On November 9, 2018, Chen Zhiming, Academician of CAS and researcher of Academy of Mathematics and Systems Science, Chinese Academy of Sciences gave a lecture about Mathematical Methods in computational Electromagnetics in Peiyang Maths Forum presided over by Sun Xiaotao, dean of School of Mathematics which was held in the lecture hall of the administrative building of Peiyang Park Campus.
Chen Zhiming talked from Coulomb's Law and Divergence Theorem to Maxwell's Equations, and then he talked about computational electromagnetics is derived from Maxwell's Equations. Through demonstration of electromagnetic field modeling, he derived the development history and research status of some mathematical methods in calculation.
Chen Zhiming firstly introduced development history and establishment process of finite element method. He mentioned that finite element method originated from Galerkin method and pointed out that finite element method was an important method in mathematics which had been widely used. Priori estimate showed shortcomings of traditional finite element method in convergence speed, and then posteriori error estimates and adaptive finite element method gradually embarked on historical stage.
Next, Chen Zhiming illustrated how mathematics played an important role in solving real problems through giving examples of eddy current and electromagnetic field calculation.
Finally, Chen Zhiming concluded that solution of mathematical model was not equal to solution of practical problems, and then expounded that uniqueness of solution in mathematical thinking is very important. He pointed out that scientific and engineering calculation is the third means of human to carry out scientific research.
A freshmen questioned that if a model dose not match the fact, where dose the error come from and from which aspects should it be perfected? Chen Zhiming answered that this might be an error model and it needed to be verified through experiments if it was, or this might be something wrong on calculation with algorithm not accurate enough, so we should first ensure the correctness of algorithm to explore the correctness of modeling when solving problems. Another student questioned that whether AI would exist without computational mathematics. Chen responded with smile that there was no clear and definite link between computational mathematics and AI. Mathematical research concentrated on theoretical issues while AI paid more attention with practical issues. Software is the pillar of AI, and the core of software is algorithm. It also requires us to devote a lot of energy and efforts to breaking through various development constraints. Professor Chen believed that the scientists have been working hard to seek the truth.