摘要
为更加高效地求解含有精细结构的波动问题,提出了一种基于加权Laguerre多项式求解波动方程的新方法。在求解过程中,将波动方程的各项基于Laguerre正交基函数进行展开,利用伽辽金原理和各阶基函数的正交性质,消除方程中的时间变量项,对空间项采用中心差分格式处理,形成可求解的矩阵方程。为验证该方法的效率,以含有精细结构的二维声波问题为例,利用本文方法和传统有限差分法等数值方法对其传播过程进行了求解,数值结果表明:本文方法在求解该问题时具有较大的效率优势,其计算时间仅为有限差分法的0.054%。
A new method for solving the wave equation based on the weighted Laguerre polynomials has been proposed,and this proposed method is focus on the efficiency of the problem which has a fine structure.The wave equation can be expanded by the Laguerre polynomials,by applying a Galerkin method and using the orthogonal property of these functions,the time variables can be eliminated and space variables can be handled by using the central difference scheme.One can get the numerical results by solving the matrix equation.To validate the efficiency of this proposed method,a two-dimensional acoustic wave problem with fine structure has been conducted.The numerical results shown that this proposed method has a big advantage in efficiency,the computational time is about 0.054%compared with the finite difference method.
作者
张迪
罗伟
Zhang Di;Luo Wei(Center of Engineering Quality Supervision,Logistics Support Department,Beijing 100083,China)
出处
《科技通报》
2020年第9期1-5,共5页
Bulletin of Science and Technology
