Xiaoming He

Professor

Department of Mathematics and Statistics

Faculty Fellow

Office of Vice Chancellor of Research

 

Missouri University of Science & Technology


Phone (office): 573-341-6208
Fax: 573-341-4741
Email: hex@mst.edu

 

 

● Education                                                                                                

Ph.D. in Mathematics

Virginia Tech (08/05---05/09)

Advisor: Prof. Tao Lin

Dissertation: Bilinear Immersed Finite Elements For Interface Problems [Download from VT library]

 

M. S. in Mathematics

Virginia Tech (08/05---05/07)           

Advisor: Prof. Tao Lin

 

M. S. in Computational Mathematics

Sichuan University (08/02---06/05)

Advisor: Prof. Tao Lü

 

B. S. in Computational Mathematics

Sichuan University (08/98---06/02)

Thesis Advisor: Prof. Xiaoping Xie

 

● Positions

Professor

Department of Mathematics & Statistics

Missouri University of Science & Technology (09/21---present)

 

Faculty Fellow

Office of Vice Chancellor of Research

Missouri University of Science & Technology (07/21---present)

 

Associate Professor

Department of Mathematics & Statistics

Missouri University of Science & Technology (09/16---08/21)

 

Assistant Professor

Department of Mathematics & Statistics

Missouri University of Science & Technology (09/10---08/16)

 

Postdoctoral research associate (supervised by Prof. Max Gunzburger)

Department of Scientific Computing

Florida State University (05/09---08/10)

 

● SIAM Committee on Programs & Conferences (Committee Member)

● SIAM Central States Section (Founding President)

● Missouri Institute for Computational and Applied Mathematical Sciences

● Seminar of Missouri Institute for Computational and Applied Mathematical Sciences (Co-organizer)

● Editorship

Managing editor, International Journal of Numerical Analysis and Modeling, 2022-present

Associate editor, International Journal of Numerical Analysis and Modeling, 2016-2021

Associate editor, International Journal of Numerical Analysis and Modeling, Series B, 2013-2015

Guest editor, the special issue of Electronic Research Archive on PDEs in fluid flow problems

Guest editor, the special issue of Applied Numerical Mathematics for the 20th IMACS World Congress

Guest editor, the special issue of Discrete and Continuous Dynamical Systems - Series B for the SIAM Central States Section

Managing guest editor, the special issue of Computers and Mathematics with Applications for the 2nd Annual Meeting of SIAM Central States Section

Managing guest editor, the special issue of Journal of Computational and Applied Mathematics for the 1st Annual Meeting of SIAM Central States Section

Guest editor, the special issue of International Journal of Numerical Analysis and Modeling for 2013 International Conference on Engineering and Computational Mathematics

● Research Interests

Interface problems, multi-phase problems, computational fluid dynamics, data assimilation, stochastic PDEs, boundary integral equations, feedback control

Finite element methods, domain decomposition methods, lattice Boltzmann methods, extrapolations

Computational plasma physics (Particle-In-Cell method)

● Award and Fellowship

Faculty Research Award, Missouri University of Science and Technology, 2019.

Affordable and Open Educational Resources Initiative Award, University of Missouri, 2019.

Humboldt Research Fellowship for Experienced Researchers, 2018.

Faculty Research Award, Missouri University of Science and Technology, 2014.

● Funding

National Science Foundation, DMS-2152609, “Collaborative Research: Laboratory data enabled phase field modeling and data assimilation for coupled two-phase fluid flow and porous media flow”, August 2022 - July 2025, Xiaoming He (PI) and Baojun Bai (Co-PI), total amount for Missouri University of Science and Technology (leading institute of this collaborative research): $160,000, shared credit 70%. (The collaborative NSF grant for this collaborative research: DMS-2152623, Leo Rebholz (PI), Clemson University)

 

National Science Foundation, DMS-2111039, “Collaborative Research: Lab-data-enabled modeling, numerical methods, and validation for a three-dimensional interface inverse problem for plasma-material interactions”, August 2021 - July 2024, Daoru Han (PI) and Xiaoming He (co-PI), total amount for Missouri University of Science and Technology: $169,156, shared credit 30%. (The collaborative NSF grant for this collaborative research: DMS-2110833, Xu Zhang (PI), Oklahoma State University  (leading institute of this collaborative research))

 

National Science Foundation, DMS-1818642, “Collaborative Research: Models, algorithms, simulations, and applications for two-phase ferrofluid flows in contact with a solid surface”, August 2018 - July 2022, Xiaoming He (PI) and Cheng Wang (Co-PI), total amount for Missouri University of Science and Technology (leading institute of this collaborative research): $160,000, shared credit 70%. (The collaborative NSF grant for this collaborative research: DMS-1818783, Xiaofeng Yang (PI), University of South Carolina)

