RESEARCH

Research Interests

  1. Numerical methods for partial differential equations (higher-order compact schemes, finite difference, finite element, stability, convergence)

  2. Numerical heat transfer (thin films, multi-layer thin films, bio-heat transfer)

  3. Computational fluid dynamics (finite difference, control volume)

  4. Numerical simulations for bioelectromagnetics (Cole-Cole expression, finite difference time domain (FDTD) method)

  5. Numerical methods for micro-fabrications (X-ray lithography, laser chemical vapor deposition, melt crystallization)

  6. Image processing using the partial differential equation method

Thesis and Dissertation

  1. M.S. thesis "The general three level explicit difference schemes for solving parabolic equations with variable coefficients and mixed derivatives". Advisor: Professor Chuandan Chen, Dept. of Mathematics, Xiamen University, Xiamen, P. R. China

  2. Ph.D. dissertation "A numerical solution of unsteady incompressible Navier-Stokes equations using the explicit finite analytic method". Advisor: Professor and Chair Ching-Jen Chen, Department of Mechanical Engineering, University of Iowa, Iowa (Currently, he is a Professor and Dean, FAMU/FSU College of Engineering, Florida State University, Florida)

Dissertation Advisees

  1. Teng Zhu, Ph.D. in CAM (May 2000) Title: A hybrid finite element-finite difference method for thermal analysis in a double-layered thin film. He was an associate professor at Grambling State University, Louisiana.

  2. Chaoyang Zhang, Ph.D. in CAM (February 2001)  Title: Mathematical modeling for fabricating a microstructure with a pre-specified geometry using laser-induced chemical vapor deposition. Currently, he is an associate professor and interim director at Southern Mississippi University, Mississippi.

  3. Lixin Shen, Ph.D. in CAM (November 2003) Title: A three-level finite difference scheme for solving a three-dimensional dual-phase-lagging heat transport equation in spherical coordinates. Currently, he is a post-doc at Vanderbilt University, Tennessee.

  4. Ibrahima Kaba, Ph.D. in CAM (May 2004) Title: A three-level finite difference scheme for solving parabolic two-step heat transport equations in spherical coordinates. Currently, he is an assistant professor at Embry-Riddle Aeronautical University, Florida.

  5. Haofeng Yu, Ph.D. in CAM (August 2004) Title: A higher-order compact finite different scheme for solving bioheat transfer equations in a three-dimensional triple-layered skin structure. Currently, he works in a company ALFRA, Georgia.

  6. Le Zhang, Ph.D. in CAM (May 2005) Title: A numerical method for optimizing the laser power in the irradiation of a 3D triple-layered skin structure. He was a post-doc at Harvard University, Massachusetts, and currently is an assistant professor at Michigan Tech University.

  7. Shengjun Su, Ph.D. in CAM (May 2005) Title: Numerical simulation of nanopulse penetration of biological matter using the z-transform. Currently, he works in the Unigraphic Solution (UGS) company, Michigan.

  8. Brian R. Barron, Ph.D. in CAM (November 2005) Title: A FE-FD hybrid scheme for solving parabolic two-step micro heat transport equations in irregularly shaped three dimensional double-layered thin films exposed to ultrashort-pulse lasers. Currently, he is a lecturer at Louisiana Tech University.

  9. Xingui Tang, Ph.D. in CAM (May 2006) Title: A numerical method for obtaining an optimal temperature distribution in a 3D  triple layered skin structure embedded with multi-level blood vessels. Currently, she works in a company NEWEGG, California.

  10. Haojie Wang, Ph.D. in ENGR (May 2007) Title: A numerical method for studying thermal deformation in 2D thin films exposed to ultrashort-pulsed lasers. Currently, he is in the MS Program in Computational Finance at Carnegie Mellon University.

  11. Xudong Du, Ph.D. in CAM (August 2007) Title: A finite difference method for studying thermal deformation in a 3D micro-sphere exposed to ultrashort pulsed lasers. Currently, he works in a stock company in China.

  12. Tianchan Niu, Ph.D. in CAM (November 2007) Title: A hyperbolic two-step model based finite difference method for studying thermal deformation in a thin film exposed to ultrashort pulsed lasers. Currently, she is a staff at Georgetown University in DC.

  13. Suyang Zhang, Ph.D. in CAM (August 2008) Title: A finite difference method for studying thermal deformation in 3D thin films exposed to ultrashort-pulsed lasers.

