Symmetric boundary knot method

Abstract

The boundary knot method (BKM) is a recent boundary-type radial basis function

Some variants of the method of fundamental solutions: regularization using radial and nearly radial basis functions

“…The optimal value of is inversely proportional to the distance of neighboring boundary points. The Laplace equation can be regularized also in other ways using the sixth-order operator ∆(I − ∆/ 2 ) 2 or even the eighth-order operator ∆(I − ∆/ 2 ) 3 . As can be easily checked, the associated fundamental solutions have the form…”

“…(Recall that the domain Ω is assumed to be strictly convex, therefore both E and ∂E /∂ are smooth function over Ω.) The situation exhibits some similarities to the boundary knot method (Chen et al [3,4]), which is based also on nonsingular solutions of the original equation. However, in contrast to the boundary knot method, the above approach is based on non-radial basis functions (17).…”

“…A similar technique is the singular boundary method (SBM, see [11,12]) which is based on the concept of origin intensity factors, thus avoiding the direct computation of singular terms. A completely different method is the use of nonsingular solutions instead of the fundamental solutions (boundary knot method, see Chen et al [3,4]), where the problem of singularities does not appear at all. Unfortunately, this leads to extremely ill-conditioned linear systems again.…”

The Methods of External Excitation for Analysis of Arbitrarily-Shaped Hollow Conducting Waveguides

“…This admits of applying very effective meshless numerical techniques to solve (3), (4): the MFS, the boundary knot method [35], the boundary integral method [36].…”

Mathematical analysis and treatment for the true and spurious eigenequations of circular plates by the meshless method using radial basis function

“…The initial idea of a meshless method dates back to the smooth particle hydrodynamics (SPH) method for modeling astrophysical phenomena (Gingold and Maraghan, 1977). Basically, the meshless method is classified among the domain-based methods, including the element-free Galerkin method (Belystcho et al, 1994), the reproducing kernel method (Liu et al, 1995), and boundary-based methods including the boundary node method (Mukherjee and Mukherjee, 1997), the meshless local Petrov-Galerkin approach (Atluri and Zhu, 1998), the local boundary integral equation method (Sladek et al, 2000), the RBF approach (Chen, 2000b;Chen and Tanaka, 2000a;2000b;Golberg et al, 2000), and the boundary knot method (BKM) (Chen, 2000c;Hon and Chen, 2003).…”