Multiscale Discretization And Adaptive Algorithm Based On The Rayleigh Quotient Inverse Iteration Method For The Laplace Model For Fluid-Solid Vibrations

The Laplace model for fluid-solid vibrations is an important problem in nuclear engineering,and its numerical method has received academic attention in recent years.In this paper,for the Laplace model for fluid-solid vibrations we establish the multi-scale discretization scheme based on the Rayleigh quotient inverse iteration and the adaptive algorithm.First,we propose the multi-scale discretization scheme.With this scheme,the solution of an eigenvalue problem on fine meshes is reduced to the solution of the eigenvalue problem on coarse meshes and the solutions of linear algebraic systems.Then we analyze and give the error estimates of the proposed scheme.Second,we give the a posteriori error indicator and the adaptive finite element algorithm.Finally we present numerical experiments to validate the efficiency of the scheme.