TY  - EJOU
AU  - Bai, Ziqiang 
AU  - Qu, Wenzhen 
AU  - Wu, Guanghua 

TI  - An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2024
VL  - 138
IS  - 3
SN  - 1526-1506

AB  - In the past decade, notable progress has been achieved in the development of the generalized finite difference method (GFDM). The underlying principle of GFDM involves dividing the domain into multiple sub-domains. Within each sub-domain, explicit formulas for the necessary partial derivatives of the partial differential equations (PDEs) can be obtained through the application of Taylor series expansion and moving-least square approximation methods. Consequently, the method generates a sparse coefficient matrix, exhibiting a banded structure, making it highly advantageous for large-scale engineering computations. In this study, we present the application of the GFDM to numerically solve inverse Cauchy problems in two- and three-dimensional piezoelectric structures. Through our preliminary numerical experiments, we demonstrate that the proposed GFDM approach shows great promise for accurately simulating coupled electroelastic equations in inverse problems, even with 3% errors added to the input data.
KW  - Generalized finite difference method; meshless method; inverse Cauchy problems; piezoelectric problems; electroelastic analysis

DO  - 10.32604/cmes.2023.031474