大规模三角线性方程的高效求解

大规模三角线性方程求解是科学与工程应用中重要的计算核心,受限于处理器的缓存容量和结构设计,其在CPU和GPU等平台上的计算效率不高。大规模三角线性方程的分块求解中,矩阵乘是主要运算,其计算效率对提升三角线性方程求解的计算效率至关重要。以矩阵乘计算效率较高的矩阵乘协处理器为计算平台,针对其结构特点提出了矩阵乘协处理器上大规模三角线性方程分块求解的实现方法和性能分析模型。实验结果表明,矩阵乘协处理器上大规模三角线性方程求解的计算效率最高可达85.9%,其实际性能和资源利用率分别为同等工艺下GPU的2.42倍和10.72倍。

An efficient solver for large-scale triangular linear equations

Large scale triangular solver is an important computational kernel in scientific and engineering applications. However, execution of this kernel is not efficient on existing CPU and GPU platforms, due to limited cache capacity and the underlying problems of the architecture design. In the block solving of large-scale triangular linear equations, matrix multiplication is the main operation and its computational efficiency is crucial for improving the computational efficiency of solving triangular linear equations. Taking advantage of the high computation efficiency of the matrix multiplication coprocessor as the computing platform, and according its architectural features, we propose a block solving method and a performance analysis model of large-scale triangular linear equations on the matrix multiplication coprocessor. Experimental results show that a highly-efficient large scale triangular solver can be implemented on the matrix multiplication coprocessor with a computational efficiency up to 85.9%. Compared with the GPUs under the same process technology mode, the proposed triangular solver on the coprocessor can achieve 2.42× actual performance and 10.72× resource utilization.