A preconditioned conjugate projected gradient method for computing eigenvector derivatives with repeated eigenvalues

Abstract

A preconditioned conjugate projected gradient (PCPG) method is given to solve the repeated eigenvector derivatives with respect to design parameters in finite element models. The factored stiffness matrix is used as a preconditioner, the new method can provide the approximate solutions to repeated eigenvector derivatives. This method can be used as an eigenvector sensitivities solver which can be coupled as an eigensolver/derivative software. Moreover, the new method can be used for industrial-size models. Finally, a numerical example is provided to illustrate the superior efficiency of the present method.