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On the application of multipoint Root-Solvers for improving global convergence of fracture problems

机译：关于多点根溶剂在提高骨折问题的全局收敛中的应用

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摘要

Achieving accelerated global convergence of finite element analysis is advantageous especially when implementing complex fracture models. This exploratory study investigates the performance of cubic, fourth order and fifth order multipoint root-solvers that require only first order derivatives for solving the nonlinear equations encountered in the global finite element problem in the context of fracture analysis. To this end, influence of various parameters - including number of loading steps, problem size and convergence criterion used while implementing a typical fracture model (Gurson model) - on the computational time, rate of convergence and number of iterations consumed by various higher order root-solvers is studied. Although with an additional computational overhead, the higher order root-solvers exhibited superior convergence rates and consumed less number of global iterations when compared to the Newton Raphson method during fracture analysis. In addition, new hybrid root-solvers are introduced to alleviate the convergence issues encountered in fracture analysis to accelerate the performance of higher order root-solvers.
机译：实现有限元分析的实现加速全局收敛是有利的，特别是在实现复杂的裂缝模型时。该探索性研究调查了只需要一阶衍生物的立方，第四阶和第五阶多点根求解器的性能，以解决在断裂分析的背景下全球有限元问题中遇到的非线性方程。为此，各种参数的影响 - 包括在实现典型的裂缝模型（Gurson Model）的同时使用的加载步骤，问题大小和收敛标准 - 在计算时间，收敛速率和各种高阶根消耗的迭代速度-Solvers是研究过的。尽管在额外的计算开销中，与在断裂分析期间，较高的根系溶剂表现出优异的收敛速度，并且在与牛顿Raphson方法相比时消耗少量全球迭代。此外，还引入了新的混合根溶剂来缓解断裂分析中遇到的收敛性问题，以加速高阶根系溶剂的性能。

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