 

National Science Foundation, DMS-1722647, “Collaborative Research: Data-enabled modeling, numerical method, and data assimilation for coupling dual porosity flow with free flow”, August 2017 - July 2021, Xiaoming He (PI), Baojun Bai (Co-PI), and Mingzhen Wei (Co-PI), total amount for Missouri University of Science and Technology (leading institute of this collaborative research): $180,000, shared credit 70%. (The collaborative NSF grant for this collaborative research: DMS-1722692, Craig Douglas (PI), University of Wyoming)

 

National Science Foundation, DMS-1418624, “Non-Iterative multi-physics domain decomposition method for the Navier-Stokes-Darcy model”, September 2014 - August 2017, Xiaoming He (PI) and Mingzhen Wei (Co-PI), total amount $95,500, shared credit 80%.

 

Department of Energy, DE-FE0009843, “Robust ceramic coaxial cable down-hole sensors for long term in situ monitoring of geologic CO2 injection and storage”, October 2012 – June 2016, Runar Nygaard (PI), Hai Xiao (Co-PI),  and Xiaoming He (Co-PI), total amount $1,447,193, sponsor amount $1,156,668, shared credit 30%.

 

National Science Foundation, DMS-2023264, “Midwest Numerical Analysis Day 2020”, April 2020 - March 2022, Xiaoming He (PI) and Jue Yan (Co-PI), total amount: $5,000.

 

NASA-EPSCoR, “PIFE-PIC: A 3D Parallel Immersed-Finite-Element Particle-in-Cell Framework for Kinetic Modeling of Plasma-Material Interaction”, Daoru Han (PI) and Xiaoming He (Co-PI), October 2017 - May 2019, total amount: $24,119, sponsor amount: $10,000, shared credit 50%.

 

Simons Foundation, Collaboration Grant for Mathematicians, “Numerical methods and mathematical analysis for interface problems”, September 2014 – August 2019, Xiaoming He (PI), total amount $35,000. (This grant needs to be returned to Simons Foundation before September 2015 since the PI is funded by NSF)

 

Department of Transportation, “NUTC/reliability-based optimization design of geosynthetic reinforced road embankment”, May 2013 – December 2013, Ronaldo Luna (PI) and Xiaoming He (Co-PI), total amount $16,052, shared credit 50%.

 

AMS-Simons Travel Grant, July 2012 – June 2014, Xiaoming He (PI), total amount $4,800.

 

Missouri University of Science and Technology, Educational Research Mini-Grant, “The conceptualized and interactive guided coding for Math 5601 (Introduction to Numerical Analysis)”, August 2021 - July 2022, Xiaoming He (PI), total amount: $2,500.

 

University of Missouri, Course Sharing Grant, “Finite element methods II”, May 2018 – May 2019, Xiaoming He (PI), total amount $9,731.

 

Missouri Research Board Grant, “Coupling dual porosity flow with free flow: modeling, numerical method, and data assimilation”, Xiaoming He (PI), January 2017 - January 2018, total amount: $11,200.

 

Missouri Interdisciplinary Intercampus Research Grant, “Development and application of a hybrid material point and immersed finite element method (MPM-IFE) to soil-water flow modeling considering hydrophobicity”, August 2015 - July 2016, Zhiqiang Chen (PI for UMKC), Xiaoming He (PI for Missouri S&T), total amount: $59,399, amount for Missouri S&T: $25,000.

 

Missouri Research Board Grant, “Novel numerical methods for a moving interface problem”, Xiaoming He (PI), August 2014 – July 2015, total amount $10,000.

 

Missouri University of Science and Technology, Educational Research Mini-Grant, “Development of a conceptualized guided coding for the course of Mathematical Foundation of Finite Element Methods”, June 2014 - May 2015, Xiaoming He (PI), total amount: $4,732.

   

University of Missouri, Course Sharing Grant, “Mathematical Foundation of Finite Element Methods”, June 2014 - May 2015, Xiaoming He (PI), total amount: $7,769.

 

Missouri Research Board Grant, “Parallel numerical methods for realistic coupled Stokes-Darcy model”, Xiaoming He (PI), January 2011 – January 2012, total amount $13,000.

● Journal Publications

  1. Yingzhi Liu, Yassine Boubendir, Xiaoming He, and Yinnian He. New optimized Robin-Robin domain decomposition methods using Krylov solvers for the Stokes-Darcy system, SIAM Journal on Scientific Computing, accepted for publication, 2022.

 

  1. Xiaofeng Yang and Xiaoming He. Numerical approximations of flow coupled binary phase field crystal system: fully discrete finite element scheme with second-order temporal accuracy and decoupling structure, Journal of Computational Physics, accepted for publication, 2022.

