Quality is the most important factor when achieving research leadership in a collegial environment while quantity of the same high quality is another indicator of scientific enthusiasm, diligence, and especially creativity. 

Le-We Li is ranked as the most highly cited people in the NUS Microwave & RF Group and as one of the most highly cited people in Asia-Pacific region (IEEE Region 10) in the area of the AP/MTT societies due to life citations by others (in accordance with the data referenced by Science Citation Index - SCI). A paper is considered a good one if it is published in a journal whose impact factor is much smaller than the citations received by the paper. Otherwise it is a poor one even if it is published in a high impact factor journal.

MILESTONES OF RESEARCH

• The First Software for Computing Spheroidal Wave Functions of Complex Arguments

  • Spheroidal wave functions (prolate and oblate) represent a class of special functions in mathematical physics. They provide an exact solution to the vector-wave boundary value problems. In the past, only spheroidal wave functions of real arguments can be computed. So, only lossless media can be considered and calculated.

  • The PI developed a new package based on Mathematica software to be able to compute the spheroidal wave functions of arbitrary arguments (for both lossy and lossles media). Also, the package can be used to compute the spheroidal wave functions for the physical problems of arbitrary size. Because of excellent applicability, the PI received a lot of requests from professionals all of the world for a copy of inhouse-developed codes.

  • It was the world's first software package developed for the general (both lossy and lossless) solutions to practical problems. It is considered as a classic one among other classic ones in a review by WJ Thomthson, a mathematician who published a Mathematics Handbook in 1997. Please refer to his paper published for details: WJ Thomthson, Spheroidal Wave Functions, IEEE Computational Science and Engineering, vol. 1, no. 3, pp. 84-87, May-June 1999.

  • The work results in a book published, that is, Le-Wei Li, Xiao-Kang Kang, Mook-Seng Leong, Spheroidal Wave Functions in Electromagnetic Theory, Wiley: New York, 320 pages, Wiley-Interscience Series, ISBN No.: 0-471-03170-4, November, 2001.  

• Leading Work on Green's Functions of Various Geometries & Their Fast Solutions

  • Green's functions represent the medium/material electromagnetic response to the source physically or a necessary integral kernel for the integral equation methods (method of moments and boundary element method). Therefore, they are very important in the development of codes for the computational electromagnetics, their associated fast solvers, and their applications to various practical physical and engineering problems.

  • The PI has formulated Green's functions in various (a) canonical geometries (waveguides and cavities, planar multilayers, circular and elliptical cylinders of multilayers, radially multilayered spheres, and multilayered spheroids), (b) various coordinates (Cartesian, cylindrical, elliptic, spherical and prolate and oblate spheroidal), and (c) various media or materials (isotropic, chiral, bi-isotropic, anisotropic, and bi-anisotropic). The results are essential for the computational electromagnetics community and fundamental for electromagnetic theory community. 

  • In addition, various closed-form solutions (for planar and cylindrical layered structures) to the analytical expressions of the Green's functions defined for electric scalar potential and magnetic vector potential have been derived. These works serve to the computational electromagnetics community for the development of various integral-equation-based fast solvers, such as the Adaptive Integral Method (AIM), the Fast Multipole Method (FMM) or its high-level version Multi-Level Fast Mulltipole Algorithm (MLFMA), and the Pre-corrected Fast Fourier Transform (pFFT) Method.

  • As a result, a book is in preparation in this field and will be published soon. 

• Leading Work on Adaptive Integral (Equation) Method (AIM)

  • The PI with his group has been developing the Adaptive Integral Method for the past many years and has a close contact with the originator of this approach, Dr E Bleszenski who continuously provides suggestions on the work to the group. With the financial support from Defence Science and Technology Agency (DSTA) of Singapore, the group has successfully developed the fast solver for electrically large problems. At the same time, help from a couple of friend groups such as University of Illinois at Urbana Champaign and Duke University is also a big push to the group in the earlier stage development.

  • The work was further extended from the surface integral equation (SIE), via the volume integral equation (VIE), to the hybrid volume-surface integral equations (VSIE). Also, various preconditioners were implemented and tested for the optimum convergence studies.

  • The work has attracted various attentions (including the Boeing company in Seattle, Washington) and also additional funding from local and overseas agencies (including the Ministry of Education, DSTA, and US Air Force). Now, the work is further extended to the time-domain and also applied to several other practical scientific and engineering applications.

• Pioneering Work on Pre-corrected  Fast Fourier Transform (pFFT) Method

  • The idea in the pre-corrected fast Fourier transform (pFFT) method was initiated by Professor Jacob White at MIT. It was proposed to solve Laplacian equations for designing the static very large-scale integrated circuits (VLSI). It was developed in a different community as the Adaptive Integral Method was developed in parallel at that time.

  • With the funding from the DSTA, the PI with his group has extended the original idea of the pFFT method to the radio frequency problems and successfully developed the fast solver codes for scattering problems. It was the first work on the pFFT method applied for generalized scattering problems (including the radar scattering cross sections of  arbitrary shapes and materials). Since then it was recognized as the pioneering work in the field and was cited by other colleagues in USA and Europe.

  • The method was further extended from the SIE, to the VIE, and then to VSIE hybrid. Applications were further explored to various antenna radiation problems of multilayers and are now to multilayered integrated circuit designs, where the approach enjoys the flexibility of using the multilayered closed-form Green's functions for the fast solvers.