  14. Pan Wang, Ph.D. in CAM (November 2008) Title: A hyperbolic two-step model based finite difference method for studying thermal deformation in 3D micro spheres exposed to ultrashort-pulsed lasers. Currently, he works in the EPIC Systems Corporation, Wisconsin.

  15. Fei Zhu, Xiaoqi Zheng, Di Zhao, Connor Johnson, Ranzhou Liu, current students in the Ph.D. Program in CAM.

Grants

  1. "Three-dimensional numerical method for thermal analysis in X-ray lithography", granted by LEQSF (Louisiana Education Quality Support Fund), $29,682, 06/01/96 - 06/30/98. Principal Investigator

  2. "High pressure, convectively-enhanced laser chemical vapor deposition for rapid prototyping and automated part manufacture", granted by LEQSF, $199,068, 06/01/97 - 06/30/00. Investigator

  3. "Development of a center for advanced mold/mask process and applications", granted by Army Research Office, $1,994,501, 03/15/96 - 03/14/01. Investigator

  4. "Upgrade of SGI Parallel Computer and ImmersaDesk Visualization System", granted by BoRSF, $100,000, 7/99-6/00. Investigator

  5. "Bioeffects of electromagnetic nanopulses", granted by Air Force Office of Scientific Research, $2,221,000, 3/1/02 - 9/30/04. Investigator

  6. "An approximate analytic method for solving a dual-phase-lagging heat transport equation in microscale thin films", granted by BoRSF, $108,315, 6/01/02-6/30/05. Investigator

  7. "Investigation of unique ECG sensors for detection of atrial activation patterns in the presence of ventricular depolarization through computer simulation and development of sensors, granted by CEnIT, Louisiana Tech University, $32,600, 11/01/02 - 10/31/03. Investigator

  8. "Development of a numerical method for obtaining optimizing temperature distribution in a 3d triple layered skin structure embedded with blood vessels", granted by Louisiana Tech University summer grant, $2,000, 6/1/05-9/15/05.

  9. "An efficient method for simulating diffusion inside nano-tubes for drug delivery systems", granted by BoRSF, $83,793, 7/1/07-9/1/10. Co-PI.

  10. "A hybrid method for solving inverse medium and obstacle problems with limited or synthetic aperture", granted by BoRSF, $116,394, 7/1/08-9/1/11. Co-PI.

Other Professional Services

  1. Editorial Board Member for     

  2. Panelist for a Review Panel on Bio-Transport in National Science Foundation, 2008

  3. Reviewer for (I have reviewed more than 100 publications)
           Mathematical Reviews (MR), American Mathematical Society
           Zentralblatt MATH (ZMATH), European Mathematical Society

  4. Journal Referee for
            Applied Mathematics Letters
            Applied Mathematical Modelling
            Applied Numerical Mathematics
            ASME Journal of Fluid Engineering
            ASME Journal of Heat Transfer
            Australian and New Zealand Industrial and Applied Mathematical Journal
            Communications in Numerical Methods in Engineering
            Current Nanoscience
            Heat and Mass Transfer
            International Journal of Computer Mathematics
            International Journal of Differential Equations
            International Journal of Heat and Mass Transfer

            International Journal of Modeling and Simulation

           International Journal of Nonlinear Science and Numerical Simulation
           International Journal for Numerical Methods in Engineering
           International Journal of Thermal Sciences
           Journal of Applied Mathematics and Computing
           Journal of Applied Physics
           Journal of Applied Polymer Science
           Journal of Computational and Applied Mathematics
           Journal of Computational Physics
           Journal of Physics and Chemistry of Solids
           Journal of Thermophysics and Heat Transfer
           Letters in Mathematical Physics
           Numerical Heat Transfer
           Numerical Methods for Partial Differential Equations
           Physica A
            SIAM Journal on Numerical Analysis
           Special Issue of American Institute of Mathematical Sciences

  5. International Conferences

           Member of Conference Committee for Congress on Engineering and Computer Science World,                             

                WCECS 2007, San Francisco, USA, October 24-26, 2007
                WCECS 2008, San Francisco, USA, October 22-24, 2008
           Member of Conference Committee for International Multi-Symposiums on Computer and Computational Sciences,
                Hangzhou, China, June 22-24, 2006
           Section Chair and Reviewer for The First ASME Micro/Nanoscale Heat Transfer International Conference (MNHT08),
                Tainan, Taiwan, January 6-9, 2008
           Reviewer for International Conference on Computing, Communications and Control Technologies, Austin, Texas (2004)
                World Multiconference on Systemics, Cybernetics and Informatics, Orlando, Florida (2003) (2004) (2005) (2006) (2007)
                          (2008)
                International Symposium on Computational and Information Sciences, Shanghai, China (2004)
                2005 Hawaii International Conference  on Statistics, Mathematics and Related Fields                      
                AIMS Fifth International Conference on Dynamical Systems and Differential Equations, Pomona, California (2004)        

