标题： 基于部分积分的正则化在BEM求解三维弹性静力学问题中的作用：线积分的角色 显示英文标题

标题： Partial integration based regularization in BEM for 3D elastostatic problems: The role of line integrals

摘要： 边界元方法（BEM）是一种求解三维弹塑性问题的强大数值方法，尤其适用于断裂力学中的裂纹扩展和半空间问题。尽管具有这些优点，BEM面临着与密集系统矩阵和奇异积分核相关的重大挑战。可以使用各种快速方法来减轻计算负担；本研究采用基于切比雪夫插值的快速多极方法（FMM）。为了处理奇异核，存在多种分析和数值积分或正则化技术。一种这样的技术结合部分积分与斯托克斯定理，将超奇异和强奇异核转化为弱奇异核。然而，应用斯托克斯定理在半空间问题中引入了线积分，并且在使用FMM时，由于几何被划分为近场和远场区域并且必须作为开放表面处理。本文提出了强奇异和超奇异核所需的线积分，并展示了它们在上述问题中的意义。 显示英文摘要

摘要： The Boundary Element Method (BEM) is a powerful numerical approach for solving 3D elastostatic problems, particularly advantageous for crack propagation in fracture mechanics and half-space problems. Despite its benefits, BEM faces significant challenges related to dense system matrices and singular integral kernels. The computational expense can be mitigated using various fast methods; this study employs the Chebyshev interpolation-based Fast Multipole Method (FMM). To handle singular kernels, several analytical and numerical integration or regularization techniques exist. One such technique combines partial integration with Stokes' theorem to transform hyper-singular and strong singular kernels into weakly singular ones. However, applying Stokes' theorem introduces line integrals in half-space problems and with FMM, where the geometry is partitioned into near-field and far-field regions and must be treated as an open surface. In this paper, the necessary line integrals for strongly singular and hyper-singular kernels are presented and their significance in the aforementioned problems is demonstrated.