In this work we develop a novel domain splitting strategy for the solution of partial differential equations. Focusing on a uniform discretization of the $d$-dimensional advection-diffusion equation, our proposal is a two-level algorithm that merges the solutions obtained from the discretization of the equation over highly anisotropic submeshes to compute an initial approximation of the fine solution. The algorithm then iteratively refines the initial guess by leveraging the structure of the residual. Performing costly calculations on anisotropic submeshes enable us to reduce the dimensionality of the problem by one, and the merging process, which involves the computation of solutions over disjoint domains, allows for parallel implementation.

翻译：在这项工作中,我们为部分差异方程式的解决方案制定了一个新的领域分割战略。我们的建议侧重于美元-维对映-扩散方程式的统一分解,我们的建议是一个两级的算法,将高厌食亚米希方程式的分解所产生的解决方案合并在一起,以计算精细方程式的初始近似值。随后的算法通过利用剩余方程式的结构,反复完善了最初的猜测。对厌食亚米舍斯进行昂贵的计算,使我们能够将问题的维度降低一个,而合并过程则涉及在脱节域上计算解决方案的计算,允许平行实施。</s>