • N. Crouseilles, M. Lemou and F. Méhats, Asymptotic preserving schemes for highly-oscillatory kinetic equations, J. Comput. Phys. 248, pp. 287-308, 2013.
  • N. Crouseilles, M. Lemou, F. Méhats and X. Zhao, Uniformly accurate Particle-In-Cell method for the long time solution of the two-dimensional Vlasov-Poisson equation with uniform strong magnetic field, to appear in J. Comput. Phys.
  • N. Crouseilles, M. Lemou, F. Méhats and X. Zhao, Uniformly accurate forward semi-Lagrangian methods for highly-oscillatory Vlasov-Poisson equations, SIAM MMS 15, pp. 723-744, 2017.
  • N. Crouseilles, M. Lemou, and G. Vilmart, Asymptotic Preserving numerical schemes for multiscale parabolic problems, C. R. Acad. Sci. Paris; Ser. I 354, pp. 271-276, 2016.
  • S. Jin, Efficient Asymptotic Preserving (AP) schemes for some multiscale kinetic equa-tions, SIAM J. Sci. Comp. 21, pp. 441-454, 1999.
  • L. Pareschi and S. Jin, Asymptotic Preserving (AP) Schemes for Multiscale Kinetic Equations: a Unified Approach , pp 573-582, in Hyperbolic Problems: Theory, Nu-merics, Applications, Ed. H. Freistuhler and G. Warnecke, Birkhauser-Verlag, Berlin, 2001.
  • S. Jin and Y. Shi, A micro-macro decomposition based asymptotic preserving scheme for the multispecies Boltzmann equation, SIAM J. Sci. Comp. 31, pp. 4580-4606, 2010.
  • F. Filbet and S. Jin, A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comp. Phys. 229, pp. 7625-7648, 2010.
  • S. Jin and B. Yan, A class of asymptotic preserving schemes for the Fokker-Planck-Landau equation, J. Comp. Phys. 230, pp. 6420-6437, 2011.
  • S. Jin and L. Wang, An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime, Acta Mathematica Scientia 31, pp. 2219-2232, 2011.
  • S. Jin and Q. Li, A BGK-penalization asymptotic preserving scheme for the multispecies Boltzmann equation, Numerical Methods for Partial Differential Equations 29, pp. 1056-1080, 2013.
  • S. Jin and B. Yan, A successive penalty-based asymptotic preserving scheme for kinetic equations, SIAM J. Sci. Comput. 35, pp. 150-172, 2013.
  • T. Goudon, S. Jin, J.G. Liu and B. Yan, Asymptotic Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density, International Journal for Numerical Methods in Fluids 75, pp. 81-102, 2014.
  • S. Jin and L. Wang, Asymptotic preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime, SIAM J. Sci. Comp. 35, pp. 799-819, 2013.
  • W. Ren, H. Liu and S. Jin, An Asymptotic Preserving Monte Carlo Method for the Boltzmann Equation, , J. Comp. Phys. 276, pp. 380-404, 2014.
  • J. Hu, S. Jin and L. Wang, An asymptotic preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: a splitting approach, Kinetic and Related Models 8, pp. 707-723, 2015.
  • K. Kupper, M. Frank and S. Jin, An asymptotic preserving 2-D staggered grid method for multiscale transport equations, SIAM J. Num. Anal. 54, pp. 440-461, 2016.
  • B. Zhang, H. Liu and S. Jin, An Asymptotic Preserving Monte Carlo method for the multispecies Boltzmann equation, J. Comp. Phys. 305, pp. 575-588, 2016.
  • A. Fannjiang, S. Jin and G. Papanicolaou, High frequency behavior of the focusing nonlinear Schrödinger equation with random inhomogeneities, SIAM J. Appl. Math. 63, pp. 1328-1358, 2003.
  • W.Z. Bao, S. Jin and P. Markowich, On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime, J. Comp. Phys., 175, pp. 487-524, 2002.
  • W.Z. Bao, S. Jin and P. Markowich, Numerical study of time-splitting spectral dis-cretizations of nonlinear Schrödinger equations in the semiclassical regimes, SIAM J. Sci. Comp. 25, pp. 27-64, 2003.
  • S. Jin and X.T. Li, Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs. Wigner, Physica D 182, pp.
    46- 85, 2003.
  • L. Gosse, S. Jin and X.T. Li, On two moment systems for computing multiphase semi-classical limit of the Schrödinger equation, Math. Models Meth. Appl. Sci. 13, pp. 1689-1723, 2003.
  • H.L. Liu, S. Osher and R. Tsai, Computing multivalued physical observables for the semiclassical limit of the Schrödinger equations, J. Comp. Phys. 205, pp. 222-241, 2005.
  • S. Jin and K. Novak, A semiclassical transport model for thin quantum barriers, Mul-tiscale Modeling and Simulation 5(4), pp. 1063-1086, 2006.
  • S. Jin, X. Liao and X. Yang, The Vlasov-Poisson equations as the semiclassical limit of the Schrödinger-Poisson equations: a numerical study, J. Hyperbolic Diff. Eqn. 5(3), pp. 569-587, 2008.
