New investigations into the BKM for inverse problems of Helmholtz equation

The boundary knot method (BKM) is an inherent boundary-type meshless collocation method for partial differential equations (PDEs). Using non-singular general solutions, numerical solutions of the PDE can be obtained based on the boundary points. In this paper, we investigate the applications of the BKM to solve Helmholtz problems involving various boundary conditions. We use the effective condition number to investigate the ill-conditioned interpolation system. Different from previous investigations, numerical results in this paper reveal that the BKM is promising in dealing with Helmholtz problems under only partially accessible boundary conditions.