Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related linear systems. When contact is modeled with the aid of Lagrange multipliers, the impenetrability condition is enforced exactly, but the associated Jacobian matrix is indefinite and needs a special treatment for a fast numerical solution. In this work, a constraint preconditioner is proposed where the primal Schur complement is computed after augmenting the zero block. The name Reverse is used in contrast to the traditional approach where only the structural block undergoes an augmentation. Besides being able to address problems characterized by singular structural blocks, often arising in contact mechanics, it is shown that the proposed approach is significantly cheaper than traditional constraint preconditioning for this class of problems and it is suitable for an efficient HPC implementation through the Chronos parallel package. Our conclusions are supported by several numerical experiments on mid- and large-size problems from various applications. The source files implementing the proposed algorithm are freely available on GitHub.
翻译:典型的是,这是一个非常棘手的非线性问题,往往需要牛顿的多次迭代才能在相关线性系统的解决方案中集中并造成麻烦。当接触与拉格朗变异器的帮助形成模型时,不易穿透性条件是完全强制执行的,但相关的雅各格矩阵是无限期的,需要为快速数字解决方案提供特殊治疗。在这项工作中,在增加零块后,原始Schur补充物将计算成一个制约性先决条件。使用名称反向器时,与只有结构块进行扩增的传统方法形成对照。除了能够解决以单一结构块为特征的问题外,通常在接触机械中出现的问题,还表明拟议的方法比这类问题的传统限制要便宜得多,适合通过Chronos平行包高效地执行HPC。我们的结论得到了关于各种应用的中大问题的若干数字实验的支持。实施拟议算法的源文件可以在GitHub上自由查阅。