Parallel multilevel iterative methods for large-scale systems
Spectral graph theory, graph algorithms and applications
Adaptive finite element methods
Eigenvalue problems
Poromechanics and reservoir simulation
Seminar
I am a co-organizer of the Computational and Applied Mathematics
Seminar. See here for
more details.
Publications
Mudified AMG Coarse Spaces with Weak Approximation Property
to Exhibit Approximation in Energy Norm, with P.
S. Vasselevski, submitted to SIAM Journal on Matrix Analysis
and Applications, 2018.
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.
A Weak Galerkin Finite Element Method for the
Navier-Stokes Equations, with L. Mu and X. Ye,
submitted to Journal of Computational and Applied Mathematics,
2017.
Newton Solvers for Drift-Diffusion and Electrokinetic
Equations, with A. Bousquet, M. Metti, and J. Xu,
submitted to SIAM Journal of Scientific Computing, 2017
Vector-potential Finite-element formulations for
Two-dimensional Resistive Magnetohydrodynamics,
with J. Adler, Y. He, and S. P. MacLachlan, submitted to
Mathematical Modeling and Numerical Analysis, 2017.
Using Hierarchical Matrices in the Solution of the
Time-fractional Heat Equation by Multigrid Waveform
Relaxation, with C. Rodrigo and F. J. Gaspar,
submitted to SIAM Journal of Scientific Computing, 2017.
New Stabilized Discretizations for Poroelasticity
and the Stokes's Equations, with C. Rodrigo, P.
Ohm, J. H. Adler, F. J. Gaspar, and L. T. Zikatanov, submitted
to Computer Methods in Applied Mechanics and Engineering,
2017.
Robust Block Preconditioners for Biot's Model,
with J. H. Adler, F. J. Gaspar, C. Rodrigo, and L. T.
Zikatanov, submitted to Proceedings of the 24th International
Conference on Domain Decomposition Methods, 2017.
Computing the Diffusion State Distance on Graphs via
Algebraic Multigrid and Random Projections, with
J. Lin, L. J. Cowen, and B. Hescott, Numerical Linear Algebra
with Applications, accepted.
A Compatible High-order Meshless Method for the Stokes
Equations with Applications to Suspension Flows,
with N. Trask and M. Maxey, Journal of Computational Physics,
accepted
Adaptive Finite Element Method for fractional
differential equations using Hierarchical Matrices,
with X. Zhao, W. Cai, and G. Karniadakis, Computer Methods in
Applied Mechanics and Engineering, 325, 56-76, 2017.
Weak Galerkin Method for the Biot's Consolidation
Model, with L. Mu and X. Ye, Computer &
Mathematics with Applications, available online: August 23,
2017.
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,
14(4-5). 591-603, 2017.
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, 627-636, 2017.
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, first online; May 04, 2017.
On the Approximation of Laplacian Eigenvalues in Graph
Disaggregation, with J. C. Urschel and L.
Zikatanov, Linear and Multilinear Algebra, 65(9), 1805-1822,
2017.
Robust Solvers for Maxwell's Equations with
Dissipative Boundary Conditions, with J. Adler and
L. Zikatanov, SIAM Journal of Scientific Computing, 39(5),
S3-S23, 2017.
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.
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
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.
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.
Robust Preconditioners for Incompressible MHD Models,
with Y. Ma, K. Hu, and J. Xu, Journal of Computational
Physics, 316, 721-746, 2016.
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.
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.
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
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
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.
Acceleration
of Two-grid Method for Eigenvalue Problems, with
X.-L. Cheng, Math. Comp., 80:1287-1301, 2011.
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.
Preconditioners
for Elliptic Problems via Non-uniform Meshes, with
X.-F. Ling, Appl. Math. Comput., 181(2):1182-1198, 2006.
On the
Iterative Algorithm for Large Sparse Saddle Point Problems,
with X.-F. Ling, Appl. Math. Comput., 178(2):372-379, 2006.
Invited Talks
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.