当前位置: X-MOL 学术Finite Elem. Anal. Des. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Computation of absorbing boundary conditions at the discrete level for acoustic waves in the frequency domain
Finite Elements in Analysis and Design ( IF 3.5 ) Pub Date : 2020-02-01 , DOI: 10.1016/j.finel.2019.103346
Denis Duhamel

Abstract The calculation of wave radiation in exterior domains by finite element methods can lead to large computations even if we consider linear problems in the frequency domain as in this article. Here, we study two-dimensional acoustics described by the Helmholtz equation. A large part of the exterior domain is meshed and this computational domain is truncated at some distance where local or global boundary conditions are imposed at this artificial boundary. These conditions at finite distance must simulate as closely as possible the exact radiation condition at infinity and are generally obtained by discretizing an operator on the boundary. Here, we propose a different approach, still based on the finite element method. Instead of finding an absorbing operator and then discretizing it, we will estimate the absorbing operator directly at the discrete level and build a sparse matrix approximating the absorbing condition. This discrete absorbing matrix is added to the dynamic stiffness matrix of the problem which is then solved in a classical way. The coefficients of the absorbing matrix are found from the solutions of small size linear systems for each node on the radiating boundary. This is done using a set of radiating functions for which a boundary condition is written. The precision of the method is estimated from the number of functions in the test set and from the number of coefficients allowed in the sparse matrix. Finally, some examples are computed to validate the method.

中文翻译:

频域中声波离散级吸收边界条件的计算

摘要 即使我们像本文一样考虑频域中的线性问题,通过有限元方法计算外部域中的波辐射也会导致大量计算。在这里,我们研究由亥姆霍兹方程描述的二维声学。外部域的很大一部分是网格化的,这个计算域在一定距离处被截断,在这个人工边界上施加局部或全局边界条件。有限距离的这些条件必须尽可能地模拟无限远的精确辐射条件,并且通常通过在边界上离散算子来获得。在这里,我们提出了一种不同的方法,仍然基于有限元方法。而不是找到一个吸收算子然后将其离散化,我们将直接在离散水平上估计吸收算子,并建立一个近似吸收条件的稀疏矩阵。该离散吸收矩阵被添加到问题的动态刚度矩阵中,然后以经典方式求解。吸收矩阵的系数是从辐射边界上每个节点的小尺寸线性系统的解中找到的。这是使用一组辐射函数来完成的,其中写入了边界条件。该方法的精度是根据测试集中的函数数量和稀疏矩阵中允许的系数数量来估计的。最后,计算了一些示例以验证该方法。该离散吸收矩阵被添加到问题的动态刚度矩阵中,然后以经典方式求解。吸收矩阵的系数是从辐射边界上每个节点的小尺寸线性系统的解中找到的。这是使用一组辐射函数来完成的,其中写入了边界条件。该方法的精度是根据测试集中的函数数量和稀疏矩阵中允许的系数数量来估计的。最后,计算了一些示例以验证该方法。该离散吸收矩阵被添加到问题的动态刚度矩阵中,然后以经典方式求解。吸收矩阵的系数是从辐射边界上每个节点的小尺寸线性系统的解中找到的。这是使用一组辐射函数来完成的,其中写入了边界条件。该方法的精度是根据测试集中的函数数量和稀疏矩阵中允许的系数数量来估计的。最后,计算了一些示例以验证该方法。该方法的精度是根据测试集中的函数数量和稀疏矩阵中允许的系数数量来估计的。最后,计算了一些示例以验证该方法。该方法的精度是根据测试集中的函数数量和稀疏矩阵中允许的系数数量来估计的。最后,计算了一些示例以验证该方法。
更新日期:2020-02-01
down
wechat
bug