 

  1. Jianxun Zhao, Xiaoming He, Guirong Yan, and Daoru Han. Kinetic particle simulations of plasma and dust environments at robotic construction sites near the lunar terminator, Journal of Aerospace Engineering, accepted for publication, 2022.

 

  1. Yuanyuan Hou, Wenjing Yan, Lioba Boveleth, and Xiaoming He. A decoupled, parallel, iterative finite element method for solving the steady Boussinesq equations. International Journal of Numerical Analysis and Modeling, accepted for publication, 2022.

 

  1. David Lund, Xiaoming He, Xu Zhang, and Daoru Han. Weak scaling of the parallel immersed finite element particle-in-cell (PIFE-PIC) framework with lunar plasma charging simulations, Computational Particle Mechanics, doi: 10.1007/s40571-022-00470-0.

 

  1. Yali Gao, Xiaoming He, and Yufeng Nie. Second-order, fully decoupled, linearized, and unconditionally stable SAV schemes for Cahn-Hilliard-Darcy system, Numerical Methods for Partial Differential Equations, doi: 10.1002/num.22829.

 

  1. Yali Gao, Daozhi Han, Xiaoming He, and Ulrich Rüde. Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities, Journal of Computational Physics, 454: #110968, 2022.

 

  1. Guodong Zhang, Xiaoming He, and Xiaofeng Yang. A fully decoupled linearized finite element method with second-order temporal accuracy and unconditional energy stability for incompressible MHD equations, Journal of Computational Physics, 448: #110752, 2022.

 

  1. Xiaofeng Yang and Xiaoming He. A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system, Computer Methods in Applied Mechanics and Engineering, 389: #114376, 2022.

 

  1. Jiangyong Hou, Dan Hu, Xiaoming He, and Changxin Qiu. Modeling and a Robin-type decoupled finite element method for dual-porosity-Navier-Stokes system with application to flows around multistage fractured horizontal wellbore, Computer Methods in Applied Mechanics and Engineering, 388: #114248, 2022.

 

  1. Zhipeng Yang, Ju Ming, Changxin Qiu, Maojun Li, and Xiaoming He. A multigrid multilevel Monte Carlo method for Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition, Journal of Scientific Computing, 90: #68, 2022.

 

  1. Yuanyuan Hou, Wenjing Yan, Maojun Li, and Xiaoming He. A decoupled and iterative finite element method for generalized Boussinesq equations, Computers and Mathematics with Application, 115: 14-25, 2022.

 

  1. Zhipeng Yang, Xuejian Li, Xiaoming He, and Ju Ming. A stochastic collocation method based on sparse grid for a stochastic Stokes-Darcy model, Discrete and Continuous Dynamical Systems - Series S, 15(4): 893-912, 2022.

 

  1. Guodong Zhang, Xiaoming He, and Xiaofeng Yang. Decoupled, linear, and unconditionally energy stable fully-discrete finite element numerical scheme for a two-phase ferrohydrodynamics model, SIAM Journal on Scientific Computing, 43(1): B167-B193, 2021.

 

  1. Daoru Han, Xiaoming He, David Lund, and Xu Zhang. PIFE-PIC: Parallel Immersed-Finite-Element Particle-in-Cell for 3-D kinetic simulations of plasma-material interactions, SIAM Journal on Scientific Computing, 43(3): C235-C257, 2021.

 

  1. Jinwei Bai, Yong Cao, Xiaoming He, and Peng E. An implicit particle-in-cell model based on anisotropic immersed-finite-element method, Computer Physics Communications, 261: #107655, 2021.

 

  1. Yandong Zhang, Jiaming Geng, Junchen Liu, Baojun Bai, Xiaoming He, Mingzhen Wei, and Wen Deng. Direct pore-level visualization and verification of in-situ oil-in-water pickering emulsification during polymeric nanogel flooding for EOR in a transparent three-dimensional micromodel. Langmuir, 37: 13353-13364, 2021.

 

  1. Jianxun Zhao, Xinpeng Wei, Xiaoping Du, Xiaoming He, and Daoru Han. Photoelectron sheath and plasma charging on the lunar surface: semi-analytic solutions and fully-kinetic particle-in-cell simulations, IEEE Transactions on Plasma Science, 49(10): 3036-3050, 2021.

 

  1. Yijia Gu, Xiaoming He, and Daozhi Han, On the phase-field modeling of rapid solidification, Computational Materials Science, 199: #110812, 2021.

 

  1. Xinpeng Wei, Jianxun Zhao, Xiaoming He, Zhen Hu, Xiaoping Du, and Daoru Han. Adaptive Kriging method for uncertainty quantification of the photoelectron sheath and dust levitation on the lunar surface, Journal of Verification, Validation and Uncertainty Quantification, 6(1): #011006, 2021.

