轴对称表面上Stokes双层势的容差驱动近距离评估
Tolerance-driven close evaluation of the Stokes double layer potential on axisymmetric surfaces
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中文总结 AI 辅助
针对轴对称粒子Stokes问题，提出容差驱动的双层势离面评估工作流，通过快速分类器选择最优求积方案，实现高效高精度计算，实验验证了其准确性和广泛适用性。
中文摘要 AI 辅助
我们考虑涉及光滑轴对称粒子的Stokes迁移率和阻力问题的边界积分方法。一个主要的数值挑战是在靠近粒子表面的离面点处准确且高效地评估层势。我们提出了一种容差驱动的工作流程，用于在此类评估点（目标点）处以指定精度评估Stokes双层势，同时避免不必要的计算成本。对于每个目标-粒子相互作用，一个快速分类器在标准、上采样和特殊求积中选择估计满足容差的最廉价选项。几何相关的单位密度误差指示器被预先计算并以缩减的柱坐标制表，然后与局部层密度修正因子实时结合，使其成本相对于评估势而言可忽略不计。需要特殊求积的目标使用稳定化的奇点交换表面求积处理：首先使用平移奇点交换求积评估周期方位角积分，以防止表面附近的严重抵消，然后在极角方向使用由误差指示器引导的自适应Gauss-Legendre求积。我们将此工作流程集成到一个边界积分求解器中，该求解器使用预计算的展开求积处理表面上的自相互作用，并针对椭球粒子的挑战性配置展示了该工作流程的性能。数值结果表明目标分类高度准确。对于几乎所有目标-粒子相互作用，规定的容差均被满足，在少数剩余情况下，误差保持在容差的适度倍数以内。尽管实验侧重于椭球的Stokes双层势，但离面框架适用于一般光滑轴对称表面，并可轻松适应其他Stokes层势。
英文摘要
We consider boundary integral methods for Stokes mobility and resistance problems involving smooth axisymmetric particles. A primary numerical challenge is the accurate and efficient evaluation of layer potentials at off-surface points close to particle surfaces. We present a tolerance-driven workflow for evaluating the Stokes double layer potential at such evaluation points (targets) to prescribed accuracy while avoiding unnecessary computational cost. For each target--particle interaction, a fast classifier selects the least costly option estimated to meet the tolerance among standard, upsampled, and special quadrature. Geometry-dependent unit-density error indicators are precomputed and tabulated in reduced cylindrical coordinates, then combined on the fly with a local layer-density modifier, making its cost negligible relative to evaluating the potential. Targets requiring special quadrature are treated using a stabilized version of singularity swap surface quadrature: the periodic azimuthal integral is evaluated first using translated singularity swap quadrature to prevent severe cancellation near the surface, followed by adaptive Gauss--Legendre quadrature in the polar direction guided by error indicators. We integrate this workflow into a boundary integral solver with precomputed quadrature by expansion for on-surface self-interactions and demonstrate the workflow's performance for challenging configurations of spheroidal particles. Numerical results show that target classification is highly accurate. The prescribed tolerance is met for nearly all target--particle interactions and the error remains within a modest factor of the tolerance in the few remaining cases. Although the experiments focus on the Stokes double layer potential for spheroids, the off-surface framework applies to general smooth axisymmetric surfaces and can be easily adapted to other Stokes layer potentials.
发表机构
- KTH Royal Institute of Technology（皇家理工学院）
- Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克科学促进会数学研究所）
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