Xiaozhe Hu

1.

A Local Fourier Analysis for Additive Schwarz Smoothers, Á. Pé de la Riva, C. Rodrigo, F. J. Gaspar, J. H. Adler, X. Hu, and L. T. Zikatanov, submitted to Computer & Mathematics with Applications.

2.

Algebraic Multigrid Methods for Metric-perturbed Coupled Problems, A. Budiša, X. Hu, M. Kuchta, K. A. Mardal, and L. T. Zikatanov, submitted to SIAM Journal of Scientific Computing.

3.

Fast Convex Optimization via Differential Equation with Hessian Driven Damping and Tikhonov Regularization, G. Zhong, X. Hu, L. Zhong, and M. Tang, submitted to Journal and Optimization Theory and Applications.

4.

Parameter-robust preconditioners for Biot’s model, C. Rodrigo, F. J. Gaspar, J. H. Adler, X. Hu, P. Ohm, and L. T. Zikatanov, submitted to SeMA Journal.

5.

Parameter-free Preconditioning for Nearly-incompressible Linear Elasticity, J. H. Adler, X. Hu, Y. Li, and L. T. Zikatanov, submitted to Computers and Mathematics with Applications.

6.

HAZniCS - Software Components for Multiphysics Problems, A. Budiša, X. Hu, M. Kuchta, K. A. Mardal, and L. T. Zikatanov, submitted to ACM Transactions on Mathematical Software.

7.

Structure-Preserving Discretization of Fractional Vector Calculus Using Discrete Exterior Calculus, A. Jacobson and X. Hu, submitted to Computer & Mathematics with Applications.

8.

Data-driven Whitney forms for Structure-Preserving Control Volume Analysis, J .A. Actor, X. Hu, A. Huang, S. A. Roberts, and N. Trask, submitted to Journal of Computational Physics.

9.

Oscillation-free Numerical Schemes for the Biot’s Model with Automatic Stabilization, Á. Pé de la Riva,, X. Hu, C. Rodrigo, and L. T. Zikatanov, submitted to Applied Mathematics Letters.

10.

A Stable Mimetic Finite-difference Method for Convection-dominated Diffusion Equations,
J. H. Adler, C. Cavanaugh, X. Hu, A. Huang, and N. Trask, submitted to SIAM Journal of Scientific Computing.

11.

A Deep Neural Network/Meshfree Method for Dynamic Two-phase Interface Problems, X. Zhu, X. Hu, and P. Sun, submitted to SIAM Journal of Scientific Computing.

Refereed Publications

12.

Pressure-robust Enriched Galerkin Method for the Stokes Equations, X. Hu, S. Lee, L. Mu, and S. Y. Yi, Journal of Computational and Applied Mathematics, accepted.

13.

Solving Graph Laplacians via Multilevel Sparsifiers, X. Hu and J. Lin, SIAM Journal of Scientific Computing, accepted.

14.

AmgR: Algebraic Multigrid Accelerated on ReRAM, M. Fan, X. Tian, Y. He, J. Li, Y. Duan, X. Hu, Y. Wang, Z. Jin, and W. Liu, the 60th Design Automation Conference, accepted.

15.

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-anisotriopy-aligned Meshes, D. Green, X. Hu, J. Lore, L. Mu, and M. L. Stowell, SIAM Journal of Scientific Computing, accepted.

16.

Rational Approximation Preconditioners for Multiphysics Problems, A. Budiša, X. Hu, M. Kuchta, K. A. Mardal, and L. T. Zikatanov, the Tenth International Conference on Numerical Methods and Applications, Lecture Notes in Computer Science, accepted.

17.

Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems, X. Hu, E. Keilegavlen, and J. M. Nordbotten, Water Resources Research, 59(1), 1-9, 2023.

18.

A Multigrid Preconditioner for Spatially Adaptive High-order Meshless Method on Fluid-solid Interaction Problems, Z. Ye, X. Hu, and W. Pan, Computer Methods in Applied Mechanics and Engineering, 400, 115506, 2022.

19.

A Mesh-free Method Using Piecewise Deep Neural Network for Elliptic Interface Problems, C. He, X. Hu, L. Mu, Journal of Applied and Computational Mathematics, 412, 114358, 2022.

20.

An Enriched Galerkin for the Stokes Equations, S.-Y. Yi, X. Hu, S. Lee, and J. H. Adler, Computers & Mathematics with Applications, 120, 115-131, 2022.

21.

Monolithic Multigrid for a Reduced-quadrature Discretization of Poroelasticity, J. H. Adler, Y. He, X. Hu, S. MacLachlan, and P. Ohm, SIAM Journal of Scientific Computing, 0, S54-S81, 2022.

22.

Enforcing Exact Physics in Scientific Machine Learning: A Data-Driven Discrete Exterior Calculus on Graphs, N. Trask, A. Huang, and X. Hu, Journal of Computational Physics, 456, 110969, 2022.

