摘要
针对系统级封装应用时谐Maxwell方程离散系统求解中单一算法无法对所有算例取得最优性能,以及给定算例难以确定最优算法的问题,提出一种基于实测的预条件算法自适应策略。首先,结合当前该类应用普遍采用的加性Schwarz区域分解算法(ASM)和辅助子空间Maxwell算法(AMS),提出一种组合预条件算法,扩充了当前该类系统的可行算法空间。在此基础上,针对可行算法空间,在每个算例求解之前,基于对每个算法的实际测试,选择其中最优的算法用于迭代过程的求解。来自包括3个实际模型共6个典型算例的数值实验表明:该自适应策略可以取得接近现有算法空间中最优算法的性能,相对于算法空间的任意单一算法,其整体求解效率较高,具有较大的实用性和应用潜力。
We address the issue that a single preconditioner cannot achieve optimal performance for all test problems in solving the discrete system for time-harmonic Maxwell equations in system-in-package(SiP)applications,and it is always difficult to determine the optimal algorithm for a given test case.We propose an adaptive strategy of preconditioning algorithms based on real-time measurements.Firstly,we propose a combined algorithm(COM)which orderly utilizes the Additive Schwarz method(ASM)and Auxiliary Maxwell method(AMS),expanding the set of feasible algorithms for current systems.Then for the iterative process of solving a test case,the optimal algorithm is selected based on real-time measuring of each algorithm in the feasible algorithm space.Numerical experiments including six typical test cases from three different application problems show that this adaptive strategy can achieve performance mostly close to the optimal algorithm in the existing algorithm space.Compared to any other single algorithm,it has the highest overall computational efficiency,which implies its significant practicality and application potential.
作者
邓蕴桐
胡少亮
徐小文
DENG Yuntong;HU Shaoliang;XU Xiaowen(Graduate School of China Academy of Engineering Physics,Beijing 100088,China;Institute of Applied Physics and Computational Mathematics,Beijing 100094,China;Software Center for High Performance Numerical Simulation,China Academy of Engineering Physics,Beijing 100088,China)
出处
《计算物理》
北大核心
2025年第4期381-390,共10页
Chinese Journal of Computational Physics
基金
国家重点研发计划(2023YFB3001605)
国防基础科学挑战专题项目(TZZT2019)资助。
