论文标题
在不断发展的乘数域中积分方程的平行骨架化
Parallel Skeletonization for Integral Equations in Evolving Multiply-Connected Domains
论文作者
论文摘要
本文提出了一种将层次矩阵骨架化因素应用于具有可能缺陷的积分运算符的边界积分方程的数值解决方案的一般方法。等级缺陷型运算符出现在具有多个边界成分的椭圆形部分微分方程的边界积分方法中，例如在粘性流体流中的多个囊泡的情况下。我们的广义骨骼化分解保留了“代理点方法”提供的局部属性，并允许并行化实现，其中不同的处理器同时在边界的不同部分工作。此外，当边界经历局部几何扰动（例如内部孔的运动）时，就可以有效地将分解分解相对于修改的离散节点的数量有效地重新计算。我们提出了一个应用程序，该应用程序利用骨架的并行实现，并以形状优化制度更新。
This paper presents a general method for applying hierarchical matrix skeletonization factorizations to the numerical solution of boundary integral equations with possibly rank-deficient integral operators. Rank-deficient operators arise in boundary integral approaches to elliptic partial differential equations with multiple boundary components, such as in the case of multiple vesicles in a viscous fluid flow. Our generalized skeletonization factorization retains the locality property afforded by the "proxy point method," and allows for a parallelized implementation where different processors work on different parts of the boundary simultaneously. Further, when the boundary undergoes local geometric perturbations (such as movement of an interior hole), the factorization can be recomputed efficiently with respect to the number of modified discretization nodes. We present an application that leverages a parallel implementation of skeletonization with updates in a shape optimization regime.
