Firstly, a review is given by classifying the existing fast algorithms for solving large-scale discrete linear systems arising from the Multi-Group Radiation Diffusion (MGRD) equations. Secondly, based on our recent work on parallel algebraic multigrid (AMG), two preconditioning algorithms and related theoretical frameworks are developed on a higher level. One is the approximate Schur complement type based on physical quantities and the other is the combined type based on physical and algebraic features, and the relevant components of these works are portrayed within these frameworks. Based on the above framework, a approximate Schur complement preconditioner with fundamental approximation property and low computational complexity is designed, and the corresponding spectral equivalence theory is established. Numerical experiments show that the new preconditioner has better robustness and computational efficiency. Finally, several issues that need to be further addressed are presented.

To improve the robustness and convergence speed of the Newton method and Picard method of solving radiation diffusion equations, several work is introduced when they are used to solve the three temperature radiation diffusion equation system, including the selection of initial iteration value, the treatment of physical constraints in the iterative process, the combination of the Picard iterative method and Anderson acceleration, and the improvement of Anderson acceleration method. By applying application-driven treatments and improvements, the two methods can be used to solve the nonlinear radiation diffusion equations.

To address the high computational complexity of sparse linear solvers caused by complex physical characteristics in practical applications, this paper presents a unified framework for feature-modified preconditioning algorithms. By refining the algebraic features affecting the efficiency from physical characteristics and combining multilevel feature analysis, we construct feature-modified components. The effectiveness of this framework is demonstrated through several typical feature-modified preconditioning algorithms and their application results.

Aiming at the lack of reusability and portability in the manual optimization of software, we propose and implement SEMD, a cross-platform automatic performance optimization programming tool for numerical simulation software. It abstracts numerical computing loop programming using high-level semantics, which is prevalent in the field of numerical simulation, completely shielding underlying hardware features and performance optimization implementations. Therefore, any numerical subroutines written based on SEMD can attain automatic cross-platform performance portability. Our tests demonstrate that SEMD's performance optimization effects exceed those of comparable products on three different processor architectures, including X86, ARM and GPU. Furthermore, SEMD has been successfully applied in the development of four real numerical simulation software programs in the fields of structure, fluid, and electromagnetic, resulting in an average performance improvement of 164% on hotspot subroutines.

2022年12月12日, 第八届高性能计算中间件技术研讨会(HPCMid22)成功召开。HPCMid (会议网址: http://www.caep-scns.ac.cn/HPCMid.php)每年举办一次, 面向科学与工程计算数值模拟应用在当前及下一代超级计算机上面临的挑战, 围绕高性能计算中间件关键技术, 邀请相关学者报告最新研究进展并探讨未来发展趋势。第八届研讨会以"适配新型体系结构的性能优化技术"为主题, 聚焦后摩尔时代新型体系结构为科学与工程计算带来的机遇与挑战, 探讨新型体系结构下可移植性能优化技术的发展趋势。本届研讨会的专家座谈(Panel Session)环节由莫则尧研究员和徐小文研究员共同主持, 邀请了王龙、刘杰、谭光明、刘伟峰、喻之斌5位来自高校、科研院所、企业的专家围绕"性能优化: 个性vs共性"这一主题开展了深入的讨论与交流, 翟季冬、杨海龙等多位专家也参与了讨论。专家们针对性能优化技术的研究现状与发展趋势、面临的问题与挑战以及人才培养等方面发表了许多有启发性的观点。《计算物理》编辑部特将本次讨论整理后发表, 以飨读者。限于篇幅, 略有删节。