Standard discretization techniques for boundary integral equations, e.g., the Galerkin boundary element method, lead to large densely populated matrices that require fast and efficient compression techniques like the fast multipole method or hierarchical matrices. If the underlying mesh is very large, running the corresponding algorithms on a distributed computer is attractive, e.g., since distributed computers frequently are cost-effective and offer a high accumulated memory bandwidth.

Compared to the closely related particle methods, for which distributed algorithms are well-established, the Galerkin discretization poses a challenge, since the supports of the basis functions influence the block structure of the matrix and therefore the flow of data in the corresponding algorithms. This article introduces distributed ℋ₂-matrices, a class of hierarchical matrices that is closely related to fast multipole methods and particularly well-suited for distributed computing. While earlier efforts required the global tree structure of the ℋ₂-matrix to be stored in every node of the distributed system, the new approach needs only local multilevel information that can be obtained via a simple distributed algorithm, allowing us to scale to significantly larger systems. Experiments show that this approach can handle very large meshes with more than 130 million triangles efficiently.

边界积分方程的标准离散化技术，例如伽辽金边界元法，会产生大型密集矩阵，需要快速有效的压缩技术，例如快速多极子方法或分层矩阵。如果底层网格非常大，则在分布式计算机上运行相应的算法是有吸引力的，例如，因为分布式计算机通常具有成本效益并且提供高累积存储器带宽。

与密切相关的粒子方法（分布式算法已得到完善）相比，伽辽金离散化提出了挑战，因为基函数的支持影响矩阵的块结构，从而影响相应算法中的数据流。本文介绍分布式 ℋ ₂ -矩阵，这是一类与快速多极子方法密切相关的分层矩阵，特别适合分布式计算。虽然早期的工作需要 ℋ _{2的全局树结构}-矩阵存储在分布式系统的每个节点中，新方法只需要本地多级信息，这些信息可以通过简单的分布式算法获得，使我们能够扩展到更大的系统。实验表明，这种方法可以有效地处理包含超过 1.3 亿个三角形的超大型网格。