Subdomain collocation method for multilayered piezoelectric material

Point collocation based on radial basis function approximation is one of the main methods used in meshless method. Because of the simplicity implementation and exponential convergence, it has been widely used in solving partial differential equations. In general, the problem domain has the same kind of material (uniformity). Thus, for a variety of material combination problems, the material discontinuity needs special treatment. Because the piezoelectric structures usually consists of piezoelectric materials and substrate materials, leading to different material properties, which will destroy the continuity in the problem domain between the material layers when solving the multilayered piezoelectric problem. Thus, by the use of smooth and global radial basis function, there will be difficult to solve this kind of problem. In this paper, the problem domain was divided into some subdomains based on the heterogeneity of material property. A subdomain collocation method is presented to solve the multilayered piezoelectric problem using the fully-coupled approach. The continuity and compatibility conditions of the stress and electrical are imposed on the interface. The accuracy and stability of the numerical solution are enhanced. Numerical experiments provided the accuracy and efficiency of the subdomain collocation method.