Publication PublicationJournal Papers |
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| ✎ | Y. Kuang and G. Hu. A novel splitting strategy to accelerate solving generalized eigenvalue problem from Kohn-Sham density functional theory. submitted.[ arXiv ] |
| ✎ | G. Hu, R. Li, and H. Zhan. A gradient flow model for ground state calculations in wigner formalism based on density functional theory. under review.[ arXiv ] |
| ✎ | H. Zhan, L. Jia, H. Li, and G. Hu. A general tetrahedral spectral element method and its implementation to Kohn-Sham equation. under review. |
| ✎ | G. Hu, R. Li, and J. Wang. A multi-mesh approach for accurate computation of multi-target functionals in aerodynamics design. under review.[ arXiv ] |
| ✎ | J. Wang and G. Hu. A mechanism-driven reinforcement learning framework for shape optimization of airfoils. under review.[ arXiv ] |
| ✎ | X. Meng, Y. Qin, and G. Hu. Convergence analysis of isogeometric analysis for the Cahn-Hilliard equation. under review (2nd round). |
| ✎ | H. Zhan, T. Wang, and G. Hu. A tetrahedral spectral element method for an unconditionally energy-stable and orthonormality-preserving scheme for the Kohn-Sham gradient flow based model. Communications in Computational Physics, accepted. |
| ✎ | Y. Kuang, Y. Shen, and G. Hu. Towards chemical accuracy using a multi-mesh adaptive finite element method in all-electron density functional theory. Journal of Computational Physics, 518:113312, 2024.[ DOI ] |
| ✎ | Z. Cai, Y. Chen, Y. Di, G. Hu, R. Li, W. Liu, H. Wang, F. Yang, C. Yao, and H. Zhan. AFEPack: A general-purpose c++ library for numerical solutions of partial differential equations. Communications in Computational Physics, 36(1):274--318, 2024.[ DOI ] |
| ✎ | Z. Cui, L. Yang, J. Wu, and G. Hu. A treecode algorithm for the Poisson equation in a general domain with unstructured grids. Numerical Algorithms, 2024.[ DOI ] |
| ✎ | J. Wang and G. Hu. Towards the efficient calculation of quantity of interest from steady Euler equations II: a CNNs-based automatic implementation. Communications in Computational Physics, in press.[ arXiv ] |
| ✎ | J. Wang and G. Hu. Towards the efficient calculation of quantity of interest from steady Euler equations I: A dual-consistent dwr-based h-adaptive Newton-GMG solver. Communications in Computational Physics, 35(3):579--608, 2024.[ DOI ] |
| ✎ | G. Hu, R. Li, and X. Meng. A numerical study of integrated linear reconstruction for steady Euler equations based on finite volume scheme. Advances in Applied Mathematics and Mechanics, 16(2):279--304, 2024.[ DOI ] |
| ✎ | C. Liu and G. Hu. An MP-DWR method for h-adaptive finite element methods. Numerical Algorithms, 94(3):1309--1329, 2023.[ DOI ] |
| ✎ | Y. Gu, Z. Gao, G. Hu, P. Li, and Q. Fu. High order well-balanced positivity-preserving scale-invariant aWENO scheme for Euler systems with gravitational field. Journal of Computational Physics, 488:112190, 2023.[ DOI ] |
| ✎ | Y. Shen, T. Wang, J. Zhou, and G. Hu. A convergence analysis of a structure-preserving gradient flow method for the all-electron Kohn-Sham model. Numerical Mathematics: Theory, Methods and Applications, 16(3):597--621, 2023.[ DOI ] |
| ✎ | T. Wang, J. Zhou, and G. Hu. An SAV method for imaginary time gradient flow model in density functional theory. Advances in Applied Mathematics and Mechanics, 15(3):719--736, 2023.[ DOI ] |
