论文标题
用于具有非局部相互作用的模型的基于子结构的域分解方法的一般框架
A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
论文作者
论文摘要
为非局部问题的基于子结构的域分解方法提供了严格的数学框架，该方法具有有限距离分隔的点之间的相互作用。在这里，通过进行基本结构，这意味着使用用于局部偏微分方程问题的传统几何配置，其中计算域被细分为非重叠的子域。在非局部环境中，这种方法是基于子结构的，因为这些子域与具有有限体积的接口区域相互作用，与局部PDE设置相比，接口是较低的尺寸流形的较低尺寸流形的，分开依赖子域。关键结果包括在连续和离散级别的全局，单域非局部问题及其多域重新印象之间的等价性。这些结果为开发非本地域分解方法的有效解决方案策略提供了严格的基础。
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a traditional geometric configuration for local partial differential equation problems is used in which a computational domain is subdivided into non-overlapping subdomains. In the nonlocal setting, this approach is substructuring-based in the sense that those subdomains interact with neighboring domains over interface regions having finite volume, in contrast to the local PDE setting in which interfaces are lower dimensional manifolds separating abutting subdomains. Key results include the equivalence between the global, single-domain nonlocal problem and its multi-domain reformulation, both at the continuous and discrete levels. These results provide the rigorous foundation necessary for the development of efficient solution strategies for nonlocal domain-decomposition methods.