 

  1. Yingzhi Liu, Yinnian He, Xuejian Li, and Xiaoming He. A novel convergence analysis of Robin-Robin domain decomposition method for Stokes-Darcy system with Beavers-Joseph interface condition, Applied Mathematics Letters, 119: #107181, 2021.

 

  1. Daozhi Han, Xiaomin He, Quan Wang, and Yanyun Wu. Existence and weak-strong uniqueness of solutions to the Cahn-Hilliard-Navier-Stokes-Darcy system in superposed free flow and porous media, Nonlinear Analysis, 211: #112411, 2021.

 

  1. Hongyan Liu, Jin Huang, and Xiaoming He. Bivariate barycentric rational interpolation method for two dimensional fractional Volterra integral equations, Journal of Computational and Applied Mathematics, 389: #113339, 2021.

 

  1. Md. Abdullah Al Mahbub, Xiaoming He, Nasrin Jahan Nasu, Changxin Qiu, Yifan Wang, and Haibiao Zheng. A coupled multi-physics model and a decoupled stabilized finite element method for closed-loop geothermal system, SIAM Journal on Scientific Computing, 42(4): B951–B982, 2020.

 

  1. Changxin Qiu, Xiaoming He, Jian Li, and Yanping Lin. A domain decomposition method with Lagrange multipliers and implicit schemes for the time-dependent Navier-Stokes-Darcy model with defective boundary condition, Journal of Computational Physics, 411: #109400, 2020.

 

  1. Chang Lu, Jie Wan, Yong Cao, and Xiaoming He. A fully decoupled iterative method with three-dimensional anisotropic immersed finite elements for Kaufman-type discharge problems, Computer Methods in Applied Mechanics and Engineering, 372: #113345, 2020.

 

  1. Hongtao Liu, Feng Shi, Jie Wan, Xiaoming He, and Yong Cao. Discrete unified gas kinetic scheme for a reformulated BGK-Vlasov-Poisson system with a wide range of Knudsen number and normalized Debye length, Computer Physics Communications, 255: #107400, 2020.

 

  1. Chang Lu, Zhi Yang, Jinwei Bai, Yong Cao, and Xiaoming He. Three-dimensional immersed finite element method for anisotropic magnetostatic/electrostatic interface problems with non-homogeneous flux jump, International Journal for Numerical Methods in Engineering, 121(10): 2107-2127, 2020.

 

  1. Xiaoming He, Nan Jiang, and Changxin Qiu, An artificial compressibility ensemble algorithm for a stochastic Stokes-Darcy model with random hydraulic conductivity and interface conditions, International Journal for Numerical Methods in Engineering, 121(4): 712-739, 2020.

 

  1. Feng Bai, Daozhi Han, Xiaoming He, and Xiaofeng Yang. Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields, Communications in Nonlinear Science and Numerical Simulation, 85: #105213, 2020.

 

  1. Rui Li, Yali Gao, Jie Chen, Li Zhang, Xiaoming He, and Zhangxin Chen. Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model, Advances in Computational Mathematics, 46: #25, 2020.

 

  1. Yanan Xing, Lina Song, Xiaoming He, and Changxin Qiu. A generalized finite difference method for solving elliptic interface problems, Mathematics and Computers in Simulation, 178: 109-124, 2020.

 

  1. Guodong Zhang, Xiaoming He, and Xiaofeng Yang. Fully decoupled, linear and unconditionally energy stable time discretization scheme for solving the magneto-hydrodynamic equations, Journal of Computational and Applied Mathematics, 369: #112636, 2020.

 

  1. Jinjin Yang, Shipeng Mao, Xiaoming He, Xiaofeng Yang, and Yinnian He. A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamics flows, Computer Methods in Applied Mechanics and Engineering, 356: 435-464, 2019.

 

  1. Guodong Zhang, Xiaoming He, Xiaofeng Yang. A decoupled, linear and unconditionally energy stable  scheme with finite element discretizations for magneto-hydrodynamic equations, Journal of Scientific Computing, 81: 1678–1711, 2019.

 

  1. Md. Abdullah Al Mahbub, Xiaoming He, Nasrin Jahan Nasu, Changxin Qiu, and Haibiao Zheng. Coupled and decoupled stabilized mixed finite element methods for non-stationary dual-porosity-Stokes fluid flow model, International Journal for Numerical Methods in Engineering, 120(6): 803-833, 2019.

 

  1. Yandong Zhang, Chuanle Zhou, Chuang Qu, Mingzhen Wei, Xiaoming He, and Baojun Bai. Fabrication and verification of a glass-silicon-glass micro-/nanofluidic model for investigating multi-phase flow in shale-like unconventional dual-porosity tight porous media, Lab on a Chip, 19: 4071-4082, 2019.