| ✎ | N. Wang, Y. Zhang, W. Wang, Z. Ye, H. Chen, G. Hu, and D. Ouyang. How can machine learning and multiscale modeling benefit ocular drug development? Advanced Drug Delivery Reviews, 196:114772, 2023.[ DOI ] |
| ✎ | X. Meng, Y. Gu, and G. Hu. A fourth-order unstructured NURBS-enhanced finite volume WENO scheme for steady Euler equations in curved geometries. Communications on Applied Mathematics and Computation, 5(1):315--342, 2023.[ DOI ] |
| ✎ | H. Zhan and G. Hu. A novel tetrahedral spectral element method for Kohn-Sham model. Journal of Computational Physics, 474:111831, 2023.[ DOI ] |
| ✎ | G. Hu, T. Wang, and J. Zhou. A linearized structure-preserving numerical scheme for a gradient flow model of the Kohn-Sham density functional theory. East Asian Journal on Applied Mathematics, 13(2):299--319, 2023.[ DOI ] |
| ✎ | G. Hu, H. Xie, and F. Xu. On accelerating a multilevel correction adaptive finite element method for Kohn-Sham equation. Journal of Computational Physics, 472:111674, 2023.[ DOI ] |
| ✎ | H. Zhan, Z. Cai, and G. Hu. Wigner ground state calculation based on imaginary time propagation method and spectral method. Chinese Journal of Computational Physics, 39(6):651--665, 2022.[ DOI ] |
| ✎ | H. Chen, G. Hu, and D. Ouyang. A numerical study of the distribution of chemotherapeutic drug carmustine in brain glioblastoma. Drug Delivery and Translational Research, 12(7):1697--1710, 2022.[ DOI ] |
| ✎ | H. Zhan, Z. Cai, and G. Hu. The wigner function of ground state and one-dimensional numerics. Journal of Computational Physics, 449:110780, 2022.[ DOI ] |
| ✎ | X. Meng and G. Hu. A NURBS-enhanced finite volume method for steady Euler equations with goal-oriented h-adaptivity. Communications in Computational Physics, 32(2):490--523, 2022.[ DOI ] |
| ✎ | B. Gao, G. Hu, Y. Kuang, and X. Liu. An orthogonalization-free parallelizable framework for all-electron calculations in density functional theory. SIAM Journal on Scientific Computing, 44(3):B723--B745, 2022.[ DOI ] |
| ✎ | Y. Gu, Z. Gao, G. Hu, P. Li, and L. Wang. High order finite difference alternative WENO scheme for multi-component flows. Journal of Scientific Computing, 89(3):52, 2021.[ DOI ] |
| ✎ | Y. Kuang, Y. Shen, and G. Hu. An h-adaptive finite element method for Kohn-Sham and time-dependent Kohn-Sham equations. Journal on Numerical Methods and Computer Applications, 42(1):33--55, 2021.[ DOI ] |
| ✎ | G. Hu, R. Li, and X. Zhang. A novel stabilized Galerkin meshless method for steady incompressible Navier-Stokes equations. Engineering Analysis with Boundary Elements, 133:95--106, 2021.[ DOI ] |
| ✎ | Y. Gu, Z. Gao, G. Hu, P. Li, and L. Wang. A robust high order alternative WENO scheme for the five-equation model. Journal of Scientific Computing, 88(1):12, 2021.[ DOI ] |
| ✎ | L. Yang, J. Chen, and G. Hu. A framework of the finite element solution of the Landau-Lifshitz-Gilbert equation on tetrahedral meshes. Journal of Computational Physics, 431:110142, 2021.[ DOI ] |
| ✎ | H. Bian, Y. Shen, and G. Hu. An h-adaptive finite element solution of the relaxation non-equilibrium model for gravity-driven fingers. Advances in Applied Mathematics and Mechanics, 13(6):1418--1440, 2021.[ DOI ] |
| ✎ | G. Bao, R. Delgadillo, G. Hu, D. Liu, and S. Luo. Modeling and computation of nano-optics. CSIAM Transactions on Applied Mathematics, 1(4):616--638, 2020.[ DOI ] |
| ✎ | Y. Di, G. Hu, R. Li, and F. Yang. On accurately resolving detonation dynamics by adaptive finite volume method on unstructured grids. Communications in Computational Physics, 29(2):445--471, 2020.[ DOI ] |
