Preprints
[PP5] E. Habbershaw, C. Hauck, J. Hu, and J. Haack. A nonlinear, conservative, entropic Fokker-Planck model for multi-species collisions. Submitted, 2024 [arXiv].
[PP4] B. Ye, J. Hu, C.-W. Shu, and X. Zhong. Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampere system with Dougherty-Fokker-Planck collision operator. Submitted, 2024.
[PP3] R. Bailo, J. Carrillo, and J. Hu. The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations. Submitted, 2024 [arXiv].
[PP2] J. Coughlin, J. Hu, and U. Shumlak. Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition. Submitted, 2023 [arXiv].
[PP1] J. Carrillo, J. Hu, and S. Van Fleet. A particle method for the multispecies Landau equation. Submitted, 2023 [arXiv].
Journal Publications
[J50] J. Hu and R. Shu. Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation. Math. Comp., accepted [arXiv].
[J49] J. Hu, A. Jungel, and N. Zamponi. Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system. Kinet. Relat. Models, accepted [arXiv].
[J48] L. Einkemmer, J. Hu, and J. Kusch. Asymptotic-preserving and energy stable dynamical low-rank approximation. SIAM J. Numer. Anal., 62:73-92, 2024 [link].
[J47] B. Zhu, J. Hu, Y. Lou, and Y. Yang. Implicit regularization effects of the Sobolev norms in image processing. La Matematica, 2023 [link].
[J46] R. Bailo, J. Carrillo, and J. Hu. Bound-preserving finite-volume schemes for systems of continuity equations with saturation. SIAM J. Appl. Math., 83:1315-1339, 2023 [link].
[J45] J. Hu and X. Zhang. Positivity-preserving and energy-dissipative finite difference schemes for the Fokker-Planck and Keller-Segel equations. IMA J. Numer. Anal., 43:1450-1484, 2023 [link].
[J44] J. Coughlin and J. Hu. Efficient dynamical low-rank approximation for the Vlasov-Ampere-Fokker-Planck system. J. Comput. Phys., 470:111590, 2022 [link].
[J43] Z. Cai, J. Hu, Y. Kuang, and B. Lin. An entropic method for discrete systems with Gibbs entropy. SIAM J. Numer. Anal., 60:2345-2371, 2022 [link].
[J42] Q. He, J. Hu, and Z. Zhou. A structure preserving numerical scheme for Fokker-Planck equations of structured neural networks with learning rules. SIAM J. Sci. Comput., 44:B1045-B1067, 2022 [link].
[J41] J. Hu. Fourier spectral methods for nonlinear Boltzmann equations (invited review, in Chinese). Math. Numer. Sin., 44:289-304, 2022 [link].
[J40] J. Hu and Y. Wang. An adaptive dynamical low rank method for the nonlinear Boltzmann equation. J. Sci. Comput., 92:75, 2022 [link].
[J39] J. Hu, X. Huang, J. Shen, and H. Yang. A fast Petrov-Galerkin spectral method for the multidimensional Boltzmann equation using mapped Chebyshev functions. SIAM J. Sci. Comput., 44:A1497-A1524, 2022 [link].
[J38] S. Gottlieb, Z. Grant, J. Hu, and R. Shu. High order strong stability preserving multi-derivative implicit and IMEX Runge-Kutta methods with asymptotic preserving properties. SIAM J. Numer. Anal., 60:423-449, 2022 [link].
[J37] L. Einkemmer, J. Hu, and L. Ying. An efficient dynamical low-rank algorithm for the Boltzmann–BGK equation close to the compressible viscous flow regime. SIAM J. Sci. Comput., 43:B1057-B1080, 2021 [link].
[J36] J. Hu, L. Pareschi, and Y. Wang. Uncertainty quantification for the BGK model of the Boltzmann equation using multilevel variance reduced Monte Carlo methods. SIAM/ASA J. Uncertainty Quantification, 9:650-680, 2021 [link].
[J35] L. Einkemmer, J. Hu, and Y. Wang. An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation. J. Comput. Phys., 439:110353, 2021 [link].
[J34] J. Hu, K. Qi, and T. Yang. A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation. SIAM J. Numer. Anal., 59:613-633, 2021 [link].
[J33] J. Hu, J.-G. Liu, Y. Xie, and Z. Zhou. A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration. J. Comput. Phys., 433:110195, 2021 [link].
[J32] J. Hu and R. Shu. On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations. Math. Comp., 90:641-670, 2021 [link].
