- 有限元方法 Finite Element Methods, including conforming, nonconforming and hybrid-mixed finite element methods for solving second and fourth order, linear and nonlinear problems. Finite element methods for problems with singularities and problems on unbounded domains are also studied.
- 域分解方法 Domain Decomposition Methods. Based on the finite element discretization and conjugate gradient iteration we consider preconditioners for various kinds of problems - selfadjoint or non-selfadjoint, linear or nonlinear.
- 網格生成 Grid Generation. We develop automatic grid generation techniques for arbitrary domains using quadrilateral or triangle meshes. Applications include the tidal analysis of harbors and computer aided geometric design.
- 計算流體動力學 Computational Fluid Dynamics, including numerical methods for incompressible and compressible flows, which are governed by linear or nonlinear partial differential equations.
- 計算生物力學Computational Bio-Mechanics. Numerical methods have been developed for the mechanics and lubrication of the normal articulating joint, the load and deformational behavior of hydrated soft tissues such as articular cartilage, and meniscus and intervertebral discs.
- 譜方法 Spectral Methods. Mainly focusing on its application to computational fluid dynamics, and its application for solving problems in unbounded domain.
- 高維積分計算 Multidimensional Quadrature. We have established new error bounds for quasi-Monte Carlo methods using reproducing kernel Hilbert space techniques.
- 優化算法 Optimization, involving both theoretical and numerical aspects. The main research areas are unconstrained and constrained optimization, global optimization and large scale optimization.
- 優化控制 Optimal Control, mainly focusing on discrete-time nonlinear systems. Recent studies include nonlinear and linear optimal control and general multiobjective nonlinear control.
- 圖像處理 Image Processing, including image restoration, pattern recognition and image coding.
- 神經網絡 Neural Networks, with applications to financial analysis, image processing and graph theory.
- 並行計算 Parallel Computing. This research is concentrated on the development of parallel methodologies for large scale optimization, optimal control and numerical solutions for partial differential equations.
Prof. Zhu is an IMS Fellow and director of the University's Statistics Research and Consultancy Centre (SRCC).
- the International Symposium on Multivariate Analysis and Its Applications, March 1992
- the International Workshop on Quasi-Monte Carlo Methods and Their Applications, December 1995, and
- the International Symposium on Contemporary Multivariate Analysis and Its Applications, May 19-22, 1997
- symposium on Theory of The Uniform Design and Its Applications, October 26-29, 1999
- Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific computing, November 27 - December 1, 2000
- International Workshop on Applied Mathematics and Statistics, December 16, 2004
- International Conference on Statistics, June 20-24, 2005
- 多元分析 Multivariate Analysis, including inference, elliptically contoured distributions and tests for mulitivariate symmetry and normality.
- 數論或擬蒙特卡羅方法 Number-Theoretic or Quasi-Monte Carlo Methods, generating low discrepancy sequences and studying their applications to experimental design and inference.
- 實驗設計 Experimental design, developing theory of the uniform design and its applications, exploring relationships among the uniform, orthogonal and optimal designs.
- 統計計算 Statistical Computing, including multidimensional statistical integrals, Gibbs sampling and neural networks.
- 生存分析 Survival Analysis, including the Cox proportional hazards model, multivariate survival data and interval-censored data.
- 線性模型 Linear Models, including non-normal error inference with intra-correlation and designs of experiments.
- 空間統計 Spatial Statistics, including statistics for point processes and random sets and methods or edge-correction.
- 應用概率 Applied Probability, including stochastic geometry, random processes, and probabilistic modeling of molecular mechanisms in biology.
- 數據挖掘與生物信息學 Data mining and Bioinformatics in Chinese medicine and Chemistry, including development of new methods in data mining, microarray data analysis, repeatability and reproducibility of Chinese medicine.
- 算法設計 Algorithm Design, including linear, super-linear, and combinatorial algorithm design for sorting, transformations and suffix array constructions.
- 帶寬最小化問題 Bandwidth minimization problem, including bounds of bandwidth on graphs with small number of cycles; effects on bandwidth after graph operations such as adding edges, merging vertices, or sub-division; cyclic bandwidth; and characterization of graphs with equal bandwidth and cyclic bandwidth.
- 循環色數問題 Circular chromatic number, including the circular chromatic number of some distance graphs; and the exact determination of a class of graphs obtained by a generalization of the construction of Mycielski.
- 著色問題 Coloring problems, including chromatic numbers and/or choice number of plane graphs without certain class of cycles; total vertex-edge coloring; total vertex-face coloring; total edge-face coloring; entire coloring problems and game chromatic numbers. We also work on some related problem such as arboricity or vertex-arboricity problems.
- 距離約束標號 Distance constrained labeling, including lambda2,1-numbers of special graphs and their relationship with other graph parameters; extending labeling of graphs; complexity and algorithms; and Lj,k-labeling.
- 圖的拓撲指數 Topological indices of graphs, including Weiner numbers; Kekulé structures; Hosoya index; Merrifield index; total pi-electron energy of molecular graphs.