基于高维线性试验方程的波形松弛方法的无条件线性稳定  

UNCONDITIONALLY LINEAR STABILITY OF WAVEFORM RELAXATION METHODS BASED ON HIGH DIMENSIONAL LINEAR TEST EQUATION

作　　者：范振成 Fan Zhencheng(School of Computer and Big Data,Minjiang University,Fuzhou 350108)

机构地区：[1]闽江学院计算机与大数据学院,福州350108

出　　处：《高等学校计算数学学报》2024年第2期177-192,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：福建省自然科学基金(2021J011031);福建省发树慈善基金会资助研究专项(MFK23013.)。

摘　　要：1引言在芯片(大规模集成电路)设计领域,仿真计算作用重大.描述芯片的数学模型一般是超高维的微分代数方程组,使用诸如线性多步法、Runge-Kutta(RK)法等经典数值方法等求解时,因运算量太大而效果不理想.为了求解这些方程,Lelarasmee等提出了波形松弛(WR)方法[1],它具有并行性和多速率两个优点,与经典方法相比更具优势.The waveform relaxation(WR)method can solve effectively the weakly coupled differential equations with very high dimensions.Many models in practical applications are stiff,hence they need to be solved by the WR methods with very good property of stability such as A-stability.We present the unconditionally linear stability by extending A-stability to the high dimensional test equation,which can help investigate the influence of splitting way on stability of WR methods.In this paper,we obtain some sufficient conditions of the unconditionally linear stability of WR methods which imply that the splitting way is also the key effective factor except underlying methods for stability of WR methods.Lastly,we perform some numerical experiments and the results obtained are consistent with theoretical analysis results.

关 键 词：线性多步法 波形松弛 数学模型 微分代数方程组 线性稳定 经典方法 并行性 线性试验 

分 类 号：O241.8[理学—计算数学]