Department of Mathematics
Solving moving-boundary problems with the wavelet adaptive radial basis functions method
Moving boundaries are associated with the time-dependent problems where the momentary position of boundaries needs to be determined as a function of time. The level set method has become an effective tool for tracking, modeling and simulating the motion of free boundaries in fluid mechanics, computer animation and image processing. This work extends our earlier work on solving moving boundary problems with adaptive meshless methods. In particular, the objective of this paper is to investigate numerical performance the radial basis functions (RBFs) methods, with compactly supported basis and with global basis, coupled with a wavelet node refinement technique and a greedy trial space selection technique. Numerical simulations are provided to verify the effectiveness and robustness of RBFs methods with different adaptive techniques. © 2013 Elsevier Ltd.
Adaptive greedy algorithm, Compactly supported RBFs, Global RBFs, Level set method, Moving-boundary problems, Partial differential equations, Wavelet method
Source Publication Title
Computers and Fluids
Link to Publisher's Edition
Vrankar, Leopold, Nicolas Ali Libre, Leevan Ling, Goran Turk, and Franc Runovc. "Solving moving-boundary problems with the wavelet adaptive radial basis functions method." Computers and Fluids 86 (2013): 37-44.