The parallel solution of large scale non-linear programming problems, which arise for example from the discretization of non-linear partial differential equations, is a highly demanding task. Here, a novel solution strategy is presented, which is inherently parallel and globally convergent. Each global non-linear iteration step consists of asynchronous solutions of local non-linear programming problems followed by a global recombination step. The recombination step, which is the solution of a quadratic programming problem, is designed in a way such that it ensures global convergence. As it turns out, the new strategy can be considered as a globalized additively preconditioned inexact Newton (ASPIN) method. However, in our approach the influence of ASPIN's non-linear preconditioner on the gradient is controlled in order to ensure a sufficient decrease condition. Two different control strategies are described and analyzed. Convergence to first-order critical points of our non-linear solution strategy is shown under standard trust-region assumptions. The strategy is investigated along difficult minimization problems arising from non-linear elasticity in 3D solved on a massively parallel computer with several thousand cores.
翻译:大规模非线性编程问题的平行解决办法来自非线性部分差异方程式的分解,这种大规模非线性非线性编程问题的平行解决办法是一项非常艰巨的任务。在这里,可以提出一个新的解决办法战略,这种战略具有内在的平行和全球趋同性。每个全球非线性迭代步骤都包括当地非线性编程问题的非线性解决办法,随后是全球再组合步骤。重组步骤是四线性编程问题的解决方法,其设计方式确保了全球趋同。新战略可以被视为一种全球化的附加附加性,其先决条件是非线性牛顿(ASPIN)方法。然而,在我们的做法中,ASPIN的非线性定时梯度的影响受到控制,以确保有足够的递减条件。对两种不同的控制战略进行了描述和分析。在标准的信任区域假设下显示,对非线性方案第一阶点的趋同点的趋同性,即确保全球趋同性。这一战略与3D核心的非线性非线性弹性引起的困难最小化问题一起调查。