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.