 

  1. Xiaofeng Yang, Guodong Zhang, and Xiaoming He. Convergence analysis of an  unconditionally energy stable projection scheme for magneto-hydrodynamic equations, Applied Numerical Mathematics, 136: 235-256, 2019.

 

  1. Fubiao Lin, Xiaoming He, and Xiaoxia Wen. Fast, unconditionally energy stable large time stepping method for a new Allen-Cahn type square phase-field crystal model, Applied Mathematics Letters, 98: 248-255, 2019.

 

  1. Chen Xu, Chuanjun Chen, Xiaofeng Yang, and Xiaoming He. Numerical approximations for the hydrodynamics coupled binary surfactant phase field model: second order, linear, unconditionally energy stable schemes, Communications in Mathematical Sciences, 17(3): 835-858, 2019.

 

  1. Jing Lu, Botao Zhou, Md. Motiur Rahman, and Xiaoming He. New solution to the pressure transient equation in a two-layer reservoir with crossflow, Journal of Computational and Applied Mathematics, 362: 680-693, 2019.

 

  1. Max Gunzburger, Xiaoming He, and Buyang Li. On Ritz projection and multi-step backward differentiation schemes in decoupling the Stokes-Darcy model, SIAM Journal on Numerical Analysis, 56(1): 397-427, 2018.

 

  1. Yali Gao, Xiaoming He, Liquan Mei, and Xiaofeng Yang. Decoupled, linear, and energy stable finite element method for the Cahn-Hilliard-Navier-Stokes-Darcy phase field model, SIAM Journal on Scientific Computing, 40(1): B110-B137, 2018.

 

  1. Xiaoming He, Weiwei Hu, and Yangwen Zhang. Observer based feedback boundary stabilization of the Navier-Stokes equation, Computer Methods in Applied Mechanics and Engineering, 339(1): 542-556, 2018.

 

  1. Daoru Han, Joseph Wang, and Xiaoming He. Immersed-finite-element particle-in-cell simulations of plasma charging at lunar terminator, Journal of Spacecraft and Rockets, 55(6): 1490-1497, 2018.

 

  1. Huijun Cao, Yong Cao, Yuchuan Chu, Xiaoming He, and Tao Lin. A Huygens immersed-finite-element particle-in-cell method for modeling plasma-surface interactions with moving interface, Communications in Nonlinear Science and Numerical Simulation, 59: 132-148, 2018.

 

  1. Jinwei Bai, Yong Cao, Xiaoming He, Hongyan Liu, and Xiaofeng Yang. Modeling and an immersed finite element method for an interface wave equation, Computers and Mathematics with Application, 76(7): 1625-1638, 2018.

 

  1. Rui Li, Jian Li, Xiaoming He, and Zhangxin Chen. A stabilized finite volume element method for a coupled Stokes-Darcy problem, Applied Numerical Mathematics, 133: 2-24, 2018.

 

  1. Qiumei Huang, Xiaofeng Yang and Xiaoming He. Numerical approximations for a smectic-A liquid crystal flow model: first-order, linear, decoupled and energy stable schemes, Discrete and Continuous Dynamical Systems - Series B, 23(6): 2177-2192, 2018.

 

  1. Xiaofeng Yang, Jia Zhao, and Xiaoming He. Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method, Journal of Computational and Applied Mathematics, 343(1):80-97, 2018.

 

  1. Feng Bai, Xiaoming He, Xiaofeng Yang, Ran Zhou, and Cheng Wang. Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation, International Journal of Multiphase Flow, 93: 130-141, 2017.

 

  1. Yuchuan Chu, Daoru Han, Yong Cao, Xiaoming He, and Joseph Wang. An immersed-finite-element particle-in-cell simulation tool for plasma surface interaction, International Journal of Numerical Analysis and Modeling, 14(2): 175-200, 2017.

 

  1. Jiangyong Hou, Meilan Qiu, Xiaoming He, Chaohua Guo, Mingzhen Wei, and Baojun Bai. A dual-porosity-Stokes model and finite element method for coupling dual-porosity flow and free flow, SIAM Journal on Scientific Computing, 38(5): B710–B739, 2016.

 

  1. Daoru Han, Pu Wang, Xiaoming He, Tao Lin, and Joseph Wang. A 3D immersed finite element method with non-homogeneous interface flux jump for applications in particle-in-cell simulations of plasma-lunar surface interactions, Journal of Computational Physics, 321: 965-980, 2016.

 

  1. Daoru Han, Joseph Wang, and Xiaoming He. A non-Homogeneous immersed-finite-element particle-in-cell method for modeling dielectric surface charging in plasmas, IEEE Transactions on Plasma Science, 44(8):1326-1332, 2016.

 

  1. John A. Burns, Xiaoming He, and Weiwei Hu. Feedback stabilization of a thermal fluid system with mixed boundary control, Computers and Mathematics with Application, in honor of Max Gunzburger's 70th birthday, 71(11): 2170–2191, 2016.