  6. Research Proposal Reviewer for
           Natural Sciences and Engineering Research Council of Canada
          Kentucky Science and Engineering Foundation
                             

Awards and Honors

                     

  1. Louisiana Board of Regents Endowed Professorship (Title: McDermott International Professor) (Beginning September 2004)

  2. Research Award, College of Engineering & Science, Louisiana Tech University (2004)

  3. Honorary Professor, Zhangzhou Normal  University, Fujian, P. R. China, 2007

  4. Marquis Who's Who in America (2003) (2004) (2009)

  5. Marquis Who's Who in Science and Engineering  (2005-2006) (2006-2007) (2007-2008) (2008-2009)

  6. Outstanding Scientists of the 21st Century, International Biographical Centre, Cambridge, England, 2007

PUBLICATIONS

Book / Book Chapter

  1. R. Nassar and W. Dai, Modeling of Microfabrication Systems, Springer-Verlag, Berlin, 2003. ISBN 3-540-00252-9.

    2.  

     

  2. W. Dai, Nonstandard Finite Difference Schemes for Solving Nonlinear Micro Heat Transport Equations in Double-Layered Metal Thin Films Exposed to Ultrashort Pulsed Lasers, Chapter 5 in the Book “Advanced in the Applications of Nonstandard Finite Difference Schemes” edited by Ronald E. Mickens (Clark Atlanta University), World Scientific Publishers, 2005, pp. 191-248. ISBN 981-256-404-7.

 

Papers in Refereed Journals (Asterisk indicates the corresponding author)

  1. W. Dai*, A hyperbolic microscopic model and its numerical scheme for thermal analysis in an N-carrier system, accepted by International Journal of Heat and Mass Transfer.

  1. W. Dai* and D. Y. Tzou, A fourth-order compact finite difference scheme for solving an N-carrier system with Neumann boundary conditions, accepted by Numerical Methods for Partial Differential Equations.

  1. D. Y. Tzou* and W. Dai, Thermal lagging in multi-carrier systems, accepted by International Journal of Heat and Mass Transfer.

  1. R. Nassar*, J. Palmer, Y. Wu, W. Dai, P. Wang, and M. J. McShane, Modeling mass transfer of FITC labeled dextran from polyelectrolyte microcapsules, accepted by Chemical Engineering Communications.

  1. T. Niu and W. Dai*, A hyperbolic two-step model based finite difference scheme for studying thermal deformation in a double-layered thin film exposed to ultrashort pulsed lasers, International Journal of Thermal Sciences, vol. 48, pp. 34-49, 2009.

  1. P. Wang, and W. Dai*, A hyperbolic two-step model based finite difference method for studying thermal deformation in 3D micro sphere exposed to ultrashort-pulsed lasers, Numerical Heat Transfer, Part B, vol. 54, pp. 408-433, 2008.

  1. S. Zhang, P. Wang, and W. Dai*, A finite difference method for studying thermal deformation in 3D double-layered micro-structures exposed to ultrashort-pulsed lasers, The Open Applied Mathematics Journal, vol. 2, pp. 104-125, 2008.

  1. P. M. Jordan*, W. Dai, and R. E. Mickens, A note on the delayed heat equation: Instability with respect to initial data, Mechanics Research Communications, vol. 35, pp. 414-420, 2008.

  1. W. Dai*, H. Wang, P. M. Jordan, R. E. Mickens, and A. Bejan, A mathematical model for skin burn injury induced by radiation heating, International Journal of Heat and Mass Transfer, vol. 51, pp. 5497-5510, 2008.

  1. T. Niu and W. Dai*, A hyperbolic two-step model based finite difference scheme for studying thermal deformation in a 3D thin film exposed to ultrashort pulsed lasers, Numerical Heat Transfer, Part A, vol. 53, pp. 1294-1320, 2008.

  1. W. Dai* and T. Niu, A finite difference method for solving nonlinear hyperbolic two-step model in a double-layered thin film exposed to ultrashort pulsed lasers with nonlinear interfacial conditions, Nonlinear Analysis: Hybrid Systems C Series, vol. 2, pp. 121-143, 2008.

