Xiaozhe Hu

Research Interests

• Multilevel methods
  
• Spectral graph theory and graph algorithms
  
• Adaptive finite element methods
• Poromechanics and reservoir simulation
• Bioinformaticss
  

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

Ph.D. Students

• Junyuan (Joanne) Lin, 2014 - 2019 (Assistant Professor at Mathematics Department at Loyola Marymount University)
• Peter Ohm, 2015 - present
• Casey Cavanaugh, 2016 - present
  
• Anca Andrei, 2018 - present
• Kaiyi Wu, 2018 - present
• Michael Mayer (Mechanical Engineering), 2018 - present
  

Master Students

• Charles Colley, 2016 - 2018 (Ph.D. candidate at Purdue University)
• Yue Shen, 2017 - 2019 (Ph.D. candidate at Florida State University)

Publications

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1. Mixed-Dimensional Auxiliary Space Preconditioners, A. Budisa, W.M.Boon, and X. Hu, submitted to SIAM Journal of Scientific Computing, 2019.
   
2. Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media, A. Budisa and X. Hu, submitted to Computational Geosciences, 2019.
   
3. A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity, C. Niu, H. Rui, and X. Hu, submitted to Computational Geosciences, 2019
4. Robust Preconditioners for A New Stabilized Discretization of the Poroelastic Equations, J. H. Adler, F. J. Gaspar, X. Hu, P. Ohm, C. Rodrigo, and L. T. Zikatanov, submitted to  SIAM Journal of Scientific Computing, 2019
   
5. 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 Journal of Computational Physics, 2018
   
6. Convergence Analysis of a Generalized Full Approximation Storage Scheme for Convex Optimization Problems, L. Chen, X. Hu, and S. M. Wise, Mathematics of Computation, accepted.
   
7. Auxiliary space preconditioning for mixed finite element discretizations of Richards' equation, J. Batista,  X. Hu, and L. T. Zikatanov, Computers and Mathematics with Applications, in press
   
8. Randomized and Fault-tolerant Method of Subspace Corrections, X. Hu, J. Xu, L. T. Zikatanov, Research in the Mathematical Sciences, in press.
9. The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems, Q. Zhai, X. Hu, R. Zhang, Journal of Computational Mathematics, in press.
10. An Adaptive Multigrid Method based on Path Cover, X. Hu, J. Lin, and L. T. Zikatanov, SIAM Journal of Scientific Computing, 41(5), S220-S241, 2019.
    
11. Modifying AMG Coarse Spaces with Weak Approximation Property to Exhibit Approximation in Energy Norm, X. Hu and P. S. Vassilevski, SIAM Journal on Matrix Analysis and Applications, 40(3), 1131-1152, 2019.
    
12. A spatially adaptive high-order meshless method for fluid-structure interactions, W. Hu, N. Trask, X. Hu, and W.~Pan, Computer Methods in Applied Mechanics and Engineering, 355, 67-93, 2019.
    
13. Assessment of Network Model Identification across Complex Dieases, 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, Nature Methods, 16(9), 843-852, 2019.
14. An a Posteriori Error Estimator for the Weak Galerkin Least-Squares Finite-Element Method, J. H. Adler,  X. Hu, L. Mu, and X. Ye, Journal of Computational and Applied Mathematics, 362, 383-399, 2019.
15. A Weak Galerkin Finite Element Method for the Navier-Stokes Equations, X. Hu, L. Mu, and X. Ye, Journal of Computational and Applied Mathematics, 362, 614-625, 2019.
16. Common Randomized Shortest Paths (C-RSP): A Simple Yet Effective Framework for Multi-View Graph Embedding, A. Gamage, B. Rappaport, S. Aeron, and X. Hu, 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019.
    
17. 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, Computer Methods in Applied Mechanics and Engineering, 347, 402-424, 2019.
18. 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.
19. 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.
20. Newton Solvers for Drift-Diffusion and Electrokinetic Equations, A. Bousquet, X. Hu, M. Metti, and J. Xu, SIAM Journal of Scientific Computing, accepted.
21. Anti-myeloma Activity and Molecular Logic Operation by Natural Killer Cells in Microfluidic Droplets, S. Sarkar, S. McKenny, P. Sabhachandani, J. Adler,  X. Hu, D. Stroopinski, J. Rosenblatt, D. Avigan, and T. Konry, Sensors and Actuators B: Chemical, 282, 580-589, 2019.
    
