# Preprints

[PP4] J. Hu, S. Van Fleet, and A. Wan. Fully discrete energy-dissipative and conservative discrete gradient particle methods for a class of continuity equations. Submitted, 2024 [arXiv].

[PP3] V. Ilin, J. Hu, and Z. Wang. Transport based particle methods for the Fokker-Planck-Landau equation. Submitted, 2024 [arXiv].

[PP2] E. Habbershaw, C. Hauck, J. Hu, and J. Haack. A nonlinear, conservative, entropic Fokker-Planck model for multi-species collisions. Submitted, 2024 [arXiv].

[PP1] J. Carrillo, J. Hu, and S. Van Fleet. A particle method for the multispecies Landau equation. Submitted, 2023 [arXiv].

# Journal Publications

[J53] R. Bailo, J. Carrillo, and J. Hu. The collisional particle-in-cell method for the Vlasov-Maxwell-Landau equations. *J. Plasma Phys.*, accepted [arXiv].

[J52] 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. *J. Comput. Phys.*, 514:113219, 2024 [link].

[J51] J. Coughlin, J. Hu, and U. Shumlak. Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition. *J. Comput. Phys.*, 509:113055, 2024 [link].

[J50] J. Hu and R. Shu. Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation. Math. Comp., online first [link].

[J49] J. Hu, A. Jungel, and N. Zamponi. Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system. *Kinet. Relat. Models*, online first [link].

[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].