  The boundary knot method (BKM) is a recent boundary-type radial basis
function (RBF) collocation scheme for general PDEs. Like the method of
fundamental solution (MFS), the RBF is employed to approximate the
inhomogeneous terms via the dual reciprocity principle. Unlike the MFS, the
method uses a nonsingular general solution instead of a singular fundamental
solution to evaluate the homogeneous solution so as to circumvent the
controversial artificial boundary outside the physical domain. The BKM is
meshfree, superconvergent, integration free, very easy to learn and program.
The original BKM, however, loses symmetricity in the presense of mixed
boundary. In this study, by analogy with Hermite RBF interpolation, we
developed a symmetric BKM scheme. The accuracy and efficiency of the symmetric
BKM are also numerically validated in some 2D and 3D Helmholtz and diffusion
reaction problems under complicated geometries.