[J31] J. Hu and K. Qi. A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels. J. Comput. Phys., 423:109806, 2020 [link].
[J30] R. Bailo, J. Carrillo, and J. Hu. Fully discrete positivity-preserving and energy-dissipating schemes for aggregation-diffusion equations with a gradient flow structure. Commun. Math. Sci., 18:1259-1303, 2020 [link].
[J29] J. Carrillo, J. Hu, L. Wang, and J. Wu. A particle method for the homogeneous Landau equation. J. Comput. Phys. X, 7:100066, 2020 [link].
[J28] J. Hu, J. Shen, and Y. Wang. A Petrov-Galerkin spectral method for the inelastic Boltzmann equation using mapped Chebyshev functions. Kinet. Relat. Models, 13:677-702, 2020 [link].
[J27] J. Hu and X. Huang. A fully discrete positivity-preserving and energy-dissipative finite difference scheme for Poisson-Nernst-Planck equations. Numer. Math., 145:77-115, 2020 [link].
[J26] J. Hu and R. Shu. A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations. Multiscale Model. Simul., 17:1123-1146, 2019 [link].
[J25] J. Hu, S. Jin, and R. Shu. On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime. J. Comput. Phys., 397:108838, 2019 [link].
[J24] S. Jaiswal, A. Pikus, A. Strongrich, I. Sebastiao, J. Hu, and A. Alexeenko. Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts (special issue on Direct Simulation Monte Carlo - The Legacy of Graeme A. Bird). Phys. Fluids, 31:082002, 2019 [link].
[J23] S. Jaiswal, A. Alexeenko, and J. Hu. A discontinuous Galerkin fast spectral method for the multi-species Boltzmann equation. Comput. Methods Appl. Mech. Engrg., 352:56-84, 2019 [link][code].
[J22] J. Hu and Z. Ma. A fast spectral method for the inelastic Boltzmann collision operator and application to heated granular gases. J. Comput. Phys., 385:119-134, 2019 [link].
[J21] S. Jaiswal, A. Alexeenko, and J. Hu. A discontinuous Galerkin fast spectral method for the full Boltzmann equation with general collision kernels. J. Comput. Phys., 378:178-208, 2019 [link][code].
[J20] J. Hu, R. Shu, and X. Zhang. Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation. SIAM J. Numer. Anal., 56:942-973, 2018 [link].
[J19] J. Hu and X. Zhang. On a class of implicit-explicit Runge-Kutta schemes for stiff kinetic equations preserving the Navier-Stokes limit (special issue dedicated to Chi-Wang Shu on the occasion of his 60th birthday). J. Sci. Comput., 73:797-818, 2017 [link].
[J18] I. Gamba, J. Haack, C. Hauck, and J. Hu. A fast spectral method for the Boltzmann collision operator with general collision kernels. SIAM J. Sci. Comput., 39:B658-B674, 2017 [link].
[J17] R. Shu, J. Hu, and S. Jin. A stochastic Galerkin method for the Boltzmann equation with multi-dimensional random inputs using sparse wavelet bases (special issue dedicated to Zhenhuan Teng on the occasion of his 80th birthday). Numer. Math. Theor. Meth. Appl., 10:465-488, 2017 [link].
[J16] J. Sun, S. Fomel, T. Zhu, and J. Hu. Q-compensated least-squares reverse time migration using low-rank one-step wave extrapolation. Geophysics, 81:S271-S279, 2016 [link].
[J15] J. Hu and S. Jin. A stochastic Galerkin method for the Boltzmann equation with uncertainty. J. Comput. Phys., 315:150-168, 2016 [link].
[J14] J. Hu, S. Jin, and D. Xiu. A stochastic Galerkin method for Hamilton-Jacobi equations with uncertainty. SIAM J. Sci. Comput., 37:A2246-A2269, 2015 [link].
[J13] J. Hu, S. Jin, and L. Wang. An asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: a splitting approach. Kinet. Relat. Models, 8:707-723, 2015 [link].
[J12] J. Hu, S. Fomel, and L. Ying. A fast algorithm for 3D azimuthally anisotropic velocity scan. Geophysical Prospecting, 63:368-377, 2015 [link].
[J11] J. Hu, Q. Li, and L. Pareschi. Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy. J. Sci. Comput., 62:555-574, 2015 [link].
[J10] J. Hu and L. Wang. An asymptotic-preserving scheme for the semiconductor Boltzmann equation toward the energy-transport limit. J. Comput. Phys., 281:806-824, 2015 [link].
