In this talk, I will present a novel numerical approach based on minimizing movement (also known as JKO) schemes for a class of gradient flows arising widely in applications in material science and biology such as porous medium, tumor growth, phase separation, crystal defects migration, surface-diffusion-driven dynamics. By leveraging the underlying variational structure and its intrinsic connection to optimal transport, we construct structure-preserving fully discrete JKO scheme that ends up with a series of linearly constrained convex optimization problems, which can be solved by tailored primal dual operator splitting methods. Our method has built-in strictly positivity or bounds preserving, mass conservation, and entropy decreasing properties, and overcomes stability issue due to the strong nonlinearity and degeneracy. This JKO framework can be extended to cross-diffusion and mixed-metric gradient flow systems. I will show a suite of simulation examples to demonstrate the effectiveness and applicability of our approach.

报告人简介：魏朝祯，电子科技大学校“百人计划”特聘研究员，四川省特聘青年专家，博士生导师。本科毕业于四川大学，博士毕业于美国纽约州立大学水牛城分校，先后于香港科技大学赛马会高等研究院、美国伍斯特理工学院担任博士后学者。从事数学与材料学交叉领域的研究，主要研究薄膜材料生长、晶体缺陷动力学、生物组织演化等材料界面问题的多尺度可计算建模、以及相关非线性梯度流的保结构变分格式与高效优化算法，代表性工作发表在PNAS,FoCM,SINUM,SIAP,JMPS,CMAME等权威期刊，主持与参加国家自然科学基金面上项目和重点项目。