Discontinuous Coarse Spaces for DD-Methods with Discontinuous Iterates
Discontinuous Coarse Spaces for DD-Methods with Discontinuous Iterates
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DOI：
10.1007/978-3-319-05789-7_58
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发表时间：
2014
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影响因子：
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通讯作者：
M. Gander;L. Halpern;Kévin Santugini Repiquet
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文献类型：
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作者：
M. Gander;L. Halpern;Kévin Santugini Repiquet
我们在本文中解释为什么连续粗糙空间是一个次优的选择区域分解方法，有不连续的迭代，例如限制添加剂施瓦茨方法，或优化施瓦茨方法。作为替代方案，我们提出了不连续的粗糙空间，这样的方法。对于线性问题，我们展示了如何设计一个这样的不连续的粗空间，并提出了一种算法，计算一个有效的不连续的粗空间校正的特殊情况下的优化施瓦茨方法。虽然该算法是适合于更高的维度，它有特殊的性质收敛在一个单一的粗迭代一维线性问题。我们通过数值实验说明了我们的新算法。
We explain in this paper why continuous coarse spaces are a suboptimal choice for domain decomposition methods that have discontinuous iterates, like for example restricted Additive Schwarz methods, or optimized Schwarz methods. As an alternative, we propose discontinuous coarse spaces for such methods. For linear problems, we show how to design one such discontinuous coarse space and present an algorithm that computes an efficient discontinuous coarse space correction for the special case of an optimized Schwarz method. While the algorithm is suitable for higher dimensions, it has the special property of converging in a single coarse iteration for one-dimensional linear problems. We illustrate our new algorithm by numerical experiments.