TY - EJOU
AU - Nie, Y.F.
AU - Atluri, S.N.
AU - Zuo, C.W.
TI - The Optimal Radius of the Support of Radial Weights Used in Moving Least Squares Approximation
T2 - Computer Modeling in Engineering \& Sciences
PY - 2006
VL - 12
IS - 2
SN - 1526-1506
AB - Owing to the meshless and local characteristics, moving least squares (MLS) methods have been used extensively to approximate the unknown function of partial differential equation initial boundary value problem. In this paper, based on matrix analysis, a sufficient and necessary condition for the existence of inverse of coefficient matrix used in MLS methods is developed firstly. Then in the light of approximate theory, a practical mathematics model is posed to obtain the optimal radius of support of radial weights used in MLS methods. As an example, while uniform distributed particles and the 4^{th} order spline weight function are adopted in MLS method in two dimension domain and two kinds of norms are used to measure error, optimal results for linear and quadratic basis are gained. Finally, the test data verify that the optimal values are correct. The research idea can be used in 3-dimension problems too.
KW - MLS methods
KW - Radius of support
KW - Scaling
KW - Sobolev norm
KW - Mathematics model
KW - Matrix analysis
KW - Approximate theory
DO - 10.3970/cmes.2006.012.137