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3.24.16 Jiao

Topic: 74th CFD Seminar: Robust Adaptive High-Order Geometric and Numerical Methods Based on Weighted Least Squares

Date: Thursday, March 24, 2016

Time: 2:00pm-3:00pm (EST)

Room: NIA, Rm 137

Speaker: Xiangmin (Jim) Jiao

Webcast link: http://www.hiroakinishikawa.com/niacfds/index.html

Abstract: Numerical solutions of partial differential equations (PDEs) are important for modeling and simulations in many scientific and engineering applications. Their solutions over com- plex geometries pose significant challenges in efficient surface and volume mesh generation and robust numerical discretizations. In this talk, we present our recent work in tackling these challenges from two aspects. First, we will present accurate and robust high-order geomet- ric algorithms on discrete surface, to support high-order surface reconstruction, surface mesh generation and adaptation, and computation of differential geometric operators, without the need to access the CAD models. Secondly, we present some new numerical discretization tech- niques, including a generalized finite element method based on adaptive extended stencils, and a novel essentially nonoscillatory scheme for hyperbolic conservation laws on unstructured meshes. These new discretizations are more tolerant of mesh quality and allow accurate, stable and efficient computations even on meshes with poorly shaped elements. Based on a unified theoretical framework of weighted least squares, these techniques can significantly simplify the mesh generation processes, especially on supercomputers, and also enable more efficient and robust numerical computations. We will present the theoretical foundation of our methods and demonstrate their applications for mesh generation and numerical solutions of PDEs.

Bio: Dr. Xiangmin (Jim) Jiao is an Associated Professor in Applied Mathematics and Computer Science, and also a core faculty member of the Institute for Advanced Computational Science at Stony Brook University. He received his Ph.D. in Computer Science in 2001 from University of Illinois at Urbana-Champaign (UIUC). He was a Research Scientist at the Center for Simulation of Advanced Rockets (CSAR) at UIUC between 2001 and 2005, and then an Assistant Professor in College of Computing at Georgia Institute of Technology between 2005 and 2007. His research interests focus on high-performance geometric and numerical computing, including applied computational and differential geometry, generalized finite difference and finite element methods, multigrid and iterative methods for sparse linear systems, multiphysics coupling, and problem solving environments, with applications in computational fluid dynamics, structural mechanics, biomedical engineering, climate modeling, etc.

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