題目一：Sharp interface modeling and simulations of two-phase ferrofluid flows.
内容簡介：We propose a novel sharp interface model to describe the behavior of two-phase ferrofluid flows with unmatched densities. The model couples the Navier–Stokes equations for incompressible fluid motion with an advection-reaction equation for the magnetization field, incorporating precise jump conditions at the interface. Utilizing the techniques by Barrett, Garcke, and Nurnberg (BGN), we establish a mathematical relationship between the parameterization of the interface and its mean curvature, enabling an accurate description of the interface geometry and capturing the dynamics at the sharp interface explicitly. To solve the model, we develop a fully discrete backward Euler arbitrary–Lagrangian–Eulerian (ALE) finite element method, enhanced with a specialized mesh velocity governed by a harmonic equation to maintain mesh quality throughout the simulation. Extensive numerical examples are presented to verify the validity of the proposed model, illustrate the accuracy of the numerical scheme, and simulate the benchmark “Rosensweig instability” in both two and three dimensions.
報告人：王冀魯
報告人簡介：哈爾濱工業大學（深圳）教授、博士生導師，國家高層次青年人才，此前為北京計算科學研究中心特聘研究員。王冀魯的研究興趣為偏微分方程數值解，包括關于淺水波方程、多孔介質中不可壓混溶驅動模型、薛定谔方程以及分數階方程的數值方法。主持國家自然科學基金面上項目和深圳市傑出青年研究項目，參與國家自然科學基金重點項目等。
題目二：High-order structure-preserving Runge-Kutta methods for the nonlinear schrodinger equation.
内容簡介：A novel family of high-order structure-preserving methods is proposed for the nonlinear Schrodinger equation. The methods are developed by applying the multiple relaxation idea to the different Runge--Kutta methods. It is shown that the multiple relaxation Runge--Kutta methods can achieve high-order accuracy in time and preserve multiple original invariants at the discrete level. Several numerical experiments are carried out to support the theoretical results and illustrate the effectiveness and efficiency of the proposed methods.
報告人：李東方
報告人簡介：華中科技大學數學與統計學院教授，博導，國家級青年人才。主持國家級課題6項。主要從事微分方程數值解、機器學習和信号處理等領域的研究工作。尤其在微分方程保結構算法和分數階微分方程的高效數值算法和理論上取得一些有意義的進展。相關工作發表在《SIAM. J. Numer. Anal.》，《SIAM. J. Sci. Comput.》、《Math. Comput》、《J. Comp. Phys.》等多個國際著名計算學科SCI期刊上，多篇為高被引論文。
時 間：2025年3月25日（周二）下午18：30開始
地 點：石牌校區南海樓124會議室
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