Current Research Interests

Numerical analysis
Partial differential equations
Meshfree method
Radial basis function
Adaptive greedy algorithm
Inverse problems

 

 

Selected Publications

1. On variable and random shape Gaussian interpolations.
   S.N. Chiu, L. Ling and M. McCourt.
   Applied Mathematics and Computation. 377: 125159. 2020.
   
   
2. Extrinsic Meshless Collocation Methods for PDEs on Manifolds.
   M. Chen and L. Ling .
   SIAM Journal on Numerical Analysis. 58(2): 988-1007. 2020.
   
   
3. Kernel-based meshless collocation methods for solving coupled bulk-surface PDEs.
   M. Chen and L. Ling .
   Journal of Scientific Computing. 81(1): 375-391. 2019.
   
   
4. Discrete least-squares radial basis functions approximations.
   S. Li, L. Ling and K.C. Cheung.
   Applied Mathematics and Computation. 355: 542-552. 2019.
   
   
5. A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces.
   A. Petras, L. Ling, C. Piret and S. Ruuth.
   Journal of Computational Physics. 381: 146-161. 2019.
   
   
6. Doubly stochastic radial basis function methods.
   F. L. Yang, L. Yan and L. Ling.
   Journal of Computational Physics. 363: 87-97. 2018.
   
   
7. On meshfree numerical differentiation.
   L. Ling and Q. Ye.
   Analysis and Applications. 16(5): 717-739. 2018.
   
   
8. Fully adaptive kernel-based methods.
   L. Ling and S.N. Chiu.
   International Journal for Numerical Methods in Engineering. 114(4): 454-467. 2018.
   
   
9. A kernel-based embedding method and convergence analysis for surfaces PDEs.
   K.C. Cheung and L. Ling.
   SIAM Journal on Scientific Computing. 40(1), A266-A287. 2018.
   
   
10. H²-convergence of least-squares kernel collocation methods.
    K.C. Cheung, L. Ling and R. Schaback.
    SIAM Journal on Numerical Analysis. 56(1): 614-633. 2018.
    
    
11. A fast block-greedy algorithm for quasi-optimal meshless trial subspace selection.
    L. Ling .
    SIAM Journal on Scientific Computing. 38(2): A1224–A1250. 2016.
    
    
12. Numerical Caputo differentiation by radial basis functions.
    M. Li, Y. Wang, and L. Ling.
    Journal of Scientific Computing. 62(1):300–315. 2015.
    
    
13. Numerical simulations of 2D fractional subdiffusion problems.
    H. Brunner, L. Ling and M. Yamamoto .
    Journal of Computational Physics. 229(18):6613-6622. 2010.
    
    
14. Stable and convergent unsymmetric meshless collocation methods.
    L. Ling and R. Schaback.
    SIAM Journal on Numerical Analysis. 46(3):1097-1115. 2008.
    
    
15. Applicability of the method of fundamental solutions.
    T. W. Drombosky, A. L. Meyer and L. Ling .
    Engineering Analysis with Boundary Elements. 33(5): 637-643. 2009.