标题： 一种用于三维对流扩散问题的自适应粗空间BDDC方法 显示英文标题

标题： A BDDC method for three-dimensional advection-diffusion problems with an adaptive coarse space

摘要： 非对称正定（NSPD）系统在对流扩散问题中的求解是科学和工程领域的重要研究课题。 自适应BDDC方法是一种重要的非重叠区域分解方法，通常用于求解对称正定问题。 在本文中，我们将自适应BDDC方法应用于求解对流扩散问题的NSPD系统。 此外，通过基于先前选择的原始约束设计一类边界的广义特征值问题，进一步减少了原始未知数的数量。 数值实验验证了所提出方法的有效性。 显示英文摘要

摘要： The solution of nonsymmetric positive definite (NSPD) systems for advection-diffusion problems is an important research topic in science and engineering. The adaptive BDDC method is a significant class of non-overlapping domain decomposition methods, which is often used for solving symmetric positive definite problems. In this paper, we apply the adaptive BDDC method to solve the NSPD systems of te advection-diffusion problems. Moreover, by designing a class of edge generalized eigenvalue problems based on prior selected primal constraints, the number of primal unknowns is further reduced. Numerical experiments have verified the effectiveness of the proposed methods.