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Computing partial differential equations on point clouds
【2013.8.14 10:00am,Z311】

 Date:03-12-2013 Page Views:
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  Colloquia & Seminars 




Prof.Hongkai Zhao,University of California at Irvine, USA



    Computing partial differential equations on point clouds 




    2013.8.14 10:00am 






I will present a general framework for solving partial differential equations on manifolds represented by meshless points, i.e., point clouds, without parametrization or connection information. Our method is based on a local approximation of the manifold, such as using least squares, in a local intrinsic coordinate system constructed by local principal component analysis (PCA) using K-nearest neighbors (KNN). Once the local reconstruction is available, differential operators on the manifold can be approximated discretely. The framework extends to manifolds of any dimension. The complexity of our method scales well with the total number of points and the true dimension of the manifold (not the embedded dimension). Applications to point cloud analysis and manifold learning will be discussed. 



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