Research Interests


Seminar

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

Publications
  1. Optimal Interpolation and Compatible Relaxation in Classical Algebraic Multigrid, with J. Brannick, F. Cao, K. Kahl, and R. Falgout, submitted to SIAM Journal of Scientific Computing.
  2. Adaptive Finite Element Method for fractional differential equations using Hierarchical Matrices, with X. Zhao, W. Cai, and G. Karniadakis, submitted to Computer Methods in Applied Mechanics and Engineering.
  3. Weak Galerkin Method for the Biot's Consolidation Model, with L. Mu and X. Ye, submitted to Computer & Mathematics with Applications.
  4. A Compatible High-order Meshless Method for the Stokes Equations with Applications to Suspension Flows, with N. Trask and M. Maxey, submitted to Journal of Computational Physics.
  5. Vector-potential Finite-element formulations for Two-dimensional Resistive Magnetohydrodynamics, with J. Adler, Y. He, and S. P. MacLachlan, submitted to Numerische Mathematik.
  6. Modeling Myeloma Cell Dynamics and Cytolysis in Microfluidic Droplets, with S. Sarkar, P. Sabhachandani, J. Adler, D. Stroopinski, J. Rosenblatt, D. Avigan, and T. Konry, submitted to Scientific Reports.
  7. Microphysics of Neutron Star Outer Envelopes in the Periodized, Magnetic Thomas-Fermi Model, with T.A. Engstrom, V.H. Crespi, B.J. Owen, and J. Brannick, submitted to Astrophysical Journal.
  8. A Simple Finite Element Method of the Cauchy Problem for Poisson Equation, with L. Mu and X. Ye, International Journal of Numerical Analysis and Modeling, accepted.
  9. Algebraic Multigrid for Least Squares Problems on Graphs with Applications to HodgeRank, with C. Colley, J. Lin, and S. Aeron, Graph Algorithms Building Blocks, 31st IEEE International Parallel and Distributed Processing Symposium, accepted.
  10. Multigrid Algorithms for hp-version Interior Penalty Discontinuous Galerkin Methods on Polygonal and Polyhedral meshes, with P. Antonietti, P. Houston, M. Sarti, and M. Verani, Calcolo, accepted.
  11. On the Approximation of Laplacian Eigenvalues in Graph Disaggregation, with J. C. Urschel and L. Zikatanov, Linear and Multilinear Algebra, accepted.
  12. Robust Solvers for Maxwell's Equations with Dissipative Boundary Conditions, with J. Adler and L. Zikatanov, SIAM Journal of Scientific Computing, accepted.
  13. Numerical Studies of A Class of Linear Solvers for Fine-Scale Petroleum Reservoir Simulation, with Z. Li, S. Wu, C.-S. Zhang, J. Xu, and C. Feng, Computing and Visualization in Science, 18(2), 93-102, 2017.
  14. A Nonconforming Finite Element Method for the Biot's Consolidation Model in Poroealsticity, with C. Rodrigo, J. Gasper, and L. Zikatanov, Journal of Computational and Applied Mathematics, 310, 143-154, 2017
  15. Fast Multilevel Solvers for A Class of Discrete Fourth Order Parabolic problems, with B. Zheng, L.P. Chen, L. Chen, R.H. Nochetto, and J. Xu, Journal of Scientific Computing, 69(1), 201-226, 2016.
  16. Compact Moving Least Squares: An Optimization Framework for Generating High Order Compact Meshless Discretizations, with N. Trask and M. Maxey, Journal of Computational Physics, 326, 596-611, 2016.
  17. Robust Preconditioners for Incompressible MHD Models, with Y. Ma, K. Hu, and J. Xu, Journal of Computational Physics, 316, 721-746, 2016.
  18. A Two-grid SA-AMG Convergence Bound the Improves When Increasing the Polynomial Degrees, with P. Vassilevski and J. Xu, Numer. Linear Algebra Appl, 23(4), 746-771, 2016.
  19. A Finite Element Framework for Some Mimetic Finite Difference Discretizations, with C. Rodrigo, F.J. Gaspar, and L. Zikatanov, Computers & Mathematics with Applications, 70(11):2661-2673, 2015.
