計算量を削減したRBF離散化手法の性能評価

Abstract

A sparse interpolation matrix is constructed as the differentiation matrix using Gaussian radial basis functions (RBF). Error convergence and eigenvalue stability analysis are investigated in a test case for shallow water models (SWM) with a local nonlinear zonal geostrophic flow. The convergence study shows that the SWM made with the sparse interpolation matrix is more accurate than made with the RBF-FD (finite-difference) method. The former model is more stable than the latter because the eigenvalues of the former model lie more closely along by the imaginary axis than those of the latter.