Fast solvers for large-scale sparse linear systems
Parallel computing (CPU & GPU)
Eigenvalue problems
Reservoir Simulation
Computational fluid dynamics
Publications
A
Parallel Auxiliary Grid AMG method for GPU, with L.
Wang, J. Cohen, and J. Xu, arXiv:1209.5421, submitted to SIAM
Journal on Scientific Computing, 2012.
Parallel
Unsmoothed Aggregation Algebraic Multigrid Algorithms on
GPUs, with J. Brannick, Y. Chen, and L. Zikatanov,
submitted to Proceedings of Symposium in honor of Raytcho
Lazarov's 40 years research in Computational Methods and
Applied Mathematics, Springer Proceedings in Mathematics and
Statistics, 2012.
Combined
Preconditioning with Applications in Reservoir Simulation,
with S. Wu, X. Wu, J. Xu, C.-S.Zhang, S. Zhang, and L.
Zikatanov, arXiv:1205.6113, submitted to Multiscale Modeling
and Simulation, 2012.
On
Adaptive Eulerian-Lagrangian Method for Linear
Convection-Di usion Problems, with Y.-J. Lee, J. Xu,
and C.-S. Zhang, arXiv:1209.1364, submitted to Journal of
Scientific Computing, 2012.
Comparative
Convergence Analysis of Nonlinear AMLI-cycle Multigrid,
with P. Vassilevski and J. Xu, arXiv:1202.1987, submitted to
SIAM J. Numer. Anal., 2011
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.
Work in Progress
Application
of Auxiliary Space Preconditioning in Field-Scale Reservoir
Simulations, with J. Xu and C.-S. Zhang.
A Class
of Multilevel Preconditioners for Petroleum Reservoir
Simulation, with J. Xu, S. Wu, C.-S. Zhang, X. Li, Q.
Li, and B. Wang.
Auxiliary
Space Preconditioning for the Stokes Equations, with
L. Wang, and J. Xu.
Fast
Solvers for the Fourth Order Parabolic problems, with
L. Chen, J. Xu and B. Zheng.
Time
Adaptive Parareal Algorithm, with J. Xu and C.-S.
Zhang.
Two-Grid Method for Maxwell Eigenvalue Problems,
with J. Zhou, L. Chen, S. Shu, and L. Zhong.
A New Simple Adaptive Finite Element Method for
Eigenvalue Problems, with J. Hu, and N. Yi.
A Simple Cascade Algorithm for Computing the
Fiedler Vector of Graph Laplacians, with J. Urshel
and J. Xu.
Invited Talks
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 Scienti c Computing and
Applications, University of Nevada, Las Vegas, 04/03/2012.
E ffective
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
Deigo, 02/08/2011.
