TY - JOUR
T1 - A new class of oscillatory radial basis functions
AU - Fornberg, B.
AU - Larsson, E.
AU - Wright, G.
PY - 2006/4
Y1 - 2006/4
N2 - Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only nonoscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as a special case) leads to nonsingular interpolants with intriguing features especially as they are scaled to become increasingly flat. This flat limit is important in that it generalizes traditional spectral methods to completely general node layouts. Interpolants based on the new radial functions appear immune to many or possibly all cases of divergence that in this limit can arise with other standard types of radial functions (such as multiquadrics and inverse multiquadratics).
AB - Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only nonoscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as a special case) leads to nonsingular interpolants with intriguing features especially as they are scaled to become increasingly flat. This flat limit is important in that it generalizes traditional spectral methods to completely general node layouts. Interpolants based on the new radial functions appear immune to many or possibly all cases of divergence that in this limit can arise with other standard types of radial functions (such as multiquadrics and inverse multiquadratics).
KW - Bessel functions
KW - Multivariate interpolation
KW - Radial basis functions
KW - RBF
UR - http://www.scopus.com/inward/record.url?scp=33745894671&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2006.04.004
DO - 10.1016/j.camwa.2006.04.004
M3 - Article
AN - SCOPUS:33745894671
SN - 0898-1221
VL - 51
SP - 1209
EP - 1222
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 8 SPEC. ISS.
ER -