16. Parallel Iterative Solution of Large Sparse Linear Equation Systems on the Intel MIC Architecture

Many important scientific, engineering, and smart city applications require solving large sparse linear equation systems. The numerical methods for solving linear equations can be categorised into direct methods and iterative methods. Jacobi method is one of the iterative solvers that has been widely used due to its simplicity and efficiency. Its performance is affected by factors including the storage format, the specific computational algorithm, and its implementation. While the performance of Jacobi has been studied extensively on conventional CPU architectures, research on its performance on emerging architectures, such as the Intel Many Integrated Core (MIC) architecture, is still in its infancy. In this chapter, we investigate the performance of parallel implementations of the Jacobi method on Knights Corner (KNC), the first generation of the Intel MIC architectures. We implement Jacobi with two storage formats, Compressed Sparse Row (CSR) and Modified Sparse Row (MSR), and measure their performance in terms of execution time, offloading time, and speedup. We report results of sparse matrices with over 28 million rows and 640 million non-zero elements acquired from 13 diverse application domains. The experimental results show that our Jacobi parallel implementation on MIC achieves speedups of up to 27.75× compared to the sequential implementation. It also delivers a speedup of up to 3.81× compared to a powerful node comprising 24 cores in two Intel Xeon E5-2695v2 processors.