论文标题
使用增量近似能量功能
Non-convex, ringing-free, FFT-accelerated solver using an incremental approximate energy functional
论文作者
论文摘要
尽管很容易发作伪像，但已经开发了傅立叶加速的微机械均质化并应用于各种问题。此外，大多数适用于FFT加速方案的傅立叶加速求解器仅适用于凸问题。我们在这里介绍了一种允许在FFT加速方案中采用现代高效和非凸位迭代求解器，例如信任区域求解器或LBFG。这些求解器需要以其标准形式的明确能量功能。我们开发了一个修改的信任区域求解器，能够处理非凸小机械均质化问题，例如使用大约增量能量功能的连续损伤。我们将开发的求解器用作无环FFT加速解决方案方案的求解器，即具有有限元离散化的投影方案。
Fourier-accelerated micromechanical homogenization has been developed and applied to a variety of problems, despite being prone to ringing artifacts. In addition, the majority of Fourier-accelerated solvers applied to FFT-accelerated schemes only apply to convex problems. We here introduce a that allows to employ modern efficient and non-convex iterative solvers, such as trust-region solvers or LBFGS in a FFT-accelerated scheme. These solvers need the explicit energy functional of the system in their standard form. We develop a modified trust region solver, capable of handling non-convex micromechanical homogenization problems such as continuum damage employing the approximate incremental energy functional. We use the developed solver as the solver of a ringing-free FFT-accelerated solution scheme, namely the projection based scheme with finite element discretization.
