基于改进LU-SGS的GPU加速隐式动力学无网格方法
GPU Accelerated Implicit Kinetic Meshfree Method based on Modified LU-SGS
AI总结：
本文提出一种基于改进LU-SGS的GPU加速隐式动力学无网格方法，通过算法微分精确计算雅可比向量乘积，在二维无粘流动测试中相比近似计算和显式求解器具有更高计算效率和更好收敛性。
摘要：
本报告介绍了使用改进的LU-SGS算法对隐式动力学无网格方法进行GPU加速。该无网格格式基于最小二乘动力学迎风方法（LSKUM）。在现有的用于动力学无网格方法的免矩阵LU-SGS方法中，分裂通量雅可比矩阵与守恒变量增量的乘积通过分裂通量的增量来近似。在我们改进的LU-SGS方法中，雅可比向量乘积使用算法微分（AD）精确计算。具有雅可比向量乘积精确计算和近似计算的隐式GPU求解器被应用于二维无粘流动的标准测试算例。数值结果表明，与采用雅可比向量乘积近似的求解器相比，采用雅可比向量乘积精确计算的GPU求解器计算效率更高，并具有更好的收敛速率。文中给出了基准测试，以评估隐式GPU求解器相对于显式GPU求解器和隐式串行LSKUM求解器的性能。
英文摘要：
This report presents the GPU acceleration of implicit kinetic meshfree methods using modified LU-SGS algorithms. The meshfree scheme is based on the least squares kinetic upwind method (LSKUM). In the existing matrix-free LU-SGS approaches for kinetic meshfree methods, the products of split flux Jacobians and increments in conserved vectors are approximated by increments in the split fluxes. In our modified LU-SGS approach, the Jacobian vector products are computed exactly using algorithmic differentiation (AD). The implicit GPU solvers with exact and approximate computation of the Jacobian vector products are applied to the standard test cases for two-dimensional inviscid flows. Numerical results have shown that the GPU solvers with the exact computation of the Jacobian vector products are computationally more efficient and yield better convergence rates than the solvers with approximations to the Jacobian vector products. Benchmarks are presented to assess the performance of implicit GPU solvers compared to the explicit GPU solver and the implicit serial LSKUM solver.
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