Research Interests


Seminar

I am a co-organizer of the Computational and Applied Mathematics Seminar. See here for more details.

Ph.D Students


Publications
  1. The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems, Q. Zhai, X. Hu, R. Zhang, submitted to Journal of Computational Mathematics, 2018.
  2. Randomized and Fault-tolerant Method of Subspace Corrections, X. Hu, J. Xu, L. T. Zikatanov, submitted to Research in the Mathematical Sciences, 2018.
  3. A Consistent Spatially Adaptive Smoothed Particle Hydrodynamics Method for Fluid-Structure Interactions, W. Hu, G. Guo, X. Hu, D. Negrut, Z. Xu, and W. Pan, submitted to Computer Methods in Applied Mechanics and Engineering, 2018.
  4. Open Community Challenge Reveals Molecular Network Modules with Key Roles in Diseases, S. Choobdar, M. E. Ahsen, J. Crawford, M. Tomasoni, D. Lamparter, J. Lin, B. Hescott, X. Hu, J. Mercer, T. Natoli, R. Narayan, The Dream Module Identification Challenge Consortium, A. Subramanian, G. Stolovitzky, Z. Kutalik, K. Lage, D. K. Slonim, J. Saez-Rodriguez, L. J. Cowen, S. Bergmann, and D. Marbach, submitted to Cell, 2018.
  5. An a Posteriori Error Estimator for the Weak Galerkin Least-Squares Finite-Element Method, J. H. Adler,  X. Hu, L. Mu, and X. Ye, submitted to Journal of Computational and Applied Mathematics, 2018.
  6. Modified AMG Coarse Spaces with Weak Approximation Property to Exhibit Approximation in Energy Norm, X. Hu and P. S. Vasselevski, submitted to SIAM Journal on Matrix Analysis and Applications, 2018.
  7. A Weak Galerkin Finite Element Method for the Navier-Stokes Equations, X. Hu, L. Mu, and X. Ye, submitted to Journal of Computational and Applied Mathematics, 2017.
  8. Vector-potential Finite-element formulations for Two-dimensional Resistive Magnetohydrodynamics, J. Adler, Y. He, X. Hu, and S. P. MacLachlan, submitted to Mathematical Modeling and Numerical Analysis, 2017.
  9. Using Hierarchical Matrices in the Solution of the Time-fractional Heat Equation by Multigrid Waveform Relaxation, X. Hu, C. Rodrigo, and F. J. Gaspar, submitted to SIAM Journal of Scientific Computing, 2017.
  10. New Stabilized Discretizations for Poroelasticity and the Stokes's Equations, C. Rodrigo, X. Hu, P. Ohm, J. H. Adler, F. J. Gaspar, and L. T. Zikatanov, submitted to Computer Methods in Applied Mechanics and Engineering, 2017.
  11. Newton Solvers for Drift-Diffusion and Electrokinetic Equations, A. Bousquet, X. Hu, M. Metti, and J. Xu, SIAM Journal of Scientific Computing, accepted.
  12. Robust Block Preconditioners for Biot's Model, J. H. Adler, F. J. Gaspar, X. Hu, C. Rodrigo, and L. T. Zikatanov, In Domain Decomposition Methods in Science and Engineering XXIV, Lecture Notes in Computational Science and Engineering. Springer-Verlag, accepted.
  13. Optimal Interpolation and Compatible Relaxation in Classical Algebraic Multigrid, J. Brannick, F. Cao, K. Kahl, R. Falgout, and X. Hu, SIAM Journal of Scientific Computing, 40(3), A1473-A1493, 2018.
  14. A Compatible High-order Meshless Method for the Stokes Equations with Applications to Suspension Flows, N. Trask, M. Maxey, and X. Hu, Journal of Computational Physics, 355, 310-326, 2018.
