Simulation of Antiplane Piezoelectricity Problems with Multiple Inclusions by the Meshless Method of Fundamental Solution with the LOOCV Algorithm for Determining Sources

This paper provides a high-accuracy and efficient method for addressing antiplane piezoelectricity problems with multiple inclusions. The method of fundamental solutions is a boundary-type meshless method that applies the linear combination of fundamental solutions as approximate solutions with the collocation method for determining the unknowns. To avoid the singularity of fundamental solutions, sources are placed away from the physical boundary. The leave-one-out cross-validation algorithm is employed to identify the optimal source placements to mitigate the influence of this singularity on numerical results. Numerical results of the stress concentration and electric field concentration at the interface between circular and elliptic inclusions and matrix are studied and compared well with references. Furthermore, the stability of the method is verified. Perturbations are added to the boundary conditions. Accuracy on the order of 10 −11 is obtained without noise. After adding the disturbance, the calculation accuracy is the same order of magnitude as the disturbance.