Orientation preserving mesh optimisation and preconditioning
Orientation preserving mesh optimisation and preconditioning
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DOI：
10.1002/nme.5764
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发表时间：
2018-05
影响因子：
2.9
通讯作者：
J. Paul
中科院分区：
文献类型：
--
作者：
J. Paul
提出了一种鲁棒的网格优化方法，该方法直接强制所产生的变形保持方向。受数学弹性的启发，网格变形的能量泛函可以与超弹性材料的储能泛函相关。在变形梯度的主不变量中制定泛函允许对所产生的变形进行细粒度控制。提出了求解非凸高度非线性系统的方法。针对现有预条件子的不足，提出了一种基于偏微分方程的预条件子。
A robust mesh optimisation method is presented that directly enforces the resulting deformation to be orientation preserving. Motivated by aspects from mathematical elasticity, the energy functional of the mesh deformation can be related to a stored‐energy functional of a hyperelastic material. Formulating the functional in the principal invariants of the deformation gradient allows fine‐grained control over the resulting deformation. Solution techniques for the arising nonconvex and highly nonlinear system are presented. As existing preconditioners are not sufficient, a partial differential equation–based preconditioner is developed.