Ungor_research_teaching - Research and Teaching Statement...

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Unformatted text preview: Research and Teaching Statement Alper ¨ Ung¨or Department of Computer & Information Science & Engineering University of Florida 1 Research Statement My research areas are design and analysis of algorithms , computational geometry , mesh gen- eration , and their applications. Geometric algorithms play a fundamental role in many areas such as scienti c computing , graphics , visualization , computer aided design , computer vision , structural biology , and geographic information systems . The overall goal of my research is to understand the mathematical structure of problems in these areas; and to design, analyze and implement e cient algorithmic solutions with both theoretical bounds and good performance in practice. This enables me to have an inter-disciplinary impact on various scienti c applications. Mesh Generation. A principal component of my research is meshes (triangulations) , which are subdivisions of geometric domains into small and simple elements. Meshes are essential to numer- ical simulations. Two of their key requirements are to ensure that the shape of the mesh elements are of good quality and that the size of the mesh is small. Mesh element quality is critical in determining interpolation error in applications and hence is an important factor in the accuracy of the simulations as well as the convergence speed. Mesh size is also critical because between two meshes with the same quality bound, the one with fewer elements is generally preferred as it implies faster processing by the numerical algorithm in use. In collaboration with many researchers from various institutions 1 , I made a number of signi cant contributions in the mesh generation area. I co-designed the rst time-optimal Delaunay meshing algorithm [13]. I designed the currently best performing simplicial meshing algorithm [23, 9]. I co-developed three-dimensional meshing algorithms including the rst sliver-free mesh smoothing algorithm [3], a scheme for re-meshing solid models [19], and a method for constructing sparse well-spaced point sets for quality tetrahe- dralizations [14]. Dynamic Modeling. Modeling motion and evolving geometry is a challenging problem and falls into my areas of interest. I co-developed algorithm that model geometric deformations in engineer- ing simulations [17], parametric solid modeling [19], and protein modeling [4]. More importantly, I proposed an unconventional approach to dynamic geometric modeling, which addresses the prob- lem directly in the space-time continuum rather than looking at a nite number of static spatial problems. My work on space-time meshing [6, 25], which has been pioneering in the area, supports e cient linear-time numerical solution strategies by novel space-time numerical methods....
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