Atkinson developed a strategy which splits solution of a PDE system into
homogeneous and particular solutions, where the former have to satisfy the
boundary and governing equation, while the latter only need to satisfy the
governing equation without concerning geometry. Since the particular solution
can be solved irrespective of boundary shape, we can use a readily available
fast Fourier or orthogonal polynomial technique O(NlogN) to evaluate it in a
regular box or sphere surrounding physical domain. The distinction of this
study is that we approximate homogeneous solution with nonsingular general
solution RBF as in the boundary knot method. The collocation method using
general solution RBF has very high accuracy and spectral convergent speed and
is a simple, truly meshfree approach for any complicated geometry. More
importantly, the use of nonsingular general solution avoids the controversial
artificial boundary in the method of fundamental solution due to the
singularity of fundamental solution.Comment: Comments to [email protected]
