A new radial basis integration method applied to the boundary element analysis of 2D scalar wave equations

Abstract

A new integration method named the Radial Basis Integration Method (RBIM) that include the Kriging Integration Method (KIM) Narváez and Useche (2020) as a particular case and performs boundary only offline precomputations for the creation of a meshless quadrature was developed for its application in boundary elements. Herein, as in DR-BEM, the inertial term is approximated using radial basis functions, however, its particular solution is not needed. The quadrature is now obtained in a simpler way than in KIM, because the evaluations of domain integrals necessary to compute the weights of quadrature points, is done transforming those to the boundary instead of using the Cartesian Transformation Method. Using RBIM, weakly singular domain integrals may be computed with good accuracy over complex domains. The results obtained in some scalar wave propagation problems using both Houbolt-α and Newmark-α time marching methods show that this procedure can be even more accurate than other used in BEM analysis.