22. Vector-potential Finite-element formulations for Two-dimensional Resistive Magnetohydrodynamics, J. Adler, Y. He, X. Hu, and S. P. MacLachlan, Mathematical Modeling and Numerical Analysis, 77(2), 476-493, 2019.
23. 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, 2018.
24. 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.
25. 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.
    
26. 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. 
27. Weak Galerkin Method for the Biot's Consolidation Model, X. Hu, L. Mu, and X. Ye, Computer & Mathematics with Applications, 75, 2017-2030, 2018.
28. 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.
    
29. 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.
30. 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.
31. 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.
32. 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.
    
33. 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.
    
34. 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
    
35. 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.
    
36. 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.
    
37. Robust Preconditioners for Incompressible MHD Models, Y. Ma, K. Hu, X. Hu, and J. Xu, Journal of Computational Physics, 316, 721-746, 2016.
    
38. 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.
    
39. 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.
40. 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
    
41. 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.
    
42. 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.
    
43. A Simple Cascade Algorithm for Computing the Fiedler Vector of Graph Laplacians, J. Urshel, J. Xu, X. Hu, and L. T. Zikatanov,  Journal of Compputational Mathematics, 33(2), 209-226, 2015.
44. 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.
    
45. 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.
    
46. 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.
    
47. 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.
    
48. 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.
    
49. 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.
    
50. 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.
    
51. 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
    
52. 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.
    
53. 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.
    
54. Acceleration of Two-grid Method for Eigenvalue Problems, X. Hu and X.-L. Cheng, Mathematics of Computation, 80:1287-1301, 2011.
55. 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.
56. 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.
57. Preconditioners for Elliptic Problems via Non-uniform Meshes, X. Hu and X.-F. Ling, Applied Mathematics and Computation, 181(2):1182-1198, 2006. 
58. 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

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• Robust Preconditioners for Mixed-dimensional Models of Flow in Fractured Porous Media, InterPore2019, 11th Annual Meeting, Valencia, Spain, 05/07/2019.
• Robust Preconditioners for Mixed-dimensional Models of Flow in Fractured Porous Media, AMS Spring Central and Western Joint Sectional Meeting, Hawaii, 03/22/2019.
• Stable Discretizations and Robust Preconditioners for the Biot's Model, SIAM Conference on Computational Science and Engineering, Spokane, Washington, 02/27/2019.
  
• Robust Preconditioners for the Biot's Model, SIAM Conference on Life Sciences, Minneapolis, 08/09/2018.
• Adaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matrices, Fractional PDEs: Theory, Algorithm and Applications, ICERM, 06/22/2018.
  
• Stable Discretizations and Robust Preconditioners for the Biot’s Model, The Computational Mathematics Aspects of Porous Media, and Fluid Flow, Lorentz Center, Leiden, Netherlands, 05/22/2018.
  
• Adaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matrices, Computational and Applied Mathematics Seminar, Mississippi State University, 03/23/2018.
  
• Robust Discretization and Preconditioners for the Biot's Model, Workshop on Solvers for Materials with High-Aspect-Ratio Inclusions, Finse, Norway, 01/09/2018.
  
• Adaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matrices, Mathematical Sciences Colloquium, Worcester Polytechnic Institute, 11/10/2017.
  
• Robust Preconditioners for the Biot's Model, European Conference on Numerical Mathematics & Advanced Applications, Voss, Norway, 09/26/2017.
  
• Algebraic Multigrid Methods for Computing Diffusion State Distance on Graphs, ICMSEC Seminar, Chinese Academy of Sciences, Beijing, China, 08/09/2017.
  
• Adaptive Multilevel Finite Element Method for Fractional Differential Equations using Hierarchical Matrices, Peking University, Beijing, China, 07/24/2017.
  
• Algebraic Multigrid Methods for Computing Diffusion-based Metrics on Graphs, 2017 SIAM Annual Meeting, Pittsburgh, 07/13/2017.
  
• Efficient Solvers for Mimetic Finite Difference Method for Maxwell's Equations, Polytopal Element Methods in Mathematics and Engineering, University of Milano-Bicocca, Milano, 07/05/2017.
  
• Robust Preconditioners for Coupled Problems, MAC Seminar, Centrum Wiskunde & Informatica, Amsterdam, Netherlands, 06/13/2017.
  
• Robust Preconditioners for Coupled Problems, Seminario Rubio de Francia, Universidad de Zaragoza, Zaragoza, Spain, 06/01/2017.
  