  15. Computing the Diffusion State Distance on Graphs via Algebraic Multigrid and Random Projections, J. Lin, L. J. Cowen, B. Hescott, and X. Hu, Numerical Linear Algebra with Applications, 25(3), 2018. 
  16. Weak Galerkin Method for the Biot's Consolidation Model, X. Hu, L. Mu, and X. Ye, Computer & Mathematics with Applications, 75, 2017-2030, 2018.
  17. Multigrid Algorithms for hp-version Interior Penalty Discontinuous Galerkin Methods on Polygonal and Polyhedral meshes, P. Antonietti, P. Houston, X. Hu, M. Sarti, and M. Verani, Calcolo, 54(4), 1169-1198, 2017.
  18. Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions, J. Adler, X. Hu, and L. Zikatanov, SIAM Journal of Scientific Computing, 39(5), S3-S23, 2017.
  19. Adaptive Finite Element Method for fractional differential equations using Hierarchical Matrices, X. Zhao, X. Hu, W. Cai, and G. Karniadakis, Computer Methods in Applied Mechanics and Engineering, 325, 56-76, 2017.
  20. Algebraic Multigrid for Least Squares Problems on Graphs with Applications to HodgeRank, C. Colley, J. Lin, X. Hu, and S. Aeron, Graph Algorithms Building Blocks, 31st IEEE International Parallel and Distributed Processing Symposium, 627-636, 2017.
  21. A Simple Finite Element Method of the Cauchy Problem for Poisson Equation, X. Hu, L. Mu, and X. Ye, International Journal of Numerical Analysis and Modeling, 14(4-5). 591-603, 2017.
  22. Numerical Studies of A Class of Linear Solvers for Fine-Scale Petroleum Reservoir Simulation, Z. Li, S. Wu, C.-S. Zhang, J. Xu, C. Feng, and X. Hu, Computing and Visualization in Science, 18(2), 93-102, 2017.
  23. A Nonconforming Finite Element Method for the Biot's Consolidation Model in Poroealsticity, X. Hu, C. Rodrigo, J. Gasper, and L. Zikatanov, Journal of Computational and Applied Mathematics, 310, 143-154, 2017
  24. On the Approximation of Laplacian Eigenvalues in Graph Disaggregation, X. Hu, J. C. Urschel, and L. Zikatanov, Linear and Multilinear Algebra, 65(9), 1805-1822, 2017.
  25. Compact Moving Least Squares: An Optimization Framework for Generating High Order Compact Meshless Discretizations, N. Trask, M. Maxey, and X. Hu, Journal of Computational Physics, 326, 596-611, 2016.
  26. Robust Preconditioners for Incompressible MHD Models, Y. Ma, K. Hu, X. Hu, and J. Xu, Journal of Computational Physics, 316, 721-746, 2016.
  27. A Two-grid SA-AMG Convergence Bound the Improves When Increasing the Polynomial Degrees, X. Hu, P. Vassilevski, and J. Xu, Numer. Linear Algebra Appl, 23(4), 746-771, 2016.
  28. Fast Multilevel Solvers for A Class of Discrete Fourth Order Parabolic problems, B. Zheng, L.P. Chen, X. Hu, L. Chen, R.H. Nochetto, and J. Xu, Journal of Scientific Computing, 69(1), 201-226, 2016.
  29. Stability and Monotonicity for Some Discretizations of the Biot's Consolidation Model, C. Rodrigo, J. Gasper, X. Hu, and L. Zikatanov, Computer Methods in Applied Mechanics and Engineering, 298(1), 183-204, 2016
  30. On Robust and Efficient Parallel Reservior Simulation on Tianhe-2, W. Guan, C. Qiao, H. Zhang, C.-S. Zhang, M. Zhi, Z. Zhu, Z. Zheng, W. Ye, Y. Zhang, X. Hu, Z. Li, C. Feng, Y. Xu, and J. Xu, SPE Reservoir Characterization and Simulation Conference and Exhibition, SPE 175602-MS, 2015.
