Dr Hui Zhang from XJTLU’s Department of Applied Mathematics was invited to write a review paper for Acta Numerica in cooperation with Professor Martin Gander from the University of Geneva.

The paper, Schwarz methods by domain truncation, was recently published with Dr Zhang as the corresponding author. In the history of Acta Numerica, only three papers were published in the name of institutions on the Chinese mainland.

Acta Numerica has the highest impact factor of journals in mathematics, which was 11.091 in 2020. It is a top review journal on numerical analysis and scientific computing and only accepts papers written on invitation. The editorial board meets every year to decide on who they will invite, and the invited scholars are those who have made significant contributions to numerical analysis and scientific computing.

Examining assumptions

Dr Zhang says that the paper explains and analyses a new type of domain decomposition method based on those proposed by German mathematician Schwarz in the 19th century (shown on the journal cover).

By integrating domain truncation into Schwarz’s methods, the new method can increase the speed of parallel computing. Parallel computing allows complex problems to be broken down into smaller parts and solved simultaneously.

With its ability to compute wave motion at high speed, the new method has become a hot topic of research in recent years. But Dr Zhang points out that the current understanding of the effectiveness of such computing methods is largely at the empirical level, and there are still a lot of gaps to fill on the theoretical level.

The cover of the journal: Schwarz methods

When asked about the paper’s main contributions, Dr Zhang says: “We examined the different assumptions made by domestic and foreign scholars on domain truncation and Schwartz’s theories. Based on the existing research, we made new observations, raised new questions, and pointed out new ways to understand and develop the computation methods.”

The journey

The whole process, from writing the first draft of the paper to publishing it, took about two years. Dr Zhang says he’s grateful to XJTLU for providing an inclusive research environment in which academics are encouraged to conduct research based on their interests.

Dr Zhang also says that as well as paying attention to academics’ research output, XJTLU also recognises their contribution to teaching, enabling academics to do well in teaching and research.

“Due to the pandemic, I’ve spent a lot of time working on online and hybrid teaching. I gave lectures for four different courses within two years while being the leading lecturer in two of them. I want to express my sincere gratitude for the research environment provided by XJTLU and the computing resources offered by the Laboratory for Intelligent Computing and Financial Technology for our research,” says Dr Zhang.

About the researcher

Dr Zhang joined XJTLU’s Department of Mathematics in September 2019. He completed his undergraduate, postgraduate, and doctoral education at Xi’an Jiaotong University and spent five years at the University of Geneva as a postdoctoral researcher.

With his previous research on domain decomposition methods published in SIAM Review, a first-class journal presenting research results on computing and applied mathematics, Dr Zhang will continue to work on domain decomposition and parallel computing in the future.

The paper, Schwarz methods by domain truncation, is published in Acta Numerica and can be read here.

By Luyao Wang
Edited by Arushi Agrawal and Patricia Pieterse
Translated by Xueqi Wang

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