The improved boundary knot method with fictitious points for solving high-order Helmholtz-type PDEs

Abstract

An improved boundary knot method (IBKM) is proposed to enhance the performance of BKM in solving homogeneous high-order Helmholtz-type partial differential equations. Compared with the classical BKM where the sources are always placed on the physical boundary as collocation points, the new sources named fictitious points are now placed on multi-layer extended pseudo boundaries. This modification leads to higher accuracy without the loss of efficiency. Numerical examples are presented to demonstrate the superiority of the IBKM.