This paper presents a local non-singular knot method (LNKM) to accurately solve the large-scale acoustic problems in complicated geometries. The LNKM is a domain-type meshless collocation method, which relies only on scattered nodes. Firstly, a series of subdomains corresponding to every nodes can be searched based on the Euclidean distance between nodes. To each subdomain, a small linear system can be yielded by using the non-singular general solutions of Helmholtz-type equations. Secondly, the unknown variables at every nodes can be explicitly expressed by the function values at their corresponding supporting nodes. Finally, a large sparse system of linear equations is formed and solved to obtain the numerical solutions of physical quantities at every nodes. The proposed LNKM is mathematically simple, numerically accurate, and more applicable to the large-scale computation. Four numerical examples conform its effectiveness and accuracy for the large-scale computation of Helmholtz-type equations in complicated geometries.

本文提出了一种局部非奇异结法（LNKM），可以准确解决复杂几何形状中的大规模声学问题。LNKM是一种域类型的无网格配置方法，仅依赖于分散的节点。首先，可以基于节点之间的欧几里得距离来搜索与每个节点相对应的一系列子域。对于每个子域，可以通过使用Helmholtz型方程的非奇异一般解来产生一个小的线性系统。其次，每个节点上的未知变量可以通过其相应支持节点上的函数值来明确表示。最后，形成并求解大型稀疏线性方程组，以获得每个节点处物理量的数值解。拟议的LNKM在数学上简单，在数值上准确，并且更适用于大规模计算。四个数值示例证明了其在复杂几何结构中大规模计算亥姆霍兹型方程的有效性和准确性。