  • Z.Y. Huang, S. Jin, P.A. Markowich and C. Sparber, Numerical simulation of the non-linear Schrödinger equation with multi-dimensional periodic potentials, SIAM MMS 7, pp. 539-564, 2008.
  • S. Jin, H. Wu and X. Yang, Gaussian beam methods for the Schrödinger equation in the semiclassical regime: Lagrangian and Eulerian formulations, Comm. Math. Sci. 6, pp. 995-1020, 2008.
  • S. Jin, P. Qi and Z. Zhang, An Eulerian surface hopping method for the Schrödinger equation with conical crossings, SIAM MMS 9, pp. 258-281, 2011.
  • S. Jin, D. Wei, R. Tsai and X. Yang, A level set method for the semiclassical limit of the Schrödinger equation with discontinuous potentials, J. Comp. Phys. 229, pp. 7440-7455, 2010.
  • S. Jin, P.A. Markowich and C. Sparber, Mathematical and computational methods for semiclassical Schrödinger equations, Acta Numerica 20, pp. 211-289, 2011.
  • S. Jin and D. Wei, A particle method for the semiclassical limit of the Schrödinger equation and the Vlasov-Poisson equations, SIAM J. Num. Anal. 50, pp. 3259-3279, 2012.
  • D. Yin, M. Tang and S. Jin, The Gaussian beam method for the Wigner equation with discontinuous potentials, Inverse Problems and Imaging 7, pp. 1051-1074, 2013.
  • L. Chai, S. Jin and Q. Li, Semiclassical models for the Schrödinger equation with periodic potentials and band crossings, Kinetic and Related Models 6, pp. 505-532, 2013.
  • L. Jefferis and S. Jin, Computing high frequency solutions of symmetric hyperbolic systems with polarized waves, Comm. Math. Sci. 13, pp. 1001-1024, 2015.
  • L. Jefferis and S. Jin, A Gaussian beam method for high frequency solution of symmetric hyperbolic systems with polarized waves, SIAM MMS 13, pp. 733-765, 2015
  • S. Jin and Z. Zhou, A semi-Lagrangian time splitting method for the Schrödinger equa-tion with vector potentials, Communications in Information and Systems, 13, pp. 247-289, 2013.
  • L. Chai, S. Jin, Q. Li and O. Morandi, A multi-band semi-classical model for surface hopping quantum dynamics, SIAM MMS, 13, pp. 205-230, 2015.
  • S. Jin, C. Sparber and Z. Zhou, On the classical limit of a time-dependent self-consistent field system: analysis and computation, Kinetic and Related Models 10, pp. 263-298, 2017.
  • A. Faraj and S. Jin, The Landau-Zener transition and the surface hopping method for the 2D Dirac equation for graphene , Comm. Comp. Phys., 21, pp. 313-357, 2017.
  • L. Chai, S. Jin and P.A. Markowich, A hybrid method for computing the Schrödinger equations with periodic potential with band-crossings in the momentum space, Comm. Comp. Phys., to appear.
    J. Hu and S. Jin, A stochastic Galerkin method for the Boltzmann equation with un-certainty, J. Comp. Phys. 315, pp. 575-588, 2016.
  • A. Chertock, S. Jin and A. Kurganov, An operator splitting based stochastic Galerkin method for the one-dimensional compressible Euler equations with uncertainty, submit-ted.
  • A. Chertock, S. Jin and A. Kurganov, A well-balanced operator splitting based stochas-tic Galerkin method for the one-dimensional Saint-Venant system with uncertainty, submitted.
  • S. Jin and H. Lu, An Asymptotic Preserving stochastic Galerkin method for the radia-tive heat transfer equations with random inputs and diffusive scalings, J. Comp. Phys. 334, pp. 182-206, 2017.
  • S. Jin, J.G. Liu and Z. Ma, Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition based asymptotic preserving method, Research in Math. Sci., to appear.
  • Y. Zhu and S. Jin, The Vlasov-Poisson-Fokker-Planck system with uncertainty and a one-dimensional asymptotic preserving method, SIAM Multiscale Model. Simul., to appear.
  • R. Shu, J. Hu and S. Jin, A stochastic Galerkin method for the Boltzmann equation with multi-dimensional random inputs using sparse wavelet bases, Num. Math.: Theory, Methods and Applications (NMTMA) 10, pp. 465-488, 2017.
  • S. Jin and R. Shu, A stochastic Asymptotic Preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty, J. Comp. Phys. 335, pp. 905-924, 2017.
  • S. Jin and Z. Ma, The discrete stochastic Galerkin method for hyperbolic equations with non-smooth and random coefficients, J. Sci. Comp., to appear.
  • S. Jin, H. Lu and L. Pareschi, Efficient stochastic Asymptotic Preserving IMEX methods for transport equations with diffusive scalings and random inputs, submitted.
  • S. Jin and Y. Zhu, Hypocoercivity and uniform regularity for the Vlasov-Poisson-Fokker-Planck system with uncertainty and multiple scales, submitted.
  • J. Hu and S. Jin, Uncertainty quantification for kinetic equations, submitted.

 

Comments are closed.