Accurately Solving The Poisson Equation By Combining Multiscale Radial Basis Functions And Gaussian Quadrature
Free (open access)
Z Liu & J G Korvnik
We propose a method combining multiscale radial basis functions and Gaussian quadrature that greatly improves the numerical solution accuracy when applied to the Poisson equation defined over arbitrary-shaped domains. Instead of directly using the collocation points as interpolation points, the Gaussian quadrature points are used as the interpolation points in the discretised domain. In combining the adaptive positioning of multiscale Wendland radial base functions and the symmetric collocation method, our numerical examples demonstrate that this method improves the accuracy of solution significantly, while the computational cost is no big increase and of the same order when compared with the "standard" symmetric method.