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. The related fundamental methods belong to the family of isogeometric analysis.
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.
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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.
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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.
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