This webpage contains the selected work of students for the course I taugh in the Department of Civil Engineering at National Taiwan University during my sabbatical leave in fall 2011. The title of the course is "Meshless Methods for Scientific Computing".

Assignment 1: RBF surface reconstruction   |    StudentA  StudentB  (to be appeared)
Assignment 2:
RBF collocation method  |   StudentA   StudentB
Assignment 3:
The method of fundamental solutions (MFS)  |  StudentA  StudentB  StudentC
Assignment 4: The MFS+MPS |
StudentA  StudentB  StudentC
Assignment 5:
The method of approximate particular solutions (MAPS)  |  StudentA  StudentB
Assignment 6: The localized method of approximate particular solutions (LMAPS)  |
StudentA   StudentB  StudentC
Final Project
StudentA (Presentation)  |   StudentB (Powerpoint)

The contents of the course include the following topics:

1. Radial basis functions for surface reconstruction
2. The method of fundamental solutions
3. The method of approximate particular solutions
4. The localized method of particular solutions
4. Numerical solutions for general elliptic partial differential equations.

The materials of the course are based on the manuscript of a research monograph entitled “Scientific Computing with Radial Basis Functions” and the following book chapter and papers.

• M.A. Golberg and C.S. Chen, The method of fundamental solutions for potential, Helmholtz and diffusion problems, in Boundary Integral Methods - Numerical and Mathematical Aspects, ed. M.A. Golberg, Computational Mechanics Publications, 1998, pp.103-176.  (PDF file  894K)
• C.S. Chen, Y.C. Hon, R.S. Schaback, Radial Basis Functions with Scientific Computation, Department of Mathematics, University of Southern Mississippi, 2010.
• P.H. Wen, C.S. Chen, The method of particular solution for solving scalar wave equations,  International Journal for Numerical Methods in Biomedical Engineering, 26, 1878-1889, 2010. (PDF file)
• C.S. Chen, C.M. Fan, P.H. Wen, The Method of Particular Solutions for Solving Certain Partial Differential Equations, Numerical Methods for Partial Differential Equations, 28, 506-522, 2012.  (PDF file)
• C.S. Chen, C.M. Fan, P.H. Wen,  The Method of Particular Solutions for Solving Elliptic Problems with Variable Coefficients, Journal of Computational Methods, 8, 545-559, 2011. (PDF file)
• Greg Fasshauer,  Meshfree Approximation Methods with MATLAB, Interdisciplinary Mathematical Sciences - Vol. 6, World Scientific Publishers, Singapore, 2007.