On the morning of October 10, Prof. Qing Cheng, Distinguished Researcher of School of Mathematical Sciences, Tongji University, was invited to give a lecture entitled: Highly efficient and accurate algorithms for constrained PDEs-Physical constraints preserving algorithms via Lagrange multiplier approach. The presentation was moderated by Ms. Shao Wenting.

Reporter Introduction:Qing Cheng, Ph.D., Distinguished Researcher, School of Mathematical Sciences, Tongji University, Ph.D. Graduated from Xiamen University in 2018, his research interests include numerical solution of partial differential equations, spectral methods, computational fluid dynamics, computational biology, and computational materials science, etc. He has been working in the field of computational materials science for the past five years. He has published nearly 20 papers in reputed international journals in the past five years, including 2 ESI highly cited papers. He has been selected for the Shanghai High-level Talent Program, and has presided over and participated in several National Natural Science Foundation of China (NSFC), US Natural Science Foundation of China (NSFC), and US Air Force Scientific Research Fund.

In this presentation, Prof. Cheng introduces a novel numerical solution method for solving a class of partial differential equations with physical properties, which maintains the physical properties while the algorithm achieves high accuracy and structural conservation. In particular, Prof. Cheng gave a detailed explanation on the problems of preserving positive bounds, energy dissipation, and the conservation of the modulus of a vector function. The core part of the report lies in the introduction of constraints for constant deformation of the equations using the Lagrange multiplier method, and the discrete format in the time direction is divided into two steps: prediction and correction, and the numerical solution is realized to satisfy the physical properties in the correction process. Finally, sufficient numerical results are given to illustrate the validity of the algorithm, an error analysis is given, and the numerical simulation results are in agreement with the experimental data.

Through the report of Prof. Cheng, we further realized the important application of Lagrange multiplier method in solving a class of partial differential equations with physical properties. After the presentation, some teachers and students had an in-depth exchange and discussion with Prof. Cheng.