TY - JOUR
T1 - Dimension-splitting data points redistribution for meshless approximation
AU - Kwok, Ting On
AU - Ling, Leevan
N1 - This project was supported by the CERG Grant of Hong Kong Research Grant Council and the FRG Grant of Hong Kong Baptist University.
PY - 2010/12/1
Y1 - 2010/12/1
N2 - To better approximate nearly singular functions with meshless methods, we propose a data points redistribution method extended from the well-known one-dimensional equidistribution principle. With properly distributed data points, nearly singular functions can be well approximated by linear combinations of global radial basis functions. The proposed method is coupled with an adaptive trial subspace selection algorithm in order to reduce computational cost. In our numerical examples, clear exponential convergence (with respect to the numbers of data points) can be observed.
AB - To better approximate nearly singular functions with meshless methods, we propose a data points redistribution method extended from the well-known one-dimensional equidistribution principle. With properly distributed data points, nearly singular functions can be well approximated by linear combinations of global radial basis functions. The proposed method is coupled with an adaptive trial subspace selection algorithm in order to reduce computational cost. In our numerical examples, clear exponential convergence (with respect to the numbers of data points) can be observed.
KW - Adaptive greedy algorithm
KW - Dual reciprocity method
KW - Exponential convergence
KW - Meshless interpolation
KW - Radial basis function
UR - http://www.scopus.com/inward/record.url?scp=77957899734&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2010.06.026
DO - 10.1016/j.cam.2010.06.026
M3 - Journal article
AN - SCOPUS:77957899734
SN - 0377-0427
VL - 235
SP - 736
EP - 746
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 3
ER -