[J9] J. Hu and L. Ying. A fast algorithm for the energy space boson Boltzmann collision operator. Math. Comp., 84:271-288, 2015 [link].
[J8] Y. Chen, S. Fomel, and J. Hu. Iterative deblending of simultaneous-source seismic data using seislet-domain shaping regularization. Geophysics, 79:V179-V189, 2014 [link].
[J7] G. Fang, S. Fomel, Q. Du, and J. Hu. Lowrank seismic-wave extrapolation on a staggered grid. Geophysics, 79:T157-T168, 2014 [link].
[J6] J. Hu and S. Jin. On the quasi-random choice method for the Liouville equation of geometrical optics with discontinuous wave speed. J. Comput. Math., 31:573-591, 2013 [link].
[J5] J. Hu, S. Fomel, L. Demanet, and L. Ying. A fast butterfly algorithm for generalized Radon transforms. Geophysics, 78:U41-U51, 2013 [link].
[J4] J. Hu and L. Ying. A fast spectral algorithm for the quantum Boltzmann collision operator. Commun. Math. Sci., 10:989-999, 2012 [link].
[J3] J. Hu, S. Jin, and B. Yan. A numerical scheme for the quantum Fokker-Planck-Landau equation efficient in the fluid regime. Commun. Comput. Phys., 12:1541-1561, 2012 [link].
[J2] F. Filbet, J. Hu, and S. Jin. A numerical scheme for the quantum Boltzmann equation with stiff collision terms. ESAIM: Math. Model. Numer. Anal. (M2AN), 46:443-463, 2012 [link].
[J1] J. Hu and S. Jin. On kinetic flux vector splitting schemes for quantum Euler equations. Kinet. Relat. Models, 4:517-530, 2011 [link].
Book Chapters
[BC3] J. Carrillo, J. Hu, Z. Ma, and T. Rey. Recent development in kinetic theory of granular materials: analysis and numerical methods. In G. Albi, S. Merino-Aceituno, A. Nota, and M. Zanella, editors, Trails in Kinetic Theory, volume 25, pages 1-36. SEMA SIMAI Springer Series, 2021 [link][pdf].
[BC2] J. Hu and S. Jin. Uncertainty quantification for kinetic equations. In S. Jin and L. Pareschi, editors, Uncertainty Quantification for Hyperbolic and Kinetic Equations, volume 14, pages 193-229. SEMA SIMAI Springer Series, 2017 [link][pdf].
[BC1] J. Hu, S. Jin, and Q. Li. Asymptotic-preserving schemes for multiscale hyperbolic and kinetic equations. In R. Abgrall and C.-W. Shu, editors, Handbook of Numerical Methods for Hyperbolic Problems: Applied and Modern Issues, chapter 5, pages 103-129. North-Holland, 2017 [link][pdf].
Selected Conference Publications
[C6] N. Adhikari, B. Morton, A. Alexeenko, and J. Hu. Verification of a discontinuous Galerkin fast spectral solver for the full Boltzmann equation. In Proceedings of the 32nd International Symposium on Rarefied Gas Dynamics, AIP Conf. Proc., 2996:060002, 2024 [link].
[C5] S. Jaiswal, J. Hu, and A. Alexeenko. Fast deterministic solution of the full Boltzmann equation on Graphics Processing Units. In Proceedings of the 31st International Symposium on Rarefied Gas Dynamics, AIP Conf. Proc., 2132:060001, 2019 [link].
[C4] J. Hu, S. Jin, and R. Shu. A stochastic Galerkin method for the Fokker-Planck-Landau equation with random uncertainties. In C. Klingenberg and M. Westdickenberg, editors, Theory, Numerics and Applications of Hyperbolic Problems II. HYP 2016, Springer Proceedings in Mathematics & Statistics, 2018 [link].
[C3] G. Fang, J. Hu, and S. Fomel. Weighted least square based lowrank finite difference for seismic wave extrapolation. In Technical Program Expanded Abstracts of the 85th SEG Annual Meeting, pages 3554-3559, 2015 [link].
[C2] J. Sun, S. Fomel, and J. Hu. Least-squares reverse-time migration using one-step two-way wave extrapolation by non-stationary phase shift. In Technical Program Expanded Abstracts of the 84th SEG Annual Meeting, pages 3967-3973, 2014 [link].
[C1] J. Hu, S. Fomel, L. Demanet, and L. Ying. A fast butterfly algorithm for the hyperbolic Radon transform. In Technical Program Expanded Abstracts of the 82nd SEG Annual Meeting, pages 1-5, 2012 [link].