Generalized Finite Integration Method for Nonlinear Peridynamic Model

Based on the recent development in generalized finite integration method (GFIM) for numerical approximation of stiff partial differential equations, we attempt to develop in this proposed project an efficient and effective numerical algorithm for solving nonlinear wave equation arising in a peridynamic formulation in continuum mechanics. The primary advantage of GFIM lies in its potential for approximating high dimensional problems using uniform or non-uniform discretization. The resultant blocked lower diagonal matrix gives another advantage of the GFIM in achieving a highly accurate and stable approximation of the solution. Specifically, we willapproximate the time variable using both implicit-explicit (IMEX) and time-splitting (TS) schemes and the spatial variable using GFIM. The computational efficiency of the numerical algorithm will further be improved by combining the GFIM with techniques of adaptive point allocation and unconditional stable integration schemes.