Xiaozhong Jin1, Gang Li2, N. R. Aluru3
CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.4, pp. 447-462, 2001, DOI:10.3970/cmes.2001.002.447
Abstract Meshless methods using least-squares approximations and kernel approximations are based on non-shifted and shifted polynomial basis, respectively. We show that, mathematically, the shifted and non-shifted polynomial basis give rise to identical interpolation functions when the nodal volumes are set to unity in kernel approximations. This result indicates that mathematically the least-squares and kernel approximations are equivalent. However, for large point distributions or for higher-order polynomial basis the numerical errors with a non-shifted approach grow quickly compared to a shifted approach, resulting in violation of consistency conditions. Hence, a shifted polynomial basis is better suited from More >
Login
Register
