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Iterated Ritz and conjugate gradient methods as solvers in constrained form-finding: A comparison

机译:迭代ritz和缀合物梯度方法作为受约束形式找到的溶剂:比较

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摘要

Constrained form-finding results in a nonlinear system of equations unless a linear form-finding method (force density method) is iteratively applied until the given constraints are satisfied. Because the goal of this paper is to contribute to the further development of this method, a brief overview of the method and its existing improvements is provided. Further improvement can be potentially expected by reducing the number of iteration steps in solving systems of linear equations in each application of the force density method. To explore this, a comparison of iterative linear solvers is conducted. The Iterated Ritz method, as a new promising solver (currently under development), was chosen for comparison with typically used conjugate gradients. Form-finding of several truss structures in both tension and compression was performed to compare the number of iteration steps necessary to obtain the solution. The presented form-finding examples indicated a significant reduction in the number of solver iteration steps, showing the potential of the Iterated Ritz method for use as a solver in linear procedures for constrained form-finding.
机译:除非迭代地施加线性形式发现方法(力密度法)直到满足给定的约束,否则在非线性等方程式中产生导致的制度发现结果。因为本文的目标是有助于该方法的进一步发展,提供了该方法的简要概述及其现有的改进。通过减少力密度法在每个应用中求解线性方程系统中的迭代步骤的次数来潜在地期望进一步改进。为了探索这一点,进行了迭代线性溶剂的比较。选择迭代的RITZ方法作为新的承诺解算器(目前正在开发),以与通常使用的共轭梯度进行比较。在张力和压缩中形成若干桁架结构的形成,以比较获得溶液所需的迭代步骤的数量。所提出的形式发现实施例表示求解器迭代步骤的数量显着降低,显示迭代RITZ方法用作用于约束形式发现的线性程序中的求解器的求验。

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