In this paper, a preconditioned GMRES method is developed and analyzed for solving the linear system from advection-diffusion equations with the hybridizable discontinuous Galerkin (HDG) discretization. The preconditioner is the balancing domain decomposition methods (BDDC), one of the most popular nonoverlapping domain decomposition methods. For large viscosity, if the subdomain size is small enough, the number of iterations is independent of the number of subdomains and depends only slightly on the subdomain problem size. The convergence deteriorates when the viscosity decreases. These results are similar to those with the standard finite element discretizations. Numerical results of two examples in two dimensions are provided to confirm the theory.

在本文中，开发并分析了一种预处理的 GMRES 方法，用于从具有可混合不连续伽辽金 (HDG) 离散化的对流-扩散方程求解线性系统。预处理器是平衡域分解方法（BDDC），它是最流行的非重叠域分解方法之一。对于大的粘性，如果子域大小足够小，迭代次数与子域数无关，仅与子域问题大小无关。当粘度降低时，收敛性变差。这些结果与标准有限元离散化的结果相似。提供了两个二维例子的数值结果来证实该理论。