Local And Parallel Finite Element Algorithms To Solve 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.Local and parallel finite element method is one of the efficient numerical methods to solve partial differential equations,and its advantage is that it is only on the local encryption region that the linear equations are solved in each ”iteration” and the degrees of freedom of the linear equations does not increase in the process of ”iteration”,and local computations are independently in each local region when there are more than one singular points.Thus a big problem can be turned into small problems,then the scale of calculation is reduced.This paper studies the local and parallel algorithms of finite element for the Laplace model for fluid-solid vibrations.Firstly,the local a prior error estimation of the finite element approximation for the Laplace model for fluid-solid vibrations is given.Secondly,the local and parallel finite element schemes based on local defect-correction technique are established,and the error analysis of the local computation scheme is provided.Finally,the numerical experiments on two different domains are reported.Theoretical analysis and numerical experiments show that the proposed finite element local and parallel algorithms are applicable and efficient for eigenfunctions with local low smoothness.