论文标题
亚域解决方案分解方法
Subdomain solution decomposition method for nonstationary problems
论文作者
论文摘要
通过分裂方案实现了非组织问题的数值解决方案中计算成本的降低。在这种情况下，解决一组计算较少的复杂问题提供了及时的过渡到新的水平。分裂方案的传统构建方法基于问题运营商的加性表示，并使用明确的近似近似值来单个术语。最近（Y. Efendiev，P.N。Vabishchevich。在非组织问题中解决方案分解的拆分方法。在本文中使用了这种具有子域解决方案选择的新方法来构建域分解方案。在空间差近似的矩形中，二阶抛物线方程的边界值问题是典型的。研究了有或没有重叠子域的域分解的两级和三级方案。我们的数值实验补充了理论结果。
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in time. The traditional construction approach of splitting schemes is based on an additive representation of the problem operator(s) and uses explicit-implicit approximations for individual terms. Recently (Y. Efendiev, P.N. Vabishchevich. Splitting methods for solution decomposition in nonstationary problems. \textit{Applied Mathematics and Computation}. \textbf{397}, 125785, 2021), a new class of methods of approximate solution of nonstationary problems has been introduced based on decomposition not of operators but of the solution itself. This new approach with subdomain solution selection is used in this paper to construct domain decomposition schemes. The boundary value problem for a second-order parabolic equation in a rectangle with a difference approximation in space is typical. Two and three-level schemes for decomposition of the domain with and without overlapping subdomains are investigated. Our numerical experiments complement the theoretical results.
