Conference Publications

  1. Liu X., Liu G. R., Tai K. & Lam K. Y., “Radial Basis Point Interpolation Collocation Method for 2-D Solid Problem”, Advances in Meshfree and XFEM Methods, The 2nd International Conference on Structural Stability and Dynamics, Singapore, 16-18 December 2002.

  2. Liu X., Liu G. R., Tai K. & Lam K. Y., “The Solution for Convection-Diffusion Equations using the Quasi-Interpolation Scheme with Local Polynomial Reproduction Based on Moving Least Squares”, Advances in Meshfree and X-FEM Method, The 2nd International Conference on Structural Stability and Dynamics, Singapore, 16-18 December 2002.

  3. Liu X., Liu G. R., Tai K. & Lam K. Y., “Collocation-Based Meshless Method for the Solution of Transcient Convective-Difussion Equation”, presented at The 1st EMS-SMAI-SMF Joint Conference Applied Mathematics and Applications of Mathematics (AMAM 2003), Nice, France, 10-13 February 2003.

  4. Liu G. R., “Meshfree Methods, Moving Beyond the Finite Element Method”, presented at 8th International Fracture Mechanics Summer School, Society for Structural Integrity and Life, Belgrade, Yugoslavia, 23- 27 June 2003.

  5. Liu G. R., Gu Y. T. & Wu Y. L., “A Novel Meshfree Weak-Strong (MWS) Form Method”, presented at International Workshop on Meshfree Methods (IWMM 03), Lisbon, Portugal, 21-23 July 2003.

  6. Liu G. R., Gu Y. T. & Wu Y. L., “A Novel Meshfree Weak-Strong (MWS) Form Method for Mechanics Problem”, presented at Global Chinese Workshop on Boundary Element and Meshfree Methods, Qinhuangdao, China, 4-6 September 2003.

  7. Liu G. R. & Gu Y. T., “The Meshfree Weak-Strong (MWS) Form Method for Solid and Fluid Mechanics Problems”, presented at 2nd International Workshop on Meshfree Methods for PDE, Bonn, Germany, 15-17
    September 2003.

  8. Liu G. R., “Meshfree Methods: Moving Beyond the Finite Element Method”, presented at Japan Society of Mechanical Engineers (JSME) 16th Computational Mechanics Conference, Kobe, Japan, 22-24 November 2003.

  9. Liu X., Liu G. R., Tai K., Gu Y. T. & Lam K. Y., “Thin Plate Spline Radial Point Interpolation Collocation Method (TPS-RPICM) for the Solution of Poisson- Boltzmann Equation”, presented at the 1st Asia Pacific International Conference on Computational Methods in Engineering 2003 (ICOME 2003), Sapporo City, Japan, 5-7 November 2003.

  10. Liu X., Liu G. R., Tai K., Gu Y. T. & Lam K. Y., “Polynomial Point Interpolation Collocation Method for the Solution of Partial Diferential Equations”, Computational Mathematics (AiCM) (accepted).

Micro- and Nano-Structure Simulation

Journal Publications

  1. Cai J. & Wang J.-S., “Reconstruction of Si(001) and Adsorption of Si Adatoms and Ad-Dimers On The Surface: Many Body Potential Calculations”, Physical Review B, Vol. 64, 035402 (2001).

  2. Cai J. & Wang J.-S., “Reconstruction of Si(001): A Comparison Study of Many Body Potential Calculations”, Physical Status Solidi B - Basic Research, Vol. 223, pp. 773 (2001).

  3. Cai J. & Wang J.-S., “Adsorption and Difussion of Si on the Si(001): An Empherical Potential Calculation”, International Journal of Modern Physics B, Vol. 16, No. 4, pp. 621-629 (2002).

  4. Cai J. & Wang J.-S., “Friction between a Ge Tip and the (001)-2x1 Surface: A Molecular-Dynamics Simulation”, Physical Review B, Vol. 64, 113313 (2001).

  5. Cai J. & Wang J.-S., “Molecular Dynamics Study of the Friction Properties for a Ge Tip-Surface System”, Surface Review Letters, Vol. 8, pp. 581 (2001).

  6. Cai J. & Wang J.-S., “Friction Between Si Tip and (001)-2x1 Surface: A Molecular Dynamics Simulation”, Computer Physics Communications, Vol. 147, pp. 145 (2002).

  7. Cai J. & Wang J.-S., “Modeling Generalized Stacking Fault in Au using Tight-Binding Potential Combined with a Simulated Annealing Method”, European Physical Journal B, Vol. 25, pp. 45 (2002).

  8. Cai J. & Wang J.-S., “Energy And Structure of Stacking Fault of Ag from a Tight Binding Method Calculation”, Modeling and Simulation in Materials Science and Engineering, Vol. 10, pp. 469 (2002).