  31. A Finite Element Framework for Some Mimetic Finite Difference Discretizations, C. Rodrigo, F.J. Gaspar, X. Hu, and L. Zikatanov, Computers & Mathematics with Applications, 70(11):2661-2673, 2015.
  32. A Simple Cascade Algorithm for Computing the Fiedler Vector of Graph Laplacians, J. Urshel, J. Xu, X. Hu, and L. T. ZikatanovJournal of Compputational Mathematics, 33(2), 209-226, 2015.
  33. A Multigrid Solver based on Distributive Smoother and Defect Correction for Oseen Problems, L. Chen, X. Hu, M. Wang, and J. Xu, Numerical Mathematics: Theory, Methods and  Applications, 8(2), 237-252, 2015.
  34. Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening, J.  Brannick, X. Hu, C. Rodrigo, and L. Zikatanov, Numerical Mathematics: Theory, Methods and  Applications, 8(1), 1-21, 2015.
  35. Two-Grid Method for Maxwell Eigenvalue Problems, J. Zhou, X. Hu, L. Chen, S. Shu, and L. Zhong, SIAM Journal on Numerical Analysis, 52(4), 2027-2047, 2014.
  36. On Adaptive Eulerian-Lagrangian Method for Linear Convection-Diffusion Problems, X. Hu, Y.-J. Lee, J. Xu, and C.-S. Zhang, Journal of Scientific Computing, 58(1), 90-114, 2014.
  37. Application of Auxiliary Space Preconditioning in Field-Scale Reservoir Simulations, X. Hu, J. Xu and C.-S. Zhang, SCIENCE CHINA Mathematics, 56(12), 2737-2751, 2013.
  38. A Parallel Auxiliary Grid Alegebraic Multigrid Method for Graphic Processing Units, L. Wang, X. Hu, J. Cohen, and J. Xu, SIAM Journal on Scientific Computing, 35(3), C263-C283, 2013.
  39. Combined Preconditioning with Applications in Reservoir Simulation, X. Hu, S. Wu, X. Wu, J. Xu, C.-S.Zhang, S. Zhang, and L. Zikatanov,  Multiscale Modeling and Simulation, 11(2), 507-521, 2013.
  40. Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs, J. Brannick, Y. Chen, X. Hu, and L. Zikatanov, Proceedings of Symposium in honor of Raytcho Lazarov's 40 years research in Computational Methods and Applied Mathematics, Springer Proceedings in Mathematics and Statistics, Vol 45, 2013
  41. Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid, X. Hu, P. Vassilevski, and J. Xu, SIAM Journal on Numerical Analysis, 51(2), 1349-1369, 2013.
  42. Development of A Fast Auxiliary Space Preconditioner for Numerical Reservoir Simulations, X. Hu, W. Liu, G. Qin, J. Xu, Y. Yan, and C.-S. Zhang, SPE Reservoir Characterization and Simulation Conference and Exhibition, SPE 148388, 2011.
  43. Acceleration of Two-grid Method for Eigenvalue Problems, X. Hu and X.-L. Cheng, Mathematics of Computation, 80:1287-1301, 2011.
  44. Effects of Integration and Adaptivity for the Eulerian-Lagrangian Method, J.-W. Jia, X. Hu, J. Xu, and C.-S.Zhang, Journal of Computational Mathematics, 29:367-395, 2011.
  45. The Boundary Penalty Method for the Diffusion Equation Subject to the Specification of Mass, X. Hu, L. Zhao, and A. W. Shaikh, Applied Mathematics and Computation, 186(1):735-748, 2007.
  46. Preconditioners for Elliptic Problems via Non-uniform Meshes, X. Hu and X.-F. Ling, Applied Mathematics and Computation, 181(2):1182-1198, 2006. 
  47. On the Iterative Algorithm for Large Sparse Saddle Point Problems, X.-F. Ling and X. Hu, Applied Mathematics and Computation, 178(2):372-379, 2006.

Invited Talks