Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Kernel-Based Meshless Methods for Solving PDEs

by
Prof. Robert Schaback
University of Gottingen
Germany

Date: March 12, 2008 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: Kernels arise in many areas of Mathematics, and they turned out to be practically useful for a large number of applications ranging from Machine Learning to PDE solving. The talk will provide the mathematical background of kernel applications, i.e., the approximation theory of spaces spanned by “translates” of kernels. After presentation of the basic facts concerning positive definite kernels and their use for handling multivariate functions, the talk will focus on translates of kernels as trial or test functions for solving partial differential equations. A mathematical framework is provided that allows convergence proofs of methods like Kansa’s unsymmetric collocation or Atluri’s Meshless Petrov-Galerkin (MLPG) technique. The framework is based on certain a-priori “sampling” and “stability” inequalities, which are of general interest outside of kernel techniques. Additional examples will show how specially designed new kernels lead to new numerical methods.              

** All interested are welcome **

For enquiry: 2788-9816