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.
翻译:在非静止问题的数字解决办法中,计算成本的减少是通过分裂办法实现的。在这种情况下,解决一组不那么计算复杂的问题可以向一个新的阶段过渡。传统的分裂办法的建造方法基于问题经营者的叠加代表,对个别术语使用明确的隐含近似值。最近(Y. Efendiev, P.N. Vabishchevich. ),在非静止问题中分解溶的方法。\textit{Applied Maticals and Computation}。\ textbf{397}, 125785, 2021),基于非静止问题操作者的分解而不是对解决办法本身的分解,采用了一类新的非静止问题近似解决办法。本文中使用了这种分界解决方案选择的新办法来构建域分解方案。在与空间近似差异的对调中,二级抛物线方方方程式的边界值问题是典型的。两个和三个层次的分解法方案是将域与我们的理论性结果互不重叠的补充。