Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices corresponding to the integral operators requires efficient algorithms. This article describes two approaches that allow us to solve boundary element equations on surface meshes consisting of several millions of triangles while preserving the optimal convergence rates of the Galerkin discretization.

中文翻译：

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快速大规模边界元算法

边界元方法 (BEM) 将域中的偏微分方程简化为域边界上的积分方程。它们对于解决无界域上的问题特别有吸引力，但处理与积分运算符对应的密集矩阵需要有效的算法。本文介绍了两种方法，它们使我们能够在由数百万个三角形组成的表面网格上求解边界元方程，同时保持 Galerkin 离散化的最佳收敛速度。