Lawrence Livermore National Laboratory

Lawrence Livermore National Laboratory

Charles H. Tong

Phone: 925-422-3411

Mailing address:
Charles H. Tong
Lawrence Livermore National Laboratory
Box 808, L-557
Livermore, CA 94551-0808

Charles Tong is a member of the technical staff in the Center for Applied Scientific Computing at LLNL. His current research interests include uncertainty quantification, sensitivity analysis, iterative solvers for linear systems, and parallel computing. He is currently working on several research and application projects on uncertainty quantification.


Charles received his Ph.D. degree in Computer Science from UCLA in 1990. Before joining LLNL, he held a staff position at Sandia National Laboratories, and a faculty position in the Mathematics Department at the Hong Kong University of Science and Technology.

Selected Publications

Journal and Other Published Articles

M. Brezina, C. Tong, and R. Becker, " Parallel Algebraic Multigrids for Structural Mechanics ," accepted for publication in SIAM Journal on Scientific Computing. Also appear as LLNL report UCRL-JRNL-204167, 2004. 

C. Tong, " Refinement Strategies for Stratified Sampling Methods, " accepted for publication in Reliability Engineering and System Safety . Also appear as LLNL report UCRL-JRNL-204408, 2004.

E. Chow, T. Manteuffel, C. Tong, and B. Wallin, " Algebraic Elimination of Slide Surface Constraints in Implicit Structural Analysis ," in International Journal for Numerical Methods in Engineering , Vol 57, pp. 1129-1144, 2003.

C. Tong, " Numerical Methods for Saddle Point Problems Arising from Linear Elasticity with Intersecting Slide Surfaces ," LLNL technical report LLNL-JC-148529, 2002.

R. S. Tuminaro, C. Tong, J. N. Shadid, K. D. Devine, D. M. Day, " On a Multilevel Preconditioing Module for Unstructured Mesh Krylov Solver: Two-level Schwarz ," Comm. Num. Meth. Eng. , 18, 363-389, 2002.

R.S. Tuminaro and C. Tong, "Parallel Smoothed Aggregation Multigrid: Aggregation Strategies on Massively Parallel Machines," Proceedings of Supercomputing 2000 , November 2000.

C. Tong and R.S. Tuminaro, ML 2.0 Smoothed Aggregation User's Guide , Report SAND2001-8028, Sandia National Laboratories, 2000.

C. Tong and Q. Ye, " Finite Precision Analysis of the Biconjugate Gradient Algorithm for Nonsymmetric Linear Systems ", Mathematics of Computation, 69(232), pp. 1559-1575, 2000. Also available as Stanford SCCM Report SCCM-95-11.

C. Tong, J.C. Meza, and C.D. Moen, " Simulation of Equipment Design Optimization in Microelectronics Manufacturing ", Proceeding of the 30th Annual Simulation Symposium, 1997.

J.C. Meza, C.D. Moen, T.D. Plantenga, P.A. Spence, C. Tong, B.A. Hendrickson, R.W. Leland, and G.M. Reese, Parallel Optimization Methods for Agile Manufacturing, Sandia Report SAND97-8275, 1997.

C. Tong and Q. Ye, " A Linear System Solver Based on a Modified Krylov Subspace Method for Breakdown Recovery ", Numerical Algorithms , 1996.

C. Tong, "The Analysis and Implementation of a Parallel Object-Oriented Toolkit for the Iterative Solution of Partial Differential Equations ," Proceedings of High Performance Computing, Asia , Taipei (1995).

D.M. Butler, W.E. Mason, and C. Tong, "An object-Oriented Domain Analysis of Partial Differential Equations, " Proceedings of OON-SKI , from Rogue Wave Software, Corvalis, Oregon (1994).

C. Tong, "A Family of Quasi-Minimal Residual Methods for Nonsymmetric Linear Systems, " SIAM Journal on Scientific and Statistical Computing , 15(1), pp. 89-105, January 1994.

T.F. Chan, E. Gallopoulos, V. Simoncini, T. Szeto, and C. Tong, " A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems, " SIAM Journal on Scientific Computing , 15(2), (1994).

