An Incremental SVD Method for Non-Fickian Flows in Porous Media: Addressing Storage and Computational Challenges

报告题目：An Incremental SVD Method for Non-Fickian Flows in Porous Media: Addressing Storage and Computational Challenges

报告人： 陈刚 教授  四川大学

报告时间：2026年4月16日上午9:30-10:30

报告地点：红瓦楼726

报告内容简介：It is well known that the numerical solution of the Non-Fickian flows at the current stage depends on all previous time instances. Consequently, the storage requirement increases linearly, while the computational complexity grows quadratically with the number of time steps. This presents a significant challenge for numerical simulations, and to the best of our knowledge, it remains an unresolved issue. In this talk, we assume that the solution data exhibits approximate low rank. Here, we present a memory-free algorithm, based on the incremental SVD technique, that exhibits only linear growth in computational complexity as the number of time steps increases. We prove that the error between the solutions generated by the conventional algorithm and our innovative approach lies within the scope of machine error. Numerical experiments are showed to confirm accuracy and efficiency gains in terms of both memory usage and computational expenses.

报告人简介：陈刚，四川大学教授，博士生导师，四川大学双百人。2006年9月-2017年6月在四川大学进行本科、硕士、博士的学习，2017年7月-2019年6月在电子科技大学从事博士后工作，期间访问美国密苏里科技大学、明尼苏达大学、特拉华大学。主要研究内容为微分方程数值解。主持国家自然科学基金面上项目、青年科学基金项目（B 类）、青年科学基金项目（C 类）各一项。

报告邀请人：盛长滔