An improvement for singularity in 2-D corrective smoothed particle method with application to Poisson problem

The corrective smoothed particle method (CSPM) is an improvement to the conventional smoothed particle hydrodynamics (SPH) method. It overcomes the problems of tensile instability and boundary deficiency in SPH. As a specially designed numerical method for time-dependent problems, it has been applied to transient heat conduction and structural dynamics problems. In this paper the 2-D CSPM is used to solve time-independent problems, where an extra numerical inversion needs special attention. To permit an invertible matrix for small smoothing length and hence enhance the computational efficiency, an improvement is proposed to the original CSPM. The accuracy and efficiency of the CSPM and the proposed modification is demonstrated by the numerical example.