基于有限元与宽频快速多极边界元的二维流固耦合声场分析

FEM/WIDEBAND FMBEM COUPLING ANALYSIS FOR TWO DIMENSIONAL ACOUSTIC FLUID-STRUCTURE INTERACTION PROBLEMS

采用有限元/快速多极边界元法进行水下弹性结构的辐射和散射声场分析。Burton-Miller法用于解决传统单Helmholtz边界积分方程在求解外边界值问题时出现的非唯一解的问题。该文采用GMRES和快速多极算法加速求解系统方程。针对传统快速算法在高频处效率低和对角式快速算法在低频处不稳定这一问题,该文通过结合这两种快速算法形成宽频快速算法来克服。同时该文通过观察不同参数条件设置下,宽频快速多极法得到的数值结果在计算精度和计算时间上的变化,得到最优的参数组合值。最后通过数值算例验证该文算法的正确性和有效性。

A coupling algorithm based on the FEM and wideband fast multipole boundary element method(FMBEM) is proposed for the simulation of the radiating and scattering problems of underwater structures.The Burton-Miller formulation is used to solve the non-uniqueness problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems.The iterative solver GMRES and the fast multipole method are applied to accelerate the solution of the linear system of equations.For the problems of the low computational efficiency of the original fast multipole algorithm(FMM) at high frequencies and the numerical instability of the diagonal FMM at low frequencies,a new wideband FMM formed by combining these two methods is applied to overcome the problems.A set of optimal parameters for the wideband FMBEM is obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage.A numerical example is presented to demonstrate the efficiency and validity of the proposed algorithm.