An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems
An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems
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DOI：
10.1016/j.cma.2016.11.004
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发表时间：
2017-03
影响因子：
7.2
通讯作者：
M. Schneider
中科院分区：
文献类型：
--
作者：
M. Schneider
建立在先前建立的等价的基本方案的Moulinec-Suquet的基于FFT的计算均匀化方法与梯度下降法，这项工作涉及的影响Nesterov的快速梯度法的计算均匀化的背景下。与具有中等对比度的线性问题的基本方案相比，Nesterov的方法显着提高了速度，并且与数字岩石物理和（小应变）弹塑性问题的（牛顿）共轭梯度（CG）方法相比，Nesterov的方法具有优势。我们提出了一个有效的实现需要两倍的基本方案的存储，但只有一半的CG方法的存储。
Building upon the previously established equivalence of the basic scheme of Moulinec–Suquet’s FFT-based computational homogenization method with a gradient descent method, this work concerns the impact of the fast gradient method of Nesterov in the context of computational homogenization. Nesterov’s method leads to a significant speed up compared to the basic scheme for linear problems with moderate contrast, and compares favorably to the (Newton-)conjugate gradient (CG) method for problems in digital rock physics and (small strain) elastoplasticity. We present an efficient implementation requiring twice the storage of the basic scheme, but only half of the storage of the CG method.