Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational mechanics to decompose spatial problems into multiple subproblems that can be solved in parallel, advancing solution schemes for dynamics or quasi-statics are inherently serial processes. For quasi-static simulations, however, there is no accumulating 'time' discretization error, hence an alternative approach is required. In this paper, we present an Adaptive Parallel Arc-Length Method (APALM). By using a domain parametrization of the arc-length instead of time, the multi-level error for the arc-length parametrization is formed by the load parameter and the solution norm. By applying local refinements in the arc-length parameter, the APALM refines solutions where the non-linearity in the load-response space is maximal. The concept is easily extended for bifurcation problems. The performance of the method is demonstrated using isogeometric Kirchhoff-Love shells on problems with snap-through and pitch-fork instabilities. It can be concluded that the adaptivity of the method works as expected and that a relatively coarse approximation of the serial initialization can already be used to produce a good approximation in parallel.
翻译:在当今科学的计算机景观中,平行计算是无处不在的,从台式计算机的多核心处理器开始,直到大规模平行的集群。虽然域分解方法在计算机械学上有着悠久的传统,可以将空间问题分解成可平行解决的多个子问题,但动态或准静态的推进解决方案方案本质上是序列过程。对于准静态模拟来说,没有累积“时间”离散错误,因此需要一种替代方法。在本文中,我们提出了一个适应性平行弧-龙格法(APALM) 。通过使用弧长而非时间的域准光度法, 域分解方法将空间问题分解成可平行的多重错误是由负载参数和解决方案规范形成的。通过对弧长参数应用本地精度的精度改进, APALM 改进解决方案, 在负载反应空间的非线性误差是最大化的。 概念很容易用于两极化问题。 这种方法的性表现通过使用弧度基质基质偏移法代替时间, 弧- 螺旋贝贝壳的多度误判法, 即成直径直径直径直径直径直对准法,,, 直对准的精确测法的精确测法可以得出直径对准法,,,, 直径对准法的精确地制成成成为直径直径直线,,, 直正正正准法可以制成成成成成为直线法, 。</s>