论文标题
分析索拉斯域的分解预处理因非自身辅助或无限问题的分析
Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems
论文作者
论文摘要
我们分析了应用于通用线性系统的单级重叠域分解前索拉斯（对称优化的限制性添加剂SCHWARZ）的收敛性，该系统不一定是对称/自偶会或正面确定的。通过概括[I.G.中开发的Helmholtz方程的理论格雷厄姆（E.A.） Spence和J. Zou，Siam J.Numer.Anal。，2020年]，我们确定了足以在预处理矩阵的标准上获得上限的假设和估计列表，以及其值范围的距离距离与原点的距离。我们强调的是，我们的理论是普遍的，因为它不是特定的边界价值问题。此外，它不依赖于元素足够小的粗网格。作为该框架的说明，我们证明了与异质反应反向转向扩散方程的重叠结构域分解方法的新估计值（为了证明该方程式的稳定性假设，我们考虑了强制性双线性形式的稳定性假设，但这是非对称的）。
We analyze the convergence of the one-level overlapping domain decomposition preconditioner SORAS (Symmetrized Optimized Restricted Additive Schwarz) applied to a generic linear system whose matrix is not necessarily symmetric/self-adjoint nor positive definite. By generalizing the theory for the Helmholtz equation developed in [I.G. Graham, E.A. Spence, and J. Zou, SIAM J.Numer.Anal., 2020], we identify a list of assumptions and estimates that are sufficient to obtain an upper bound on the norm of the preconditioned matrix, and a lower bound on the distance of its field of values from the origin. We stress that our theory is general in the sense that it is not specific to one particular boundary value problem. Moreover, it does not rely on a coarse mesh whose elements are sufficiently small. As an illustration of this framework, we prove new estimates for overlapping domain decomposition methods with Robin-type transmission conditions for the heterogeneous reaction-convection-diffusion equation (to prove the stability assumption for this equation we consider the case of a coercive bilinear form, which is non-symmetric, though).
