An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for piecewise linear curves. By using analytic integration of the regularized Stokeslet kernel over the triangles, the regularization parameter $\epsilon$ is effectively decoupled from the spatial discretization of the surface. This is in contrast to the usual implementation of the method in which the regularization parameter is chosen for accuracy reasons to be about the same size as the spatial discretization. The validity of the method is demonstrated through several examples, including the flow around a rigidly translating/rotating sphere, a rotating spheroid, and the squirmer model for self-propulsion. Notably, second order convergence in the spatial discretization for fixed $\epsilon$ is demonstrated. Considerations of mesh design and choice of regularization parameter are discussed, and the performance of the method is compared with existing quadrature-based implementations.

翻译：本文发展了三维空间中正则化斯托克斯方法（MRS）在三角剖分曲面上的扩展，适用于分段线性力分布。该方法将用于分段线性曲线的正则化斯托克斯线段方法推广到三角形单元。通过对三角形区域的正则化斯托克斯核进行解析积分，正则化参数$\epsilon$与曲面空间离散有效解耦。这与该方法的常规实现形成对比——常规实现中，为保证精度，正则化参数通常需与空间离散尺度保持相当。通过多个算例验证了方法的有效性，包括刚体平移/旋转球体周围的流动、旋转椭球体以及用于自推进的squirmer模型。特别地，在固定$\epsilon$条件下，空间离散实现了二阶收敛。文中还讨论了网格设计及正则化参数选择策略，并将该方法与现有基于数值积分的实现进行了性能比较。