 

  1. Xiaoming He, Jian Li, Yanping Lin, and Ju Ming. A domain decomposition method for the steady-state Navier-Stokes-Darcy model with Beavers-Joseph interface condition, SIAM Journal on Scientific Computing, 37(5): S264–S290, 2015.

 

  1. Yong Cao, Yuchuan Chu, Xiaoming He, and Tao Lin. An iterative immersed finite element method for an electric potential interface problem based on given surface electric quantity, Journal of Computational Physics, 281: 82-95, 2015.

 

  1. Honghua Jian, Yuchuan Chu, Huijun Cao, Yong Cao, Xiaoming He, and Guangqing Xia. Three-dimensional IFE-PIC numerical simulation of background pressure's effect on accelerator grid impingement current for ion optics, Vacuum, 116: 130-138, 2015.

 

  1. Chong Chen, Xiaoming He, and Jin Huang. Mechanical quadrature methods and their extrapolations for solving the first kind boundary integral equations of Stokes equation, Applied Numerical Mathematics, 96: 165-179, 2015.

 

  1. Chaolang Hu, Xiaoming He, and Tao Lü. Euler-Maclaurin expansions and approximations of hypersingular integrals, Discrete and Continuous Dynamical Systems, Series B, 20(5): 1355-1375, 2015.

 

  1. Yanzhao Cao, Max Gunzburger, Xiaoming He, and Xiaoming Wang. Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems, Mathematics of Computation, 83(288): 1617-1644, 2014.

 

  1. Xiaoming He, Tao Lin, and Yanping Lin. A selective immersed discontinuous Galerkin method for elliptic interface problems, Mathematical Methods in the Applied Sciences, 37(7): 983–1002, 2014.

 

  1. Wenqiang Feng, Xiaoming He, Yanping Lin, and Xu Zhang. Immersed finite element method for interface problems with algebraic multigrid solver, Communications in Computational Physics, 15(4): 1045-1067, 2014.

 

  1. Chaolang Hu, Jing Lu, and Xiaoming He. Numerical solutions of a hypersingular integral equation with application to productivity formulae of horizontal wells producing at constant wellbore pressure, International Journal of Numerical Analysis and Modeling, Series B, 5(3): 269-288, 2014.

 

  1. Yong Cao, Yuchuan Chu, Xiaoming He, and Mingzhen Wei. Decoupling the stationary Navier-Stokes-Darcy system with the Beavers-Joseph-Saffman interface condition, Abstract and Applied Analysis, vol. 2013, Article ID 136483, 10 pages, 2013.

 

  1. Xiaoming He, Tao Lin, Yanping Lin, and Xu Zhang. Immersed finite element methods for parabolic equations with moving interface, Numerical Methods for Partial Differential Equations, 29(2): 619-646, 2013.

 

  1. Chaolang Hu, Jing Lu, and Xiaoming He. Productivity formulae of an infinite-conductivity hydraulically fractured well producing at constant wellbore pressure based on numerical solutions of a weakly singular integral equation of the first kind, Mathematical Problems in Engineering, vol. 2012, Article ID 428596, 18 pages, 2012.

 

  1. Wenqiang Feng, Xiaoming He, Zhu Wang, and Xu Zhang. Non-iterative domain decomposition methods for a non-stationary Stokes-Darcy model with Beavers-Joseph interface condition, Applied Mathematics and Computation, 219(2): 453-463, 2012.

 

  1. Xiaoming He, Tao Lin, and Yanping Lin. The convergence of the bilinear and linear immersed finite element solutions to interface problems, Numerical Methods for Partial Differential Equations, 28(1): 312-330, 2012.

 

  1. Jin Huang, Guang Zeng, Xiaoming He, and Zicai Li. Splitting extrapolation algorithms for first kind boundary integral equations with singularities by mechanical quadrature methods, Advances in Computational Mathematics, 36(1): 79-97, 2012.

 

  1. Yanzhao Cao, Max Gunzburger, Xiaoming He, and Xiaoming Wang. Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beaver-Joseph interface condition, Numerische Mathematik, 117(4): 601-629, 2011.

 

  1. Yuchuan Chu, Yong Cao, Xiaoming He, and Min Luo. Asymptotic boundary conditions for two-dimensional electrostatic field problems with immersed finite elements, Computer Physics Communications, 182(11): 2331-2338, 2011.

 

  1. Huilei Han, Xiaoming He, Yaping Liu, and Tao Lü. Extrapolation for solving system of weakly singular nonlinear Volterra integral equations of the second kind, International Journal of Computer Mathematics, 88(16): 3507-3520, 2011.

 

  1. Xiaoming He, Tao Lin, and Yanping Lin. Immersed finite element methods for elliptic interface problems with non-homogeneous jump conditions, International Journal of Numerical Analysis and Modeling, 8(2): 284-301, 2011.

