Linear, decoupled and positivity-preserving staggered mesh schemes for general dissipative systems with arbitrary energy distributions

报告题目: Linear, decoupled and positivity-preserving staggered mesh schemes for general dissipative systems with arbitrary energy distributions

报告人：刘争光教授山东师范大学数学与统计学院

报告时间：2025年7月10日下午16:00

报告地点：红瓦楼726

报告内容简介：In this talk,we develop a novel staggered mesh (SM) approach for general nonlinear dissipative systems with arbitrary energy distributions (including cases with known or unknown energy lower bounds). Based on this framework, we propose several second-order semi-discrete schemes that maintain linearity, computational decoupling, and unconditional energy stability. Firstly, for dissipative systems with known energy lower bounds, we introduce a positive auxiliary variable V(t) to substitute the total energy functional, subsequently discretizing it on staggered temporal meshes to ensure that the energy remains non-increasing regardless of the size of time step. The newly developed schemes achieve full computational decoupling, maintaining essentially the same computational expense as conventional implicit-explicit methods while demonstrating significantly improved accuracy. Furthermore, we rigorously establish the positivity preservation of the discrete variable V^{n+1/2} which is a crucial property ensuring numerical stability and accuracy. Theoretical analysis confirms second-order temporal convergence for the proposed SM scheme. Secondly, for dissipative systems lacking well-defined energy lower bounds, we devise an alternative auxiliary variable formulation and extend the SM framework to maintain unconditional energy stability while preserving numerical effectiveness and accuracy. Finally, comprehensive numerical experiments, including benchmark problem simulations, validate the proposed schemes' efficacy and demonstrate their superior performance characteristics.

报告人简介：刘争光，教授，博士生导师，山东省泰山学者青年专家，省优青，山东师范大学东岳学者。2013-2018年山东大学计算数学专业博士。2017-2018年赴美国普渡大学访问。近年来致力于复杂梯度流模型的无条件能量稳定算法研究，获得一批应用基础性研究成果。在国际权威期刊“SIAM J Sci Comput”、“Math Comp”、 “J Comput Phys”、“Comput Methods Appl Mech Engrg”、“J Sci Comput”等发表SCI收录论文40余篇；主持国家自然科学基金，中国博士后科学基金、山东省自然科学优秀青年项目、面上项目、青年项目等。

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