23.

Random-walk based Approximate k-Nearest Neighbors Algorithm for Diffusion State Distance, L. J. Cowen, X. Hu, J. Lin, Y. Shen, and K. Wu, LSSC 2021: Large-Scale Scientific Computing, Lecture Notes in Computer Science, 3-15, 2022.

24.

An Efficient High-order Numerical Solver for Diffusion Equations with Strong Anisotropy, D. Green, X. Hu, J. Lore, L. Mu, and M. L. Stowell, Computer Physics Communications, 276, 108333, 2022.

25.

Well-posedness and Discretization for a Class of Models for Mixed-dimensional Problems with High-Dimensional Gap, E. Hodneland, X. Hu and J. M. Nordboltten, SIAM Journal on Applied Mathematics, 85(5), 2218-2245, 2021.

26.

A Posteriori Error Estimates for Multilevel Methods for Graph Laplacians, X. Hu, K. Wu, and L. T. Zikatanov, SIAM Journal of Scientific Computing, 43(5), S727-S742, 2021.

27.

A Finite-Element Framework for a Mimetic Finite-Difference Discretization of Maxwell’s Equations, J. H. Adler, C. Cavanaugh, X. Hu, and L. T. Zikatanov, SIAM Journal of Scientific Computing, 43(4), A2638-A2659, 2021.

28.

Block Preconditioners for Mixed-dimensional Discretization of Flow in Fractured Porous Media, A. Budiša and X. Hu, Computational Geosciences, 25, 671-686, 2021.

29.

A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity, C. Niu, H. Rui, and X. Hu, Computational Geosciences, 25, 757-774, 2021.

30.

Diffusion State Distances: Multitemporal Analysis, Fast Algorithms, and Applications to Biological Networks, L. Cowen, K. Devkota, X. Hu, J. M. Murphy, and K. Wu, SIAM Journal on Mathematics of Data Science, 3(1), 142-170, 2021.

31.

Mixed-Dimensional Auxiliary Space Preconditioners, A. Budiša, W. M. Boon, and X. Hu, SIAM Journal of Scientific Computing, 42(5), A3367-A3396. 2020.

32.

Using Hierarchical Matrices in the Solution of the Time-fractional Heat Equation by Multigrid Waveform Relaxation, X. Hu, C. Rodrigo, and F. J. Gaspar, Journal of Computational Physics, 416, 2020.

33.

Convergence Analysis of the Fast Subspace Descent Method for Convex Optimization Problems, L. Chen, X. Hu, and S. M. Wise, Mathematics of Computation, 89, 2249-2282, 2020.

34.

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, SIAM Journal of Scientific Computing, 42(3), B761-B791, 2020.

35.

Auxiliary space preconditioning for mixed finite element discretizations of Richards’ equation, J. Batista, X. Hu, and L. T. Zikatanov, Computers & Mathematics with Applications, 80(2), 405-416, 2020.

36.

The Shifted-inverse Power Weak Galerkin Method for Eigenvalue Problems, Q. Zhai, X. Hu, R. Zhang, Journal of Computational Mathematics, 38(4), 606-623, 2020.

37.

Randomized and Fault-tolerant Method of Subspace Corrections, X. Hu, J. Xu, and L. T. Zikatanov, Research in the Mathematical Sciences, 6(29), 2019.

38.

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.

39.

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.

40.

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.

41.

Assessment of network module identification across complex diseases, S. Choobdar, M. E. Ahsen, J. Crawford, M. Tomasoni, T. Fang, D. Lamparter, J. Lin, B. Hescott, X. Hu, J. Mercer, T. Natoli, R. Narayan, A. Subramanian, J. D. Zhang, 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.

42.

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.

43.

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.

44.

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.

45.

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.

46.

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.

47.

Vector-potential Finite-element formulations for Two-dimensional Resistive Magnetohydrodynamics, J. H. Adler, Y. He, X. Hu, and S. P. MacLachlan, Computers & Mathematics with Applications, 77(2), 476-493, 2019.

48.

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.

49.

New Stabilized Discretizations for Poroelasticity and the Stokes’ Equations, C. Rodrigo, X. Hu, P. Ohm, J. H. Adler, F. J. Gaspar, and L. T. Zikatanov, Computer Methods in Applied Mechanics and Engineering, 341, 467-484, 2018.

50.

Newton Solvers for Drift-Diffusion and Electrokinetic Equations, A. Bousquet, X. Hu, M. Metti, and J. Xu, SIAM Journal of Scientific Computing, 40(3), B982-B1006, 2018,

51.

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.

52.

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.

53.

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), e2156-e2171, 2018.

54.

Weak Galerkin Method for the Biot’s Consolidation Model, X. Hu, L. Mu, and X. Ye, Computer & Mathematics with Applications, 75, 2017-2030, 2018.

