XHYPRE: a Reliable Parallel Numerical Algorithm Library for Solving Large-Scale Sparse Linear Equations

With the rapid development of supercomputers, large-scale computing has become increasingly widespread in various scientific research and engineering fields. Meanwhile, the precision and efficiency of large-scale floating-point arithmetic have always been a research hotspot in high-performance computing. This paper studies the numerical method to solve large-scale sparse linear equations, in which the accumulation of rounding errors during the solution process leads to inaccurate results, and large-scale data makes the solver produce a long running time. For the above issues, we use error-free transformation technology and mixed-precision ideas to construct a reliable parallel numerical algorithm framework based on HYPRE, which solves large-scale sparse linear equations to improve accuracy and accelerate numerical calculations. Moreover, we illustrate the implementation details of our technique by implementing two cases. One is that we use error-free transformation technology to design high-precision iterative algorithms, such as GMRES, PCG, and BICGSTAB, which reduce rounding errors in the calculation process and make the result more accurate. The other is that we propose a mixed-precision iterative algorithm that utilizes low-precision formats to achieve higher computing power and reduce computing time. Experimental results demonstrate that XHYPRE has higher reliability and effectiveness . Our XHYPRE is on average 1.3x faster than HYPRE and reduces the number of iterations to 87.1% on average.