Chandrasekhar B, Rao Sadasiva M
Supercomputer Education and Research Center, Indian Institute of Science, Bangalore 560012, India.
J Acoust Soc Am. 2008 Dec;124(6):3390-6. doi: 10.1121/1.2998774.
In this work, a new numerical procedure is developed to generate an almost-diagonal matrix for the solution of boundary integral equation formulation dealing with acoustic scattering problems. The major drawback of the traditional boundary integral equation procedure resulting in a dense system matrix is eliminated in this new procedure by grouping the basis functions into a cluster. The geometry of the structure is modeled by planar triangles and the basis functions are defined on the nodes. By doing so, one can get a benefit of a smaller size matrix to begin with. Furthermore, by grouping these node-based basis functions into a cluster, an almost-diagonal matrix is generated. Thus, the solution procedure developed in this work may be utilized for very large scattering problems since the required computer resources are very low. The solution procedure developed in this work is validated for the scattering cross section of the simple shapes with the closed form solutions wherever available and with the other numerical solution procedures.
在这项工作中，开发了一种新的数值方法，用于生成一个近似对角矩阵，以求解处理声学散射问题的边界积分方程公式。通过将基函数分组为一个簇，在这个新方法中消除了传统边界积分方程方法导致密集系统矩阵的主要缺点。结构的几何形状由平面三角形建模，基函数在节点上定义。这样一来，一开始就可以得到一个较小规模矩阵的好处。此外，通过将这些基于节点的基函数分组为一个簇，可以生成一个近似对角矩阵。因此，由于所需的计算机资源非常低，这项工作中开发的求解方法可用于非常大的散射问题。这项工作中开发的求解方法在有封闭形式解的情况下，针对简单形状的散射截面以及其他数值求解方法进行了验证。
