Coupling of boundary integral equation and finite element methods for transmission problems in acoustics
Coupling of boundary integral equation and finite element methods for transmission problems in acoustics
复制标题
DOI：
10.1007/s11075-018-0610-3
复制
发表时间：
2018-10
影响因子：
2.1
通讯作者：
Hongrui Geng;Zhenhua Xu
中科院分区：
文献类型：
--
作者：
Hongrui Geng;Zhenhua Xu
本文提出了一种有限元法与边界积分方程法耦合求解二维声传播问题的方法。通过引入人工边界，并根据人工边界上Dirichlet数据和Neumann数据之间的关系定义透明边界条件，将原始传输问题转化为非局部边值问题.在这项工作中，这种关系描述的边界积分算子。然后，对非局部边值问题的弱形式进行了必要的数学分析。三种不同的算法被用来解决边界积分方程的计算公式，并给出了数值结果，以证明该计划的效率和精度。
In this paper, we propose a coupling of finite element method (FEM) and boundary integral equation (BIE) method for solving acoustic transmission problems in two dimensions. The original transmission problem is firstly reduced to a nonlocal boundary value problem by introducing an artificial boundary and defining a transparent boundary condition from the relation between Dirichlet data and Neumann data on the artificial boundary. In this work, such relationship is described in terms of boundary integral operators. Then, essential mathematical analysis for the weak formulation corresponding to the nonlocal boundary value problem is discussed. Three different algorithms are utilized for the solution of boundary integral equations to be involved in the computational formulations, and numerical results are presented to demonstrate the efficiency and accuracy of the schemes.