  20. Stability and Monotonicity for Some Discretizations of the Biot's Consolidation Model, with C. Rodrigo, J. Gasper, and L. Zikatanov, Computer Methods in Applied Mechanics and Engineering, 298(1), 183-204, 2016
  21. On Robust and Efficient Parallel Reservior Simulation on Tianhe-2, with W. Guan, C. Qiao, H. Zhang, C.-S. Zhang, M. Zhi, Z. Zhu, Z. Zheng, W. Ye, Y. Zhang, Z. Li, C. Feng, Y. Xu, and J. Xu, SPE Reservoir Characterization and Simulation Conference and Exhibition, SPE 175602-MS, 2015.
  22. A Simple Cascade Algorithm for Computing the Fiedler Vector of Graph Laplacians, with J. Urshel and J. Xu, J. Comp. Math., 33(2), 209-226, 2015.
  23. A Multigrid Solver based on Distributive Smoother and Defect Correction for Oseen Problems, with L. Chen, M. Wang, and J. Xu, Special Issue for Weizmann Workshop of Numerical Mathematics: Theory, Methods and  Applications, 8(2), 237-252, 2015.
  24. Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening, with J.  Brannick, C. Rodrigo, and L. Zikatanov, Special Issue for Weizmann Workshop of Numerical Mathematics: Theory, Methods and  Applications, 8(1), 1-21, 2015.
  25. Two-Grid Method for Maxwell Eigenvalue Problems, with J. Zhou, L. Chen, S. Shu, and L. Zhong, SIAM Journal on Numerical Analysis, 52(4), 2027-2047, 2014.
  26. Application of Auxiliary Space Preconditioning in Field-Scale Reservoir Simulations, with J. Xu and C.-S. Zhang, SCIENCE CHINA Mathematics, 56(12), 2737-2751, 2013.
  27. On Adaptive Eulerian-Lagrangian Method for Linear Convection-Diffusion Problems, with Y.-J. Lee, J. Xu, and C.-S. Zhang, J. Sci. Comput., published on line, 02 June, 2013.
  28. A Parallel Auxiliary Grid Alegebraic Multigrid Method for Graphic Processing Units, with L. Wang, J. Cohen, and J. Xu, Siam J. Sci. Comput., 35(3), C263-C283, 2013.
  29. Parallel Unsmoothed Aggregation Algebraic Multigrid Algorithms on GPUs, with J. Brannick, Y. Chen, 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
  30. Combined Preconditioning with Applications in Reservoir Simulation, with S. Wu, X. Wu, J. Xu, C.-S.Zhang, S. Zhang, and L. Zikatanov,  Multiscale Modeling and Simulation, 11(2), 507-521, 2013.
  31. Comparative Convergence Analysis of Nonlinear AMLI-cycle Multigrid, with P. Vassilevski and J. Xu, submitted to SIAM J. Numer. Anal., 51(2), 1349-1369, 2013.
  32. Development of A Fast Auxiliary Space Preconditioner for Numerical Reservoir Simulations, with W. Liu, G. Qin, J. Xu, and C.-S. Zhang, SPE Reservoir Characterization and Simulation Conference and Exhibition, SPE 148388, 2011.
  33. Effects of Integration and Adaptivity for the Eulerian-Lagrangian Method, with J.-W. Jia, J. Xu, and C.-S.Zhang, J. Comp. Math., 29:367-395, 2011.
  34. Acceleration of Two-grid Method for Eigenvalue Problems, with X.-L. Cheng, Math. Comp., 80:1287-1301, 2011.
  35. The Boundary Penalty Method for the Diffusion Equation Subject to the Specification of Mass, with L. Zhao and A. W. Shaikh, Appl. Math. Comput., 186(1):735-748, 2007.
  36. Preconditioners for Elliptic Problems via Non-uniform Meshes, with X.-F. Ling, Appl. Math. Comput., 181(2):1182-1198, 2006. 
  37. On the Iterative Algorithm for Large Sparse Saddle Point Problems, with X.-F. Ling, Appl. Math. Comput., 178(2):372-379, 2006.

Work in Progress
  1. Fast Solver for Drift-Diffusion and Electrokinetic Equations, with M. Metti and J. Xu.
  2. Randomized and Fault-tolerant Method of Subspace Corrections, with J. Xu and L. Zikatanov.
  3. Time Adaptive Parareal Algorithm, with J. Xu and C.-S. Zhang.

Invited Talks