A specified improved algorithm for Finite Particle Method and its application to wave propagation

Finite Particle Method (FPM) is a significant improvement to the traditional SPH method, which can greatly improve the computational accuracy for boundary particles. However, in the iteration process, long computing time and potential numerical instability are the key factors restricting the application of FPM. By conducting matrix decomposition and structural analysis on the basic equations of FPM, a Specified FPM method (SFPM) is proposed, which can not only maintain the high computational accuracy of FPM for boundary particles, but also avoid the restriction on the invertibility of the coefficient matrix in traditional FPM and greatly reduce the computing time. Finally, SFPM method is applied to the one-dimensional stress wave propagation problem, and the ideal simulation results show that SFPM is an effective improvement for traditional FPM.