  9. Wang J.-S. & Li B., “Intriguing Heat Conduction of a Chain with Transverse
    Motions”, Physical Review, Vol. 92, 074302 (2004).

Conference Publication
J. Cai & Wang J.-S., “Modeling Generalized Stacking Fault in Au using Tight- Binding Potential Combined with a Simulated Annealing Method”, presented at The 2nd Singapore-MIT Alliance Annual Symposium, Singapore, 14-16 January 2002.


Nonlinear Optimization

Journal Publications

  1. Chen X. & Sun J., “Global Convergence of a Two-Parameter Family of Conjugate Gradient Methods Without Line Search”, Journal of Computational and Applied Mathematics, Vol. 146, pp. 37-45 (2002).

  2. Han J., Sun J. & Sun W., “Global Convergence of Nonmonotone Descent Methods for Unconstrained Optimization Problems”, Journal of Computational and Applied Mathematics, Vol. 146, pp. 89-98 (2002).

Numerical Simulation on Shock Waves in Bio-MEMS and Biological Systems

Journal Publications

  1. Liu T. G., Khoo B. C. & Yeo K. S., “The Simulation of Compressible Multimedium Flow. Part I: A New Methodology with Test Applications to ID Gas-Gas and Gas-Water Cases”, Computers & Fluids, Vol. 30, pp. 291- 314 (2001).

  2. Liu T. G., Khoo B. C. & Yeo K. S., “The Simulation of Compressible Multimedium Flow. Part II: Applications to 2D Underwater Shock Refraction”, Computers & Fluids, Vol. 30, pp. 315-337 (2001).

  3. Liu T. G., Khoo B. C., Yeo K. S. & Wang C., “Underwater Shock-Free Surface- Structure Interaction”, International Journal for Numerical Method in Engineering, Vol. 58, pp. 609-630 (2003).

  4. Liu T. G., Khoo B. C. & Yeo K. S., “Ghost Fluid Method for Strong Shock Impacting on Material Interface”, Journal of Computational Physics, Vol. 190, pp. 651-681 (2003).

  5. Hu X. & Khoo B. C., “Kinetic Energy for Low Internal Energy Flows”, Journal of Computational Physics, Vol. 193, pp. 243-259 (2004).

Semidefinite Programming and Matrix Equations

Journal Publications

  1. Sun D. & Sun J., “Semismooth Matrix Valued Functions”, Mathematics of Operations Research, Vol. 27, pp. 150-169 (2002).

  2. Toh K., Zhao G. & Sun J., “A Multiple-Cut Analytic Cutting Plane Method for Semidefinite Feasibility Problems”, SIAM Journal on Optimization, Vol. 12, pp. 1126-1146 (2002).

  3. Sun J., Toh K. & Zhao G., “An Analytic Cutting Plane Method for Semidefinite Feasibility Problems”, Mathematics of Operations Research, Vol. 27, pp. 332-346 (2002).

  4. Sun D. & Sun J. “Strong emismoothness of Eigenvalues of Symmetric Matrices and Its Application in Inverse Eigenvalue Problems”, SIAM Journal on Numerical Analysis, Vol. 40, pp. 2352-2367 (2003).

  5. Pang J.-S., Sun D. & Sun J., Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems”, Mathematics of Operations Research, Vol. 28, pp. 39-63 (2003).

  6. Sun J., Sun D. & Qi L., “Quadratic Convergence of a Squared Smoothing Newton Method for Nonsmooth Matrix equations and its Applications in Semidefinite Optimization Problems”, SIAM Journal on Optimization, Vol. 14, pp. 783-806 (2004).

  7. Sun J., “Semidefinite Optimization and Semismooth Newton Methods”, Operations Research Transactions, Vol. 8, pp 41-52 (2004).

  8. Zhou G. & Toh K. C., “Polynomiality of an Inexact Infeasible Interior Point Algorithm for Semidefinite Programme”, Mathematical Programming, Vol. 99, pp, 261-282 (2004).
  9. Sun D. & Sun J., “Nonsmooth Matrix Valued Functions Defined by Singular Values”, Mathematical Programming (accepted).

  10. Sun J., Yang X. & Chen X., “Quadratic Cost Flow and the Conjugate Gradient”, Operations Research (accepted).

  11. Liu X. & Sun J., “Global Convergence Analysis of Line Search Interior Point Methods for Nonlinear Programming without Regularity Assumptions”, Journal of Optimization Theory and Applications (accepted).

  12. Liu X. & Sun J., “A Robust Primal-Dual Interior Point Algorithm for Nonlinear Programs”, SIAM Journal on Optimization (accepted).

  13. Toh K. C., “Solving Large Scale Semidefinite Programs via an Iterative Solver on the Augmented Systems”, SIAM Journal on Optimization (accepted)
     
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