中国科学院数学与系统科学研究院

科研进展与学术交流报告会

（第99期）

报告人一：徐劼 副研究员（计算数学与科学工程计算研究所）

题目一：Quasi-entropy

摘要：Liquid crystals are featured by local anisotropy usually described by angular moment tensors. When the molecule is non-axisymmetric, the free energy and dynamics both involve the maximum entropy state that is too complicated for computation and analysis. The price paid by the complexity does not match the outcome in revealing the physical characteristics and mathematical structures.
The speaker proposes an elementary-function substitution of the original entropy (by maximum entropy state), called quasi-entropy, aiming to resolve the above problems. The quasi-entropy maintains the essential properties of the original entropy: strict convexity; positive-definiteness of covariance matrix; rotational invariance; consistency in symmetry reduction. Homogeneous phase diagrams of several representative cases match well with classical results. We discuss further applications in modeling and computation, including the derivation of biaxial frame hydrodynamics and physical range preserving numerical schemes. 
We would also like to put forward several mathematical problems arising in the models, not limited to the following aspects: 1) The domain of quasi-entropy; 2) The classification of stationary points of the bulk energy (which is now certain elementary function but turns out to be nontrivial); 3) The analysis of hydrodynamics.

报告人二：刘勇 副研究员（计算数学与科学工程计算研究所）

题目二： 椭圆界面问题的高阶自适应非拟合有限元方法

摘要：在具有一般形状的域上定义的界面问题或偏微分方程（PDEs）通常涉及复杂的几何结构。高阶非拟合有限元方法（UFEM）为这类问题提供了一种有吸引力的解决方案，因为它避免了生成贴体网格的耗时过程。然而，UFEM的主要挑战是所谓的小切割单元问题，这显著影响了代数系统的稳定性和条件数。本报告以椭圆界面问题为例，介绍我们在高阶自适应非拟合有限元方面的进展。

时  间：2025.3.14(星期五), 10:40-12:00

地  点：南楼204会议室/腾讯会议907-5908-5643

报告会视频

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