On the Completeness of the Set of Radial Trefftz Functions Used by the BKM in the Solution of Viscoelasticity Problems

Abstract

The Boundary Knot Method (BKM) is a truly meshless, RBF-based method which has been used to solve many problems in mathematical physics and engineering, like the Helmholtz problem, plate vibration, Poisson, convection-diffusion, eigenanalysis in Acoustics, etc. In a recent work, the BKM has been applied to two-dimensional harmonic elasticity and viscoelasticity problems. In this paper, a new BKM representation is obtained by means of the Cauchy-Kovalevski-Somigliana solution of the displacements. The completeness of the BKM representations for elasticity and viscoelasticity problems is studied theoretically and numerically.