A projection method based on discrete normalized dynamical system for computing C-eigenpairs. (English) Zbl 1532.15006
Summary: 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.
MSC:
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 15A69 | Multilinear algebra, tensor calculus |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 37M99 | Approximation methods and numerical treatment of dynamical systems |
Software:
TenEigReferences:
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