 

  1. Yong Cao, Xiaoming He, and Tao Lü. An algorithm using finite volume element method and its splitting extrapolation for second-order elliptic problems, Journal of Computational and Applied Mathematics, 235(13): 3734-3742, 2011.

 

  1. Xiaoming He, Tao Lin and Yanping Lin. Interior penalty discontinuous Galerkin methods with bilinear IFE for a second order elliptic equation with discontinuous coefficient, dedicated to David Russell’s 70th birthday, Journal of Systems Science and Complexity, 23(3): 467-483, 2010.

 

  1. Lu Pan, Xiaoming He, and Tao Lü. High accuracy combination methods for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind, Mathematical Problems in Engineering, vol. 2010, Article ID 901587, 21 pages, 2010.

 

  1. Xiaoming He and Tao Lü. A finite element splitting extrapolation for second order hyperbolic equations, SIAM Journal on Scientific Computing, 31(6):4244-4265, 2009.

 

  1. Yong Cao, Xiaoming He, and Tao Lü. A splitting extrapolation for solving nonlinear elliptic equations with d-quadratic finite elements, Journal of Computational Physics, 228(1): 109-122, 2009.

 

  1. Xiaoming He, Tao Lin, and Yanping Lin. A bilinear immersed finite volume element method for the diffusion equation with discontinuous coefficient, dedicated to Richard E. Ewing on the occasion of his 60th birthday, Communications in Computational Physics, 6(1): 185-202, 2009.

 

  1. Joseph Wang, Xiaoming He, and Yong Cao. Modeling electrostatic levitation of dusts on lunar surface, IEEE Transactions on Plasma Science, 36(5): 2459-2466, 2008.

 

  1. Xiaoming He, Tao Lin, and Yanping Lin. Approximation capability of a bilinear immersed finite element space, Numerical Methods for Partial Differential Equations, 24(5):1265-1300, 2008.

 

  1. Xiaoming He and Tao Lü. Splitting extrapolation method for solving second-order parabolic equations with curved boundaries by using domain decomposition and d-quadratic isoparametric finite elements, International Journal of Computer Mathematics, 84(6): 767 -781, 2007.

 

● Conference Publications

  1. Jianxun Zhao, Guirong Yan, Xiaoming He, and Daoru Han. Kinetic particle simulations of plasma charging and dust transport near uneven lunar surface terrain, #AIAA 2022-1988, AIAA Scitech 2022 Forum, San Diego, California & Virtual Conference, January 3-7, 2022.

 

  1. Jianxun Zhao, Xinpeng Wei, Xiaoming He, Daoru Han, and Xiaoping Du. Fully-kinetic particle-in-cell simulations of photoelectron sheath on uneven lunar surface, #AIAA-2021-1433, AIAA Scitech 2021 Forum, Virtual Conference, January 11-15, 2021.

 

  1. Jianxun Zhao, Xinpeng Wei, Zhangli Hu, Xiaoming He, and Daoru Han. Photoelectron sheath near the lunar surface: fully kinetic modeling and uncertainty quantification analysis, #AIAA 2020-1548, AIAA Scitech 2020 Forum, Orlando, Florida, January 6-10, 2020.

 

  1. Craig Douglas, Xiukun Hu, Baojun Bai, Xiaoming He, Mingzhen Wei, Jiangyong Hou. A data assimilation enabled model for coupling dual porosity flow with free flow, DOI: 10.1109/DCABES.2018.00085, 17th International Symposium on Distributed Computing and Applications for Business Engineering and Science (DCABES), Wuxi, China, October 19-23, 2018.

 

  1. Daoru Han, Xiaoming He, Joseph Wang. PIFE-PIC: A 3-D parallel immersed finite element particle-in-cell framework for plasma simulations, #AIAA-2018-2196, 2018 AIAA Aerospace Sciences Meeting, Kissimmee, Florida, January 8-12, 2018.

 

  1. Chaohua Guo, Jiaqi Wang, Baojun Bai, Xiaoming He, and Mingzhen Wei. Multi-stage fractured horizontal well numerical simulation and its application in tight shale reservoirs, SPE-176714, Society of Petroleum Engineers, SPE Russian Petroleum Technology Conference, Moscow, Russia, October 26–28, 2015.

 

  1. Daniel Depew, Daoru Han, Joseph Wang, Xiaoming He, and Tao Lin. Immersed-Finite-Element Particle-In-Cell simulations of lunar surface charging, #199, 13th Spacecraft Charging Technology Conference, Pasadena, California, June 23-27, 2014.