M.E. Colvin, C.L. Janssen, R.A. Whiteside, and C. Tong, " Parallel Direct SCF for Large-Scale Calculations, " Theoretica Chimica Acta , 84, pp. 301-314 (1993).

C. Tong, T.F. Chan, and J.C.C. Kuo, " Multilevel Filtering Preconditioners: Extensions to More General Elliptic Problems, " SIAM Journal on Scientific and Statistical Computing , 13(1), (1992).

C. Tong, A Comparative Study of Preconditioned Lanczos Methods for Nonsymmetric Linear Systems, Sandia Report SAND91-8240B (1991).

C. Tong and P.N. Swarztrauber, Massively Parallel Hypercube FFTs: CM-2 Implementation and Error Analysis of a Parallel Trigonometric Factor Generation Method, Sandia Report, SAND91-8500 (1991).

C. Tong, T.F. Chan, and J.C.C. Kuo, " A Domain Decomposition Preconditioner Based on a Change to the Multilevel Nodal Basis, " SIAM J. on Scientific and Statistical Computing , 12(67), (1991).

C. Tong and P.N. Swarztrauber, " Ordered Fast Fourier Transforms on a Massively Parallel Hypercube Multiprocessor, " J. Parallel and Distributed Computing, 12, pp. 50-59 (1991).

H.D. Cheng, and C.H. Tong, " Clustering Analyzer, " IEEE Trans. on Circuits and Systems , Vol. 38, No. 1, pp. 124-128, (1991).

J.C.C. Kuo, T.F. Chan, and C. Tong, " Multilevel Filtering Elliptic Preconditioners, " SIAM J. Matrix Analysis and Applications , 11(3), 1991.

H. D. Cheng, C. Tong, and Y. J. Lu, " VLSI Curve Detector ", Pattern Recognition , Vol. 23, No. 1/2, pp. 35-50 (1990).

T.F. Chan, J.C.C. Kuo, and C. Tong, " Parallel Elliptic Preconditioners: Fourier Analysis and Performance on the Connection Machine, " Computer Physics Communications, 53, pp. 237-252 (1989).

C. Tong, " The Preconditioned Conjugate Gradient Method on the Connection Machine, " International Journal of High Speed Computing, 2nd Issue: Scientific Applications of the Connection Machine, (1989). Also in Proceeding on the Scientific Application of the Connection Machine, Horst Simon, Ed., World Scientific Publishing Co., pp. 188-213 (1989).

C. Tong, H.D. Cheng, "VLSI Architecture for Curve Detection ," Proc. Comput. Eur. 87, , Hamburg (1987).

C. Tong and H. D. Cheng, "Clustering Analyzer for Pattern Recognition ," SPIE Vol. 845 Visual Communications and Image Processing II , pp. 350-360 (1987).

Unpublished Articles

C. Tong, Algebraic Multilevel Preconditioners for Nonsymmetric Systems based on Compatible Relaxation, 2003.

C. Tong, Preconditioned Krylov Subspace Methods for Time-dependent Incompressible Navier Stokes Equations, 2001.

C. Tong, The Mathematics of Algebraic Multigrid (AMG) Coarsening , 2000.

C. Tong, R.S. Tuminaro, K.D. Devine, and J.N. Shadid, Design and Implementation of A Parallel Multigrid Framework for Unstructured Finite Element Calculations , 1998.

C. Tong, DOOMSDACE : A Distributed Object-Oriented Software with Multiple Samplings for the Design and Analysis of Computer Experiments, 1997.

C. Tong, Improving Parallel Efficiency and Stability of the Conjugate Gradient Squared Algorithm on Massively Parallel Computers, 1997.

C. Tong and Q. Ye, A Comparative Analysis of Different Variations of the BICG Algorithm in Finite Precision, , 1995.

C. Tong, Analysis of Some Approximate Inverse Preconditioners for Sparse Linear Systems , 1994.

C. Tong, Parallel Implementation of a Fast Multipole-like Algorithm for N-body Problems, 1993.

C. Tong, Performance Analysis of a Multilevel Preconditioner on the Connection Machine, 1990.

Updated: 2011-04-26 15:55:33