55.

Multigrid Algorithms for hp-version Interior Penalty Discontinuous Galerkin Methods on Polygonal and Polyhedral meshes, P. F. Antonietti, P. Houston, X. Hu, M. Sarti, and M. Verani, Calcolo, 54(4), 1169-1198, 2017.

56.

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.

57.

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.

58.

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, 2017 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW), Orlando / Buena Vista, FL, USA, 627-636, 2017.

59.

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.

60.

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.

61.

A Nonconforming Finite Element Method for the Biot’s Consolidation Model in Poroelasticity, X. Hu, C. Rodrigo, J. Gasper, and L. Zikatanov, Journal of Computational and Applied Mathematics, 310, 143-154, 2017.

62.

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.

63.

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.

64.

Robust Preconditioners for Incompressible MHD Models, Y. Ma, K. Hu, X. Hu, and J. Xu, Journal of Computational Physics, 316, 721-746, 2016.

65.

A Two-grid SA-AMG Convergence Bound that Improves When Increasing the Polynomial Degrees, X. Hu, P. Vassilevski, and J. Xu, Numerical Linear Algebra with Applications, 23(4), 746-771, 2016.

66.

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.

67.

Stability and Monotonicity for Some Discretizations of the Biot’s Consolidation Model, C. Rodrigo, J. Gaspar, X. Hu, and L. Zikatanov, Computer Methods in Applied Mechanics and Engineering, 298(1), 183-204, 2016.

68.

On Robust and Efficient Parallel Reservoir 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.

69.

A Finite Element Framework for Some Mimetic Finite Difference Discretizations, with C. Rodrigo, F.J. Gaspar, X. Hu, and L. Zikatanov, Computers & Mathematics with Applications, 70(11), 2661-2673, 2015.

70.

A Cascadic Algorithm for Computing the Fiedler Vector of Graph Laplacians, J. Urschel, J. Xu, X. Hu, and L. Zikatanov, Journal of Computational Mathematics, 33(2), 209-226, 2015.

71.

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.

72.

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.

73.

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.

74.

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.

75.

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.

76.

A Parallel Auxiliary Grid Algebraic 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.

77.

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.

78.

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.

79.

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.

80.

Development of a Fast Auxiliary Subspace Preconditioner for Numerical Reservoir Simulators, 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.

81.

Acceleration of Two-grid Method for Eigenvalue Problems, X. Hu and X.-L. Cheng, Mathematics of Computation, 80, No. 275, 1287-1301, 2011.

82.

Effects of Integrations 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.

83.

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.

84.

Preconditioners for Elliptic Problems via Nonuniform Meshes, X. Hu and X.-F. Ling, Applied Mathematics and Computation, 181(2), 1182-1198, 2006.

85.

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.

Proceedings

86.

Greedy Fiedler Spectral Partitionning for Data-driven Discrete Exterior Calculus, A. Huang, N. Trask, C. Brissette, and X. Hu, AAAI Spring Symposium Series on Combining Artifical Intelligence and Machine Learning with Physics Science, March 22-24, 2021.

87.

A Drift-Diffusion Solver Using a Finite-Element Method to Analyze Carrier Dynamics at Ultra-high Solar Concentrations, E. Carlson, M. Stevens, D. Emerson, X. Hu, J. H. Adler, and T. E. Vandervelde, In Proceedings of the 60th IEEE International Midwest Symposium on Circuits and Systems Conference, Boston, August 6th-9th, 2017.

Technical Reports

88.

Randomized Fast Subspace Descent Methods, L. Chen, X. Hu, and H. Wu, arXiv:2006.06589.

89.

Momentum Accelerated Multigrid Methods, X. Hu and C. Niu, arXiv:2006.16986.

90.

Ladder Polynomial Neural Networks, L. Liu, R. Gu, and X. Hu, arXiv:2106.13834, 2021.

91.

Microphysics of Neutron Star Outer Envelopes in the Periodized, Magnetic Thomas-Fermi Model, T.A. Engstrom, V.H. Crespi, B.J. Owen, J. Brannick, and X. Hu, arXiv:1409.3299 [astro-ph.SR], 24 February, 2015.

In Preparation

92.

Fast Approximate IsoRank for Scalable Global Alignment of Biological Networks, K. Devkota, A. Blumer, L. J. Cowen, and X. Hu, in preparation.

93.

MELISSA: Semi-Supervised Embedding for Protein Function Prediction Across Multiple Networks, K. Wu, X. Hu, and L. Cowen, in preparation.

94.

Control of Microfluids System Using Photosurfactants, M. Mayer, J. H. Adler, X. Hu, and M. Hodes, in preparation.

95.

A New Simple Adaptive Finite Element Method for Eigenvalue Problems, J. Hu, X. Hu, H. Wei, N. Yi, in preparation.