CPU-GPU混合计算构架在岩土工程有限元分析中的应用

Application of hybrid CPU-GPU computing platform in large-scale geotechnical finite element analysis

计算机技术的快速发展促进了岩土工程数值模拟技术的进步和有限元仿真技术的应用。对于三维有限元建模,有限元离散所获得的线性方程系统规模较大,这些线性方程系统的求解通常支配着整个有限元计算的时间。为了提高有限元求解的效率,需要采用先进的基础迭代算法和高性能计算构架。使用性价比较高的GPU计算硬件对目前流行的预处理Krylov子空间迭代法进行了加速,重点研究了GPU对Krylov子空间迭代过程中矩阵矢量乘积的加速效果。由于预处理迭代方法的计算性能依赖于计算构架,采用数值算例对几种流行的预处理迭代方法在不同计算构架下的计算性能进行了评测,对在不同计算构架下采用何种预处理迭代方法给出了相应的建议。

Rapid developments of computer technology expedite applications of three-dimensional finite element modeling and simulations of practical geotechnical problems.In three-dimensional finite element modeling,the size of linear equations arising from finite element discretization of geotechnical problems is usually very large,and their solutions often dominate the entire finite element computations.To remarkably accelerate the computational speed,the advanced fundamental iterative algorithm and the high-performance computer architecture are needed.In this study,a GPU computer device with high price/performance ratio is adopted to accelerate the preconditioned Krylov subspace iterative method,and attentions are particularly paid to the acceleration effects of GPU on the matrix-vector multiplications.Based on the numerical examples,several popular preconditioned iterative methods are assessed on different computing architectures and some suggestions on how to select the preconditioned iterative methods on different computing platforms are also given.