论文标题
从添加剂平均施瓦茨方法到非重叠的光谱添加剂施瓦茨方法
From Additive Average Schwarz Methods to Non-overlapping Spectral Additive Schwarz Methods
论文作者
论文摘要
在本文中，我们根据\ cite {MR1943457}中引入的添加剂平均施瓦茨设计和分析两种新方法。具有高度异质系数的椭圆问题的新方法设计。这些方法是非重叠类型的，亚域的相互作用通过粗糙空间获得。第一种方法是最小能量Schwarz -Mes方法。 ME具有最小能量的粗空间，每个子域内内部持续延伸。 MES方法的条件数总是比AAS方法小。第二类方法是基于每个子域中低秩能量谐波扩展的非重叠频谱添加剂Schwarz- NOSA方法。为了达到低级，我们解决了每个子域中的广义特征值问题。 NOSA具有最低能量的粗糙空间等级。 NOSA方法的条件数不取决于系数。另外，NOSA方法具有良好的并行化属性。全局问题的大小等于每个子域中选择的特征值的总数。它仅与接触子域界面的高渗透岛的数量有关。
In this paper, we design and analyze two new methods based on additive average Schwarz -- AAS method introduced in \cite{MR1943457}. The new methods design for elliptic problems with highly heterogeneous coefficients. The methods are of the non-overlapping type, and the subdomain interactions obtain via the coarse space. The first method is the minimum energy Schwarz -- MES method. MES has the minimum energy for the coarse space with constant extension inside each subdomain. The condition number of the MES method is always smaller than in the AAS method. The second class of methods is the non-overlapping spectral additive Schwarz -- NOSAS methods based on low-rank discrete energy harmonic extension in each subdomain. To achieve the low-rank, we solve a generalized eigenvalue problem in each subdomain. NOSAS have the minimum energy for a given rank of the coarse space. The condition number of the NOSAS methods does not depend on the coefficients. Additionally, the NOSAS methods have good parallelization properties. The size of the global problem is equal to the total number of eigenvalues chosen in each subdomain. It is only related to the number of high-permeable islands that touch the subdomains' interface.
