面向Frenkel-Kontorova模型准连续近似的目标导向自适应网格细化
Goal-Oriented Adaptive Mesh Refinement for the Quasicontinuum Approximation of a Frenkel-Kontorova Model
AI总结：
针对广义Frenkel-Kontorova模型的准连续近似，提出了一种误差估计器和自适应网格细化算法，以高效计算预定精度的感兴趣量。
摘要：
准连续近似是一种通过从代表原子（有限元三角剖分的节点）进行分段线性插值来减少晶体固体原子自由度的方法。在晶体中变形高度不均匀的区域（如缺陷周围），每个原子都必须是代表原子以获得足够精度，但在远离这些区域的地方，网格可以粗化以去除原子自由度，同时保持足够的精度。我们针对广义Frenkel-Kontorova模型的准连续近似提出了一种误差估计器和相关的自适应网格细化算法，使得能够高效地将感兴趣量计算到预定精度。
英文摘要：
The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are nodes for a finite element triangulation. In regions of the crystal with a highly nonuniform deformation such as around defects, every atom must be a representative atom to obtain sufficient accuracy, but the mesh can be coarsened away from such regions to remove atomistic degrees of freedom while retaining sufficient accuracy. We present an error estimator and a related adaptive mesh refinement algorithm for the quasicontinuum approximation of a generalized Frenkel-Kontorova model that enables a quantity of interest to be efficiently computed to a predetermined accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
