Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
The method of fundamental solutions for linear diffusion-reaction equations
Mathematical and Computer Modelling: An International Journal
Preconditioning for radial basis functions with domain decomposition methods
Mathematical and Computer Modelling: An International Journal
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
| Hi-index | 31.45 |
The radial basis function (RBF) collocation techniques for the numerical solution of partial differential equation problems are increasingly popular in recent years thanks to their striking merits being inherently meshless, integration-free, and highly accurate. However, the RBF-based methods have markedly been limited to handle isotropic problems due to the use of the isotropic Euclidean distance. This paper makes the first attempt to use the geodesic distance with the RBF-based boundary knot method (BKM) to solve 2D and 3D anisotropic Helmholtz-type and convection-diffusion problems. This approach is mathematically simple and easy to implement, and spectral convergence is numerically observed for problems under complex-shaped boundary. Numerical results show that the BKM based on the geodesic distance can produce highly accurate solutions of anisotropic problems with a relatively small number of knots. This study provides a promising strategy for the RBF-based methods to effectively solve anisotropic problems.