Chen's Reaserch Lab

Research Interests

   

Geometric modeling NURBS surface modeling stands as the international standard in conventional industrial product design. However, its local subdivision capability often incurs redundant computations owing to its tensor product structure, leading to limitations in achieving satisfactory local subdivision during NURBS surface modeling. In contrast, splines on T-mesh represent a distinct class of splines characterized by their local subdivision properties. Notably, the bicubic first-order smooth splines defined on the hierarchical T-mesh by our research group, referred to as "Chinese splines" by the international community, exhibit favorable attributes for adaptively addressing geometric modeling challenges. Our research group is particularly focused on exploring spline functions on T-mesh, with emphasis on several key aspects: determining the dimension and stability of spline spaces on T-mesh, constructing base functions, applying geometric analysis techniques such as curve and surface fitting, quasi-interpolation, and addressing associated challenges such as various matrix assembly problems.

   

IsoGeometric Analysis (IGA) Traditional industrial manufacturing processes typically entail three sequential stages: computer-aided design (CAD), computer-aided engineering (CAE), and computer-aided manufacturing (CAM). Notably, the representation of geometric models diverges between the initial CAD and subsequent CAE stages. While spline surfaces commonly characterize geometric models in CAD, meshes are typically employed in CAE, necessitating significant time expenditure in the conversion between these disparate representations. Isogeometric analysis, introduced by Thomas J. R. Hughes, a distinguished member of the American Academy of Sciences, in 2005, offers a numerical simulation method founded on direct finite element analysis utilizing geometric models. Its fundamental premise revolves around integrating CAD and CAE processes seamlessly. The core concept involves directly applying spline representations from the CAD stage to the CAE analysis phase. In recent years, our research group has undertaken significant investigations in IsoGeometric Analysis (IGA), encompassing several key aspects: developing splines optimized for analysis, spline parameterization, addressing matrix assembly challenges, and conducting error analyses pertinent to geometric analysis.

   

Topology optimization Topology optimization is a computational technique employed in engineering design to determine the optimal distribution of material within a given design space, subject to specified constraints, in order to achieve desired performance objectives. Its applications span various fields, including mechanical, aerospace, civil, and biomedical engineering, among others. For instance, in structural design, topology optimization can help in creating lightweight and efficient structures, reducing material and manufacturing costs while maintaining or improving structural performance. In the aerospace industry, it aids in designing aircraft components with enhanced strength-to-weight ratios, contributing to fuel efficiency and overall performance.

   

Life science big data analysis With the advancement of biotechnologies, such as single-cell sequencing and spatial multi-omics techniques, a vast amount of data in the field of life sciences requires further interpretation. Our research group primarily employs tools, such as sparse optimization, low-rank approximation, deep learning, and others, to develop appropriate analytical methods. These methods aim to assist biologists in extracting and interpreting the mathematical principles underlying the data and corresponding biological processes. Our research outcomes are poised to accelerate progress in life science research, particularly in areas such as cancer, and contribute significantly to the advancement of precision medicine.