Professor Yu’s research has centred on natural boundary reduction, boundary element methods, and numerical methods for partial differential equations in unbounded domains. Under the guidance of Professor Feng Kang, he developed the theory of natural boundary reduction and established the natural boundary element method, including natural integral equations and the associated analysis of their mathematical properties. His work addressed key numerical difficulties in boundary integral equations, including hypersingular kernels, and led to methods for coupling finite and boundary elements and for constructing artificial boundary conditions for problems in unbounded domains. He subsequently developed domain-decomposition algorithms based on natural boundary reduction and contributed to error estimation and adaptive methods for finite and boundary element calculations. His research also extended boundary element techniques to variational inequalities and ill-posed problems. His monographs The Mathematical Theory of Natural Boundary Element Methods and Natural Boundary Integral Method and Its Applications have contributed to the development and dissemination of natural boundary methods in computational mathematics. Together with Professor Houde Han, he received a Second Prize of the National Natural Science Award in 2008 for work on artificial boundary methods and numerical solutions of partial differential equations. He has published more than 120 papers and supervised numerous doctoral students and postdoctoral researchers. Through sustained research, methodological development, and academic mentorship, Professor Yu has contributed to the development of computational mathematics in China and to advances in boundary element theory and numerical methods for partial differential equations.