Overview
My research focuses on developing novel simulation-aware geometric modeling techniques for free-form, complex-shaped surfaces/volumes, motivated to address grand challenges in modern engineering design/optimization, computational science, and additive manufacturing. The related fundamental methods belong to the family of isogeometric analysis.
Highlights
Seamless integration of design, simulation and optimization
In this work, we exploit the very merit of isogeometric analysis in design of complex-shaped engineering shells, namely, computer-aided design and computer simulation are performed on the same platform without the time-consuming data exchange. This integration is possible only when simulation-required properties, e.g., expected convergence, are also built in the basis used for design. In the meanwhile, adaptivity is indispensable to locally edit a geometric model in a specific region of interest, so it is also supported in this work.
References
Analysis-aware true-volume modeling
In this work, we build smooth volume models that can be directly used in computer simulation. Such a model not only describes the shape of an object, but also discretizes its interior domain in a smooth manner, thus immediately suitable for simulations based on "bulk" geometries. Moreover, as all the simulation-related properties are already built in such geometric models, it allows downstream simulations to follow a standard procedure, and thus it is of great ease to link with commercial finite element packages such as LS-DYNA.
References
Metabolic material transport in neurons
In this work, we study how traffic of material transport is routed and balanced in a complex geometry of a neurite network. A detailed knowledge through simulation of the traffic phenomenon is crucial to elucidating how neurons operate their material transport systems and, more importantly, to understanding and controlling the structure and function of neurons.
References
Highly efficient image registration
In this work, we develop an advanced image registration technique to reveal detailed intermediate states between the two acquisition of two images, a source image representing the initial state and a target image representing the final state. Registration involves spatially aligning the two images and finding a correspondence such that monitoring a continuous change is possible. In particular, we apply the technique to monitor the changes after surgical removal of a brain tumor.
Reference
“Adaptive FEM-Based Nonrigid Image Registration Using Truncated Hierarchical B-splines”. [link]
Adaptivity with high-fidelity geometries
In this work, we explore to enable adaptivity on smooth, complex geometries. While objects in engineering and biomedicine are often complex-shaped, developing adaptivity schemes on such geometries is a challenge especially when a smooth representation is involved. Adaptivity, via local mesh refinement, is designed to locally and automatically "adapt" to where large error is expected. In this way, adaptivity can significantly enhance numerical accuracy without increasing much computational burden. This is especially beneficial in large-scale simulation that needs an enormous number of degrees of freedom.
References