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".
RBF surface reconstruction |
StudentA StudentB (to be appeared)
Assignment 2: RBF collocation method | StudentA
Assignment 3: The method of fundamental solutions (MFS) | StudentA
Assignment 4: The MFS+MPS
Assignment 5: The method of approximate particular solutions (MAPS)
Assignment 6: The localized
method of approximate particular solutions (LMAPS) | StudentA StudentB StudentC
The contents of the course include the following topics:
1. Radial basis functions for surface reconstruction
2. The method of fundamental
3. The method of approximate
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
of a research monograph entitled “Scientific
with Radial Basis Functions” and the
following book chapter and papers.
Golberg and C.S. Chen, The method
of fundamental solutions for potential, Helmholtz and diffusion
in Boundary Integral Methods - Numerical and Mathematical Aspects, ed.
M.A. Golberg, Computational Mechanics Publications, 1998, pp.103-176.
- C.S. Chen, Y.C. Hon, R.S. Schaback, Radial Basis Functions
Computation, Department of Mathematics, University of Southern
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)
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)
Chen, C.M. Fan, P.H. Wen, The Method
of Particular Solutions
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.