| ✎ | L. Yang, Y. Shen, Z. Hu, and G. Hu. An implicit solver for the time-dependent Kohn-Sham equation. Numerical Mathematics: Theory, Methods and Applications, 14(1):261--284, 2020.[ DOI ] |
| ✎ | Y. Kuang and G. Hu. On stabilizing and accelerating SCF using ITP in solving Kohn-Sham equation. Communications in Computational Physics, 28(3):999--1018, 2020.[ DOI ] |
| ✎ | L. Yang and G. Hu. An adaptive finite element solver for demagnetization field calculation. Advances in Applied Mathematics and Mechanics, 11(5):1048--1063, 2019.[ DOI ] |
| ✎ | Z. Hu and G. Hu. An efficient steady-state solver for microflows with high-order moment model. Journal of Computational Physics, 392:462--482, 2019.[ DOI ] |
| ✎ | Y. Shen, Y. Kuang, and G. Hu. An asymptotics-based adaptive finite element method for Kohn-Sham equation. Journal of Scientific Computing, 79(1):464--492, 2019.[ DOI ] |
| ✎ | X. Meng and G. Hu. A NURBS-enhanced finite volume solver for steady Euler equations. Journal of Computational Physics, 359:77--92, 2018.[ DOI ] |
| ✎ | G. Hu, H. Xie, and F. Xu. A multilevel correction adaptive finite element method for Kohn-Sham equation. Journal of Computational Physics, 355:436--449, 2018.[ DOI ] |
| ✎ | Y. Kuang and G. Hu. An adaptive fem with ITP approach for steady Schrodinger equation. International Journal of Computer Mathematics, 95(1):187--201, 2018.[ DOI ] |
| ✎ | L. Chen, G. Hu, and R. Li. Integrated linear reconstruction for finite volume scheme on arbitrary unstructured grids. Communications in Computational Physics, 24(2):454--480, 2018.[ DOI ] |
| ✎ | Z. Gao and G. Hu. High order well-balanced weighted compact nonlinear schemes for shallow water equations. Communications in Computational Physics, 22(4):1049--1068, 2017.[ DOI ] |
| ✎ | Y. Gu and G. Hu. A third order adaptive ader scheme for one dimensional conservation laws. Communications in Computational Physics, 22(3):829--851, 2017.[ DOI ] |
| ✎ | G. Hu. A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids. Journal of Computational Physics, 331:297--311, 2017.[ DOI ] |
| ✎ | Z. Gao and G. Hu. High order well-balanced weighted compact nonlinear schemes for the gas dynamic equations under gravitational fields. East Asian Journal on Applied Mathematics, 7(4):697--713, 2017.[ DOI ] |
| ✎ | G. Hu, X. Meng, and N. Yi. Adjoint-based an adaptive finite volume method for steady Euler equations with non-oscillatory k-exact reconstruction. Computers and Fluids, 139:174--183, 2016.[ DOI ] |
| ✎ | G. Hu and N. Yi. An adaptive finite volume solver for steady Euler equations with non-oscillatory k-exact reconstruction. Journal of Computational Physics, 312:235--251, 2016.[ DOI ] |
| ✎ | G. Bao, G. Hu, and D. Liu. Towards translational invariance of total energy with finite element methods for Kohn-Sham equation. Communications in Computational Physics, 19(1):1--23, 2016.[ DOI ] |
| ✎ | G. Bao, G. Hu, and D. Liu. Real-time adaptive finite element solution of time-dependent Kohn-Sham equation. Journal of Computational Physics, 281:743--758, 2015.[ DOI ] |
| ✎ | G. Hu. An adaptive finite volume method for 2D steady Euler equations with WENO reconstruction. Journal of Computational Physics, 252:591--605, 2013.[ DOI ] |
| ✎ | G. Bao, G. Hu, and D. Liu. Numerical solution of the Kohn-Sham equation by finite element methods with an adaptive mesh redistribution technique. Journal of Scientific Computing, 55(2):372--391, 2013.[ DOI ] |
