Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. We present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver strategies.

翻译：非局部模型能够描述经典偏微分方程无法捕捉的现象。高效求解器的可用性是非局部模型在实际工程应用中面临的主要问题之一。本文提出一种受经典局部方程子结构方法启发的区域分解求解器。在涉及标量和矢量整数阶及分数阶非局部方程有限元离散的数值实验中，我们观察到与常用求解策略相比，求解时间最高可提升14.6倍。