基于CUDA的多导体传输线方程迭代QR分解的并行算法

Parallelization of QR Decomposition Algorithm in Multiconductor Transmission Line Equation Based on CUDA

摘要: 基于电报方程发展的多导体传输线方程，随着导线的数量和复杂性的增加，导体的特征阻抗矩阵和导纳矩阵以及加上外部激励分布源向量的维数变得很大，从而使得求解由多导体传输线组成的电缆上的电压或电流的计算量和内存开销很大。本文考虑了有损导体和有损介质的一般情况，给出了基于CUDA的特征阻抗矩阵和导纳矩阵的迭代QR方法的并行化方法。为了证明我们的方法的有效性，我们评估了三种不同类型的实现类型：传统的单线程C++，使用OpenMP加速的C++和NvidiaCUDA。评估结果表明，当问题的维度达到数百个时，CUDA的GPU实现明显比单线程C++和OpenMP的CPU实现更有效。

Abstract: Based on the multi-conductor transmission line equation developed from the telegraph equation, as the number and complexity increase, the characteristic impedance matrix and conduction matrix and the dimension of the external excitation distribution source vector become large, resulting in the computational amount and memory overhead of solving the voltage or current on the cable composed of multi-conductor transmission lines. In this paper, we consider the general case of lossy conductor and lossy dielectric, and present the parallelization of iterative QR method for a matrix multiplied by the characteristic impedance matrix and admittance matrix based on CUDA. To prove the effectiveness of our method, we evaluate three different types of implementations: traditional single-thread C++, C++ accelerated with OpenMP and NvidiaCUDA. The evaluation result suggests that when the dimensions of problem reach hundreds, GPU implementation of CUDA is significantly more effective than CPU implementations of single-thread C++ and OpenMP.