| ✎ | G. Hu, Z. Qiao, and T. Tang. Moving finite element simulations for reaction-diffusion systems. Advances in Applied Mathematics and Mechanics, 4(3):365--381, 2012.[ DOI ] |
| ✎ | G. Bao, G. Hu, and D. Liu. An h-adaptive finite element solver for the calculations of the electronic structures. Journal of Computational Physics, 231(14):4967--4979, 2012.[ DOI ] |
| ✎ | G. Hu and P.A. Zegeling. Simulating finger phenomena in porous media with a moving finite element method. Journal of Computational Physics, 230(8):3249--3263, 2011.[ DOI ] |
| ✎ | G. Hu, R. Li, and T. Tang. A robust WENO type finite volume solver for steady Euler equations on unstructured grids. Communications in Computational Physics, 9(3):627--648, 2011.[ DOI ] |
| ✎ | G. Hu, R. Li, and T. Tang. A robust high-order residual distribution type scheme for steady Euler equations on unstructured grids. Journal of Computational Physics, 229(5):1681--1697, 2010.[ DOI ] |
| ✎ | G. Hu and X. Xie. On choices of stress modes for lower order quadrilateral Reissner-Mindlin plate elements. Numerical Mathematics: A Journal of Chinese Universities, 15(2):120--126, 2006. |
Conference Papers |
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| ✎ | D. Zhang, Q. Ye, D. Wang, W. Liang, G. Hu, and Z. Yang. Real-time location-to-image generative adversarial networks with sparse sensor data. In 2023 29th International Conference on Mechatronics and Machine Vision in Practice (M2VIP), pages 1--6, 2023.[ DOI ] |
| ✎ | G. Hu, X. Meng, and T. Tang. On robust and adaptive finite volume methods for steady Euler equations. In Christian Klingenberg and Michael Westdickenberg, editors, Theory, Numerics and Applications of Hyperbolic Problems II, pages 21--40, Cham, 2018. Springer International Publishing.[ DOI ] |
| ✎ | G. Bao, G. Hu, D. Liu, and S. Luo. Multi-physical modeling and multi-scale computation of nano-optical responses. In Hongtao Li, Jichun Yang and Eric Machorro, editors, Recent Advances in Scientific Computing and Applications, Contemporary Mathematics, volume 586, pages 21--40. American Mathematical Society, 2012.[ DOI ] |
Special Issues Edited |
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| ✎ | G. Hu, S. Lei, and S. Vong, editors. A Special Issue for Workshop on Computational Mathematics and Scientific Computing, Numerical Mathematics: Theory, Methods and Applications, volume 11(4). Global Science Press, 2018.[ DOI ] |
| ✎ | G. Hu, S. Lei, and S. Vong, editors. A Special Issue for the 11th East Asia SIAM Conference, East Asian Journal on Applied Mathematics, volume 7(4). Global Science Press, 2017.[ DOI ] |
| ✎ | G. Hu, S. Lei, and S. Vong, editors. A Special Issue for Fourth Workshop on Numerical Algebra and High Performance Computing, East Asian Journal on Applied Mathematics, volume 4(1). Global Science Press, 2014.[ DOI ] |
Theses |
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| ✎ | G. Hu. Numerical solutions of the
steady Euler equations on unstructured grids. PhD thesis, Hong
Kong Baptist University, 2010. - The Best Thesis Award of Hong Kong Mathematical Society.[ http ] |
| ✎ | G. Hu. Stablized hybrid lower order quadrilateral elements for Reissner-Midline plates and convergence analysis (in Chinese). Master thesis, Sichuan University, 2006. |
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