XIA Qi    　 Computational Modeling and Design Laboratory Department of Mechanical and Automation Engineering Address: Room 312 Engineering Building Complex-Phase II  Tel: (852) 2609-8041  Fax: (852) 2603-6002 Email:qxia@mae.cuhk.edu.hk

Brief Bio	B.Eng,  2001, Huazhong University of Science and Technology M.Eng, 2004, Huazhong University of Science and Technology PhD,    2007, The Chinese University of Hong Kong Postdoctoral Fellow, 2008, The Chinese University of Hong Kong
Research	Level Set Method
	Level Set Method, first devised and introduced by Osher and Sethian in 1988, is a simple and versatile method for numerical simulation of the motion of interfaces in two or three dimensions. Since it is transparent to topological changes, the level set method has found a wide range of applications in fluid mechanics, combustion, computer animation and image processing etc.

Shrinking Spiral (wmv)                            Shearing Circles (wmv)

	Semi-Lagrange Schemes
	Semi-Lagrange schemes is competitive with Eulerian schemes for Level Set with respect to accuracy, but it has the added advantage that this accuracy can be achieved at less computational cost, since models can be integrated stably with time steps that far exceed the maximum possible time steps of Eulerian schemes, thus circumvent the Courant-Friedrichs-Lewy (CFL) stability condition.
	Eulers  scheme                                  Lagrange scheme
	Surface Reconstruction with Radial Basis Function
	With RBF, implicit surface reconstruction is treated as a scattered data interpolation problem. It takes coordinates of a set of points as input, artificially defines function values at these points, and obtain an interpolating function using radial basis functions. To simplify the computations, we employ Orthogonal Least Squares algorithm to select the most significant RBF centers. More over, Partition of Unity is adopted to decompose the domain.
	Structural Topology and Shape Optimization
	We developed a new technique for structural topology and shape optimization based on level-set methods. The level set model allows for an implicit boundary shape representation with changes in topology. The models eliminate the conventional use of discrete elements and provides efficient and stable computation schemes. The level set based optimization techniques form a common base for structural optimization using mathematical programming.
	Optimized Minimum Mean Compliance Structures (wmv1, wmv2)
	Simultaneous Optimization of Material Property and Topology
	A level set based method is proposed for simultaneous optimization of material property and topology of functionally graded structures. The objective is to determine the optimal material property (via material volume fraction) and structural topology to maximize the performance of the structure in a given application. In the proposed method volume fraction and structural boundary are considered as design variables, with the former being discretized as a scaler field and the latter being implicitly represented by level set method. To perform simultaneous optimization, the two design variables are integrated into a common objective functional. Sensitivity analysis is conducted to obtain the descent directions. The optimization process is then expressed as the solution to a coupled Hamilton-Jacobi equation and diffusion partial differential equation.
	Homogenization
	The homogenization theory was developed since the 1970's to find the effective properties of equivalent homogenized material. From a mathematical point of view the theory of homogenization is a limit theory which uses the asymptotic expansion and the assumption of periodicity to substitute the differential equations with rapidly oscillating coefficients with differential equations whose coefficients are constant or slowly varying.
	Characteristic Displacements of a Unit Cell with a Rectangular Hole
	Inverse Homogenization
	The problem of designing composite materials with desired mechanical properties is to specify the material microstructures in terms of the topology and distribution of their constituent material phases within a unit cell of periodic microstructures. We employ an approach based on level-set model for the geometric and material representation and for numerical solution of a least squares optimization problem.
	The Unit Cell and Periodic Microstructure with Poisson's ratio -0.5 (wmv)
	The Unit Cell and Periodic Microstructure with Poisson's ratio 0 (wmv)
	The Unit Cell and Periodic Microstructure with Poisson's ratio 1
Publication	Q. Xia, M. Y. Wang Level set based topology optimization for cast part design                 Submitted, June, 2008
	Q. Xia, M. Y. Wang, and X.H. Xing Minimum stress topology optimization of thermoelastic structures using level set method, Submitted, October, 2007
	Q. Xia, M. Y. Wang Topology optimization of thermoelastic structures using level set method,  Computational Mechanics, 42(6), 837-857, 2008
	Q. Xia, M. Y. Wang Topology optimization of thermoelastic structures using level set method,  International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 1-6, June, 2008.
	Q. Xia, M. Y. Wang Simultaneous optimization of material property and topology of functionally graded structures, Computer-Aided Design, 40(6), 660-675, 2008
	Q. Xia, M. Y. Wang Level set based method for simultaneous optimization of material property and topology of functionally graded structures, ACM Solid and Physical Modeling 2007, Tsinghua University, Beijing, China
	Q. Xia, M. Y. Wang, S. Y. Wang and S. K. Chen Semi-Lagrange method for level-set based structural topology and shape optimization, Structural and Multidisciplinary Optimization, 31(6), 419-429, 2006
	Qi Xia, Michael Yu Wang and Xiaojun Wu Orthogonal Least Squares in Partition of Unity Surface Reconstruction with Radial Basis Function, Geometric Modeling and Imaging--New Trends (GMAI'06), pp. 28-33, 2006, London, UK.
	X. J. Wu, M. Y. Wang and Q. Xia 3D reconstruction methods based on radial basis functions for laser scanned data point sets, Computer-Aided Design & Applications, 3(1-4), 145-153, June 2006.
	Shikui CHEN, Michael Yu WANG, Shengyin WANG, Qi XIA Optimal Synthesis of Compliant Mechanisms Using a Connectivity Preserving Level Set Method (DETC2005-84748), ASME Proceedings of IDETC/CIE 2005, September 24-28, 2005, Long Beach, California, USA.
	X. J. Wu, M. Y. Wang and Q. Xia 3D reconstruction methods based on radial basis functions for laser scanned data point sets, in Proc. of CAD'06 - International CAD Conference & Exhibition, Phuket, Thailand, June 2006.
	X. J. Wu, M. Y. Wang and Q. Xia Implicit fitting and smoothing using radial basis functions and partition of unity, in Proc. of 9th International Computer-Aided-Design and Computer Graphics Conference (CAD/Graphics'05), Hong Kong, December 2005.
	Wu, Xiaojun; Wang, Michael Yu; Xia, Qi.  Orthogonal least square RBF based implicit surface reconstruction methods.  Lecture Notes in Computer Science, v4270 LNCS, 12th International Conference, VSMM 2006, 2006,232-241.
	Xia Qi, Shi Tielin The Algorithm of Template Localization Based on Point Pattern Matching and Energy Minimization, Journal of Huazhong University of Science and Technology. (Nature Science Edition), August,2004,Vol.32 No.8
	Xia Qi, Zhou Mincai, Wang Hongsheng, Shi Tieling Vision Alignment System in Automatic High Precision Chip Mounter and its Image Processing, Optical Technology, March, 2004, Vol.30, No.2
Copyright © 2007 Last Update, 29 July 2008