A Projection Method Based on Discrete Normalized Dynamical System for Computing C-eigenpairs

Authors：Cui, Lu-Bin; Yao, Jia-Le; Yuan, Jin-Yun^*

Source：Journal of Optimization Theory and Applications, 2024, 200(2): 768-793.

DOI：10.1007/s10957-023-02341-x

• Piezoelectric effect
• C-eigenvalue
• Dynamical system
• Projection method

The largest C-eigenvalue of piezoelectric tensors determines the highest piezoelectric coupling constant, which reflects the coupling between the elastic and dielectric properties of crystal. Here, a projection method based on discrete normalized dynamical system (PDND) is established for computing the largest C-eigenvalue. Theoretical analysis of the convergence for PDND algorithm is given. In numerical experiments, the longitudinal piezoelectric modulus and the unit uniaxial direction that the extreme piezoelectric effect along took place of different piezoelectric materials are given to display the physical meaning of the C-eigenvalues and eigenvectors. Furthermore, the largest C-eigenvalue and all the corresponding eigenvectors can be obtained, which is the advantage of the proposed method.

• Institution
  东莞理工学院