Algorithm development and analysis (Current research):

We focus on the theories and algorithms development of adaptive mesh-free methods for practical industrial problems. This work supplies new theoretical results underpinning meshless collocation methods. In particular, we study different variations of asymmetric strong collocation technique. We continue to develop and improve the adaptive trial space selection algorithms for solving large-scale engineering problems efficiently.

• Adaptive trial space selection in action [ WMV ]
• Residual reduction of overdetermined Kansa's method [ WMV ]

miniWIZ [HYmini | miniSolar] (Current research):

HYmini™ is a handheld, universal charger/adapter device that harnesses renewable wind power to recharge almost all 5V digital gadgets. This power plant is so small that it can be attached to your arm while you’re jogging, or bicycle’s handlebars, and charge your devices with the breeze. Moreover, HYmini is rated as DARK GREEN, which is the highest rating for the “good-better-best” in greenness. For that reason, HYmini is reported as the More Earth-friendly gifts for Christmas. More reviews of HYmini can be found on Treehugger.com, cover of Popular Science and pop mechanics, TIME magazine, Chicago Tribune, MSNBC, ABC news...

Theoretical analysis shows that the upper limit for the efficiency of wind turbines is 59%. The most efficient designs at present have an efficiency of about 45%. In a much smaller scale comparing to the conventional wind turbines, we are interested in the efficiency of HYmini, on the conversion of the wind’s kinetic energy to electrical energy, with respect to different wind velocities and impact angles. This project begins with experiment design, data collocation, data analysis, and end with some suggestions to design improvement and possible new products.

HYmini's reviews: Tokyo TV News Green Deets, Treehugger, Discovery Channel Good House Keeping NZ and Australia Channel 3 NEWS GreenGadget.net GoodCleanTech

Source identification:

We consider the source location determination problem for a two dimensional heat equations with unknown source locations. We show that only one measurement point is sufficient to identify the number of sources and three measurement points are sufficient to determine all unknown source positions. Our preliminary numerical reconstruction scheme can successfully identify all unknown source in the noise-free setting. The theories and numerical schemes developed in this work are being translated to other real-life problems with more available measurement points and with noisy data.

Numerical differentiation:

The previous literatures on numerical differentiation featured with plenty of nicely calculated practical solutions, but most research papers on this topic is limited to one-dimension or highly structured grids. Numerical methods for higher dimensions are very limited. Our research supplies a new, efficient, practical alternative for scientists and industrialists who need to compute numerical differentiation from real-life, large-scale and noisy multivariate data.