A scalable FETI-DP algorithm for a coercive variational inequality
A scalable FETI-DP algorithm for a coercive variational inequality
复制标题
用于强制变分不等式的可扩展 FETI-DP 算法
DOI：
10.1016/j.apnum.2004.09.009
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发表时间：
2005
影响因子：
2.8
通讯作者：
D. Stefanica
中科院分区：
文献类型：
--
作者：
Z. Dostál;D. Hořák;D. Stefanica
我们通过将双原类型的 FETI 算法与有界约束二次规划问题的最新结果相结合，开发了一种强制变分不等式数值解的最优算法。使用 FETI-DP 方法获得的模型问题的离散化版本通过凸优化的对偶理论简化为具有边界约束的二次规划问题。由此产生的问题通过一种新算法来解决，该算法具有根据二次问题的谱条件数给出的已知收敛率。我们提出保证算法可扩展性的收敛界限。这些结果通过数值实验得到证实。
We develop an optimal algorithm for the numerical solution of coercive variational inequalities, by combining FETI algorithms of dual-primal type with recent results for bound constrained quadratic programming problems. The discretized version of the model problem, obtained by using the FETI-DP methodology, is reduced by the duality theory of convex optimization to a quadratic programming problem with bound constraints. The resulting problem is solved by a new algorithm with a known rate of convergence given in terms of the spectral condition number of the quadratic problem. We present convergence bounds that guarantee the scalability of the algorithm. These results are confirmed by numerical experiments.