论文标题
自动 - 自动分化GPU的通用标准材料
AutoMat -- Automatic Differentiation for Generalized Standard Materials on GPUs
论文作者
论文摘要
我们提出了一种评估通用标准材料的通用方法，该方法极大地简化了材料法实施过程。通过自动分化和数值集成方案，自动机将实施工作减少到两个潜在功能。通过将自动机移至GPU，我们将性能差距缩小到常规评估例程，并详细说明表达式水平反向自动分化的反向模式及其扩展到二阶导数可以在CUDA内核中应用。我们通过将自动机集成到Moulinec和Suquet的基于FFT的均质化方案中，并讨论使用自动机对运行时和解决方案的准确性进行弹性 - 粘膜塑形示例，并讨论使用自动机对运行时和解决方案的准确性的好处。
We propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example.