 

  1. Chaohua Guo, Mingzhen Wei, Haowei Chen, Xiaoming He, and Baojun Bai. Improved numerical simulation for shale gas reservoirs, OTC-24913, Offshore Technology Conference Asia, Kuala Lumpur, Malaysia, March 25–28, 2014.

 

  1. Chaohua Guo, Baojun Bai, Mingzhen Wei, Xiaoming He, and Yushu Wu. Study on gas flow in nano pores of shale gas reservoirs, SPE-167179, Society of Petroleum Engineers, SPE Unconventional Resources Conference-Canada, Calgary, Canada, November 5-7, 2013.

 

  1. John A. Burns, Xiaoming He, and Weiwei Hu. Control of the Boussinesq equations with implications for sensor location in energy efficient building, American Control Conference, pp. 2232-2237, Montréal, Canada, June 27-29, 2012.

 

  1. Huilei Han, Yaping Liu, Tao Lü, and Xiaoming He. New Algorithm for the system of nonlinear weakly singular Volterra integral equations of the second kind and integro-differential equations,  Seventh International Conference on Scientific Computing and Applications, pp. 1229-1235, Dalian, China, June 13-16, 2010.

 

  1. Joseph Wang, Xiaoming He, and Yong Cao. Modeling spacecraft charging and charged dust particle interactions on lunar surface, 10th Spacecraft Charging Technology Conference, Biarritz, France, June 18-21, 2007.

 

● Teaching

Fall 2022: Math 5602 – Mathematical Foundation of Finite Element Methods;

 

Spring 2022: Math 5325 - Partial Differential Equations

 

Fall 2021: Math 5601 – Introduction to Numerical Analysis;

 

Spring 2021: Math 3304 - Elementary Differential Equations (online asynchronous)

 

Fall 2020: Math 6602 – Mathematical Foundation of Finite Element Methods; Math 5001 (Experimental Course) – Introduction to Numerical Analysis; Math 3304 - Elementary Differential Equations (online asynchronous)

 

Spring 2020: Math 6001 (Experimental Course) – Mathematical Foundation of Finite Element Methods II

 

Fall 2019: Math 6602 – Mathematical Foundation of Finite Element Methods; Math 5001 (Experimental Course) – Introduction to Numerical Analysis

 

Spring 2019: Math 6001 (Experimental Course) – Mathematical Foundation of Finite Element Methods II; Math 6601 – Numerical Analysis

 

Fall 2018: Math 6602 – Mathematical Foundation of Finite Element Methods; Math 3304 - Elementary Differential Equations

 

Fall 2017: Math 6601 – Numerical Analysis; Math 6001 (Experimental Course) – Topics in Partial Differential Equations

 

Spring 2017: Math 6602 – Mathematical Foundation of Finite Element Methods; Math 3304 - Elementary Differential Equations

 

Fall 2016: Math 6601 – Numerical Analysis; Math 3304 - Elementary Differential Equations

 

Spring 2016: Math 6602 – Mathematical Foundation of Finite Element Methods; Math 5325 - Partial Differential Equations

 

Fall 2015: Math 6601 – Numerical Analysis; Math 3304 - Elementary Differential Equations

 

Spring 2015: Math 6602 – Mathematical Foundation of Finite Element Methods

 

Fall 2014: Math 5325 - Partial Differential Equations; Math 3304 - Elementary Differential Equations

 

Spring 2014: Math 401 (Experimental Course) – Mathematical Foundation of Finite Element Methods; Math 204 - Elementary Differential Equations

 

Fall 2013:  Math 401(Experimental Course) – Numerical Analysis; Math 204 - Elementary Differential Equations

 

Spring 2013: Math 401 (Experimental Course) – Mathematical Foundation of Finite Element Methods

 

Fall 2012:  Math 401 (Experimental Course) – Numerical Analysis; Math 204 - Elementary Differential Equations

 

Spring 2012: Math 325 - Partial Differential Equations; Math 204 - Elementary Differential Equations

 

Fall 2011: Math 325 - Partial Differential Equations; Math 204 - Elementary Differential Equations

 

Spring 2011: Math 204 - Elementary Differential Equations

 

Fall 2010: Math 204 - Elementary Differential Equations

● Lecture slides of basic coding for finite element methods

Chapter 1: Finite Elements for 1D second order elliptic equation

 

Chapter 2: 2D/3D Finite Element Spaces

 

Chapter 3: Finite Elements for 2D second order elliptic equation

 

Chapter 4: Finite Elements for 2D second order parabolic and hyperbolic equation

 

Chapter 5: Finite elements for 2D steady linear elasticity equation

 

Chapter 6: Finite elements for 2D steady Stokes equation

 

Chapter 7: Finite elements for 2D steady Navier-Stokes equation

 

Chapter 8: Finite elements for 2D unsteady Stokes and linear elasticity equations

 

Chapter 9: Finite elements for 2D unsteady Navier-Stokes equations