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Computer Science Department News

The Computer Science Department will be hosting a colloquium on Friday, February 8th, 2013 in the E&CS Building first floor auditorium.

TIME: 10:30 (DONUTS) 10:40 (TALK)

Title: Toward Unified Approximation Theory and Efficient Solution Techniquesover Complex Geometries

Xiangmin Jiao
Department of Applied Mathematics and Statistics
Stony Brook University

Abstract: I will present our current work on establishing a rigorousand unified theoretical foundation for numerical approximation methodson complex geometries, and developing an integrated algorithmicframework for analyzing and solving some challenging modeling anddesign problems. Our approach tightly integrates the analysis andalgorithms in approximation theory, numerical linear algebra, andcomputational geometry. Our point of departure is a matrix-basednumerical calculus for the n-dimensional Taylor series, which leads toa new approximation theory based on rank-deficient, weighted leastsquares (RD-WLS) approximations. We prove that WLS can deliver thesame approximation power as interpolation-based approximations underrealistic assumptions, while allowing irregular meshes or pointclouds. We address rank deficiency using robust, adaptive numericaltechniques, with guaranteed consistency and stability. The RD-WLSformulation introduces two scaling matrices, which help achievingoptimal accuracy and help enhancing the diagonal dominance of theresulting linear systems without compromising accuracy, so that theresulting linear system is more amenable to the optimal multigridsolvers based on stationary iterative methods.

Short Bio:
Dr. Xiangmin Jiao is an associate professor in the Department ofApplied Mathematics and Statistics and an adjunct associate professorin the Department of Computer Science of Stony Brook University. Hereceived his Ph.D. in computer science in 2001 from University ofIllinois at Urbana-Champaign (UIUC). After receiving his Ph.D., he wasa research scientist at the Center for Simulation of Advanced Rockets(CSAR) at UIUC and then a visiting assistant professor at GeorgiaInstitute of Technology, before joining Stony Brook in 2007. Hiscurrent research interests focus on developing efficient and robustalgorithms and implementations for numerical discretizations overcomplex geometries, dynamic surfaces, optimal multigrid solvers,applied computational and differential geometry, multiphysicscoupling, and their applications in various engineering and physicalsciences.


COLLOQUIUM SCHEDULING INFORMATION IS AVAILABLE AT http://webspace.cs.odu.edu/~ibl/colloq.html

Colloquium Requirements for Graduate Students:http://webspace.cs.odu.edu/~ibl/colloqreq.htm


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