A POD-Based Fast Algorithm for the Nonlocal Unsteady Problems

Abstract

A fast algorithm for the nonlocal unsteady problems was proposed, which can be employed in the numerical simulation of nonlocal diffusion and peridynamic. The surrogate model constructed by the proper orthogonal decomposition (POD) speeds up the process of solving equations by reducing the order of linear equations. Then, the accuracy and efficiency of the proposed algorithm was verified by numerical experiments. The results showed that this approach ensures accuracy while reduces the computational burden of the nonlocal model.