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Solution of boundary-element problems using the fast-inertial-relaxation-engine method

机译：快速易放松发动机方法解决边界元件问题的解决方案

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摘要

The fast-inertial-relaxation engine (FIRE) has proven to efficiently find local minima of potential energies or related penalty functions although its implementation requires only few, additional lines of code in a molecular-dynamics or steepest-descent program. So far, FIRE has been predominantly applied to particle-based or low-dimensional problems. In this work, we demonstrate that it can also benefit the solution of boundary-value problems. Towards this end, we study the mechanical contact between an elastic body and a rigid indenter of varying complexity by augmenting Green's function molecular dynamics (GFMD) with FIRE. We find a rather remarkable speedup, which can be further enhanced when choosing the masses associated with the eigenmodes of the free elastic solid appropriately. For the investigated adhesive and randomly rough indenter with typical system size, 100 mass-weighted FIRE-GFMD iterations suffice to relax the excess energy to 10(-3) of its original value. The standard GFMD method needs 25 times more iterations. For the investigated problems, FIRE-GFMD even appears to slightly outperform conjugate-gradient based optimization.
机译：虽然其实现只需要少量，在分子动态或陡峭的程序中，但虽然其实施只需要少量，额外的代码行，但是，快速惯性放松发动机（火灾）已被证明有效地找到潜在的能量或相关罚款功能。到目前为止，火灾主要应用于基于粒子的或低维度问题。在这项工作中，我们证明它还可以使边值问题的解决方案受益。为此，我们通过增强绿色的函数分子动力学（GFMD）来研究弹性体与变化复杂性的刚性压痕之间的机械接触。 We find a rather remarkable speedup, which can be further enhanced when choosing the masses associated with the eigenmodes of the free elastic solid appropriately.对于具有典型系统尺寸的调查粘合剂和随机粗凹入，100个重量加权的火 - GFMD迭代足够放松其原始值的过量能量至10（3）。标准GFMD方法需要25倍的迭代。对于调查的问题，Fire-GFMD甚至似乎略高于偶尔的共轭梯度基于优化。

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  • 来源
    《Physical review》 |2019年第14期|144103.1-144103.8|共8页
  • 作者

    Zhou Yunong; Moseler Michael; Mueser Martin H.;

  • 作者单位

    Univ Saarland Dept Mat Sci & Engn D-66123 Saarbrucken Germany;

    Univ Freiburg Fac Phys Hermann Herder Str 3 D-79104 Freiburg Germany;

    Univ Saarland Dept Mat Sci & Engn D-66123 Saarbrucken Germany;

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