He is currently Director of KAUST Innovation Hub in Shenzhen, Professor of Applied Mathematics and Computational Sciences at King Abdullah University of Science and Technology, Director of KAUST-SRIBD Joint Lab for Scientific Computing and Machine Learning and Verne M. Willaman Professor in the Department of Mathematics at the Pennsylvania State University, University Park.

[2] In 2011, Xu was honored as a Fellow of the Society for Industrial and Applied Mathematics (SIAM)[3] for his outstanding contributions to the theory and applications of multilevel and adaptive numerical methods.

In 1995, Xu's research accomplishments were recognized with the first Feng Kang Prize for Scientific Computing[5] from the Chinese Academy of Sciences.

In honor of his achievements in computational mathematics research and teaching, he received the Humboldt Award for Senior U.S. Scientists in 2005.

In 2019, Xu was named a Fellow of the American Association for the Advancement of Science(AAAS).