A Consideration on accuracy of the approximate differentiation in the particle method and multidimensional moving least squares method with constraint

Abstract

Accuracy of the approximate differentiation in the SPH method and the MPS method is discussed, and we show that accuracy decreasing on a boundary of analytical area in SPH method is due to the original approximate differentiation formula. In order to solve the accuracy problem of the traditional particle methods, in this paper, we propose the multidimensional moving least squares method with constraint conditions. The proposed method has physically meaningful unknown parameters, for example rotations, strains and curvatures. Therefore, by implementing this method into particle methods, we can directly obtain the physical values as particle values. Through some numerical examples, we directly show an accuracy problem of the traditional particle methods and the effectiveness of the proposed method.