We obtain analytical formulas for the computation of integrals (moments) of all the most common Radial Basis Functions (usually shortened as RBFs) on polygonal regions that may be nonconvex or even multiply connected. With RBFs of finite regularity, such as Thin-Plate Splines, Wendland functions and Radial Powers, our Matlab codes, based on standard linear solvers for the corresponding moment matching systems, provide cubature rules that are reasonably accurate and numerically stable.
RBF Moment computation and meshless cubature on general polygonal regions
Sommariva A.
;Vianello M.
2021
Abstract
We obtain analytical formulas for the computation of integrals (moments) of all the most common Radial Basis Functions (usually shortened as RBFs) on polygonal regions that may be nonconvex or even multiply connected. With RBFs of finite regularity, such as Thin-Plate Splines, Wendland functions and Radial Powers, our Matlab codes, based on standard linear solvers for the corresponding moment matching systems, provide cubature rules that are reasonably accurate and numerically stable.
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