• Algebraic Multigrid Methods for Computing Diffusion State Distance on Graphs, Maseeh Mathematics \& Statistics Colloquium, Portland State University, Portland, 05/05/2017.
  
• Algebraic Multigrid Methods for Computing Diffusion-Based Metrics on Graphs, Computational Science Seminar, University of Massachusetts Dartmouth, 04/12/2017.
  
• Efficient Simulation of Asymptotically Disappearing Solutions for Wave Equations, SIAM conference on Computational Science and Engineering, Atlanta, 02/28/2017.
• (Plenary talk) Robust Preconditioners for Coupled Problems,  at the 24th International Conference on Domain Decomposition Methods, Svalbard, Norway, 02/07/2017.
• Fast Graph Laplacian Solvers and Their Applications in Protein Interaction Networks, Applied and Computational Mathematics Seminar, University of California, Irvine, 12/05/2016.
• Fast Graph Laplacian Solvers and Their Applications, CCMA Colloquium, The Pennsylvania State University, 11/28/2016.
• Distance Metrics for Protein Interaction Networks, CCMA Luncheon Seminar, The Pennsylvania State University, 11/28/2016.
• Weak Galerkin Finite Element Method for the Biot's Consolidation Model, The 2nd Annual Meeting of SIAM Central States Section, University of Arkansas at Little Rock, 10/01/2016.
• Randomized Method of Subspace Corrections, CCMA PDEs and Numerical Methods Seminar, Penn State University, 06/28/2016.
• Nonconforming Three-field Discretization of Biot's Model in Poroelasticity, 8th International Conference on Porous Media \& Annual Meeting, Cincinnati, Ohio, USA, 05/09/2016.
• Convergence Analysis of Finite Element Discretizations for Biot's Equations, Workshop ``Flow in Deformable Porous Media", Universidad de Zaragoza, 11/25/2015.
• Finite Element Multigrid Framework for Mimetic Finite Difference Discretizations, Polytopal Element Methods in Mathematics and Engineering, Georgia Institute of Technology, October 28, 2015.
• Effective Solvers for Reservoir Simulation, SIAM Conference on Mathematical and Computational Issues in the Geosciences, Stanford University, 06/29/2015.
• Algebraic Multigrid Method and Its Parallelization, Computational Science Seminar, University of Massachusetts Dartmouth, 04/29/2015.
• Cascadic Multigrid for Eigenvalue Problems and Its Application in Graph Problems, Mathematics Colloquium, Tufts University, 04/17/2015.
• Robust Preconditioners for the Incompressible MHD System, Scientific Computing Seminar, Brown University, 03/27/2015.
• Finite Element Multigrid Framework for Mimetic Finite Difference Discretizations, SIAM Conference on Computational Science and Engineering, Salt Lake City, 03/14/2015.
  
• On Adaptive Eulerian-Lagrangian Method for Linear Convection-Diffusion Problems, AMS Spring Central Sectional Meeting, Texas Tech University, 04/12/2014.
• Effective Solvers for Reservoir Simulation, Tufts University, 02/12/2014.
  
• Effective Solvers for Reservoir Simulation, Lawrence Livermore National Laboratory, 11/25/2013.
  
• Cascadic Multigrid for Eigenvalue Problems and Its Application in Graph Problems, University of California, Irvine, 09/20/2013.
  
• Parallel AMG Method on GPU, 21st International Domain Decomposition Conference, INRIA, Rennes, France, 06/26/2012.
• Parallel Auxiliary Grid AMG Method for GPU, Applied and Computational Mathematics Seminar, University of California, Irvine, 05/07/2012.
• Algebraic Multigrid Methods for Petroleum Reservoir Simulation, 8th International Conference on Scientific Computing and Applications, University of Nevada, Las Vegas, 04/03/2012.
  
• Effective Preconditioners for Reservoir Simulation, Computational and Applied Mathematics Colloquium, Department of Mathematics, The Pennsylvania State University, 01/13/2012.
  
• Effective Solvers for Reservoir Simulation, Workshop 4: Numerical Analysis of Multiscale Problems & Stochastic Modelling, Linz, Austria, 12/14/2011.
  
• Effective Solvers for Reservoir Simulation, Numerical Analysis and PDE Seminar, Department of Mathematics, University of Delaware, 11/10/2011.
  
• Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid, 8th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, 06/07/2011.
• Fast Solvers for Reservoir Simulation, 20th International Domain Decomposition Conference, University of California, San Diego, 02/08/2011.