  1. S. Zhang, W. Dai*, H. Wang, and R. V. N. Melnik, A finite difference method for studying thermal deformation in a 3D thin film exposed to ultrashort pulsed lasers, International Journal of Heat and Mass Transfer, vol. 51, pp. 1979-1995, 2008.

  1. X. Du, W. Dai*, and P. Wang, A finite difference method for studying thermal deformation in a 3D micro-sphere exposed to ultrashort pulsed lasers, Numerical Heat Transfer, Part A, vol. 53, pp. 457-484, 2008.

  1. H. Wang, W. Dai*, and L. G. Hewavitharana, A finite difference method for studying thermal deformation in a double-layered thin film with imperfect interfacial contact exposed to ultrashort pulsed lasers, International Journal of Thermal Sciences, vol. 47, pp. 7-24, 2008.

  1. J. Zhao*, W. Dai and S. Zhang, 4th order compact schemes for solving multi-dimensional heat problems with Neumann boundary conditions, Numerical Methods for Partial Differential Equations, vol. 24, pp. 165-178, 2008.

  1. H. Wang, W. Dai*, and A. Bejan, Optimal temperature distribution in a 3D triple layered skin structure embedded with artery and vein vasculature and induced by electromagnetic radiation, International Journal of Heat and Mass Transfer, vol. 50, pp. 1843-1854, 2007.

  1. J. Zhao*, W. Dai and T. Niu, Fourth order compact schemes of a heat conduction problem with Neumann boundary conditions, Numerical Methods for Partial Differential Equations, vol. 23, pp. 949-959, 2007.

  1. L. Zhang, W. Dai* and R. Nassar, A numerical algorithm for obtaining an optimal temperature distribution in a 3D triple-layered cylindrical skin structure, Computer Assisted Mechanics and Engineering Sciences, vol. 14, pp. 107-125, 2007.

  1. R. Nassar, J. Hu, J. Palmer* and W. Dai, Modeling of cyclohexene hydrogynation and dehydrogenation reactions in a continuous-flow, Catalysis Today, vol. 120, pp. 121-124, 2007.

  1. X. Tang, W. Dai*, R. Nassar, and A. Bejan, Optimal temperature distribution in a 3D triple layered skin structure embedded with artery and vein vasculature, Numerical Heat Transfer, vol. 50, pp. 809-834, 2006.

  1. S. Su and W. Dai*, Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation with a heat source, International Journal of Heat and Mass Transfer, vol. 49, pp. 2793-2801, 2006.

  1. W. Dai* and G. Li, A finite difference scheme for solving parabolic two-step micro heat transport equations in a double-layered micro sphere heated by ultrashort-pulsed lasers, Numerical Methods for Partial Differential Equations, vol. 22, 1396-1417, 2006.

  1. W. Dai*, H. Song, S. Su and R. Nassar, A stable finite difference scheme for solving hyperbolic two-step model in a 3D micro sphere exposed to ultrashort-pulsed lasers, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 16, pp. 693-717, 2006.

  1. W. Dai*, A. Bejan, X. Tang, L. Zhang and R. Nassar, Optimal temperature distribution in a 3D triple layered skin structure with embedded vasculature, Journal of Applied Physics, vol. 99, 104702 (2006). The paper has been selected for the June 1, 2006, issue of Virtual Journal of Biological Physical Research.

  1. B. R. Barron and W. Dai*, A hybrid FE-FD scheme for solving parabolic two-step micro heat transport equations in an irregularly shaped three dimensional double-layered thin film, Numerical Heat Transfer, Part B, vol. 49, pp. 437-465, 2006.

  1. H. Wang, W. Dai*, and R. Melnik, A finite difference method for studying thermal deformation in a double-layered thin film exposed to ultrashort pulsed lasers, International Journal of Thermal Sciences. vol. 45, pp. 1179-1196, 2006.

  1. L. Zhang, W. Dai* and R. Nassar, A numerical method for obtaining an optimal temperature distribution in a 3D triple-layered cylindrical skin structure embedded with a blood vessel, Numerical Heat Transfer, Part A, vol. 49, pp. 765-784, 2006.

  1. H. Wang, W. Dai*, R. Nassar and R. Melnik, A finite difference method for studying thermal deformation in a thin film exposed to ultrashort pulsed lasers, International Journal of Heat and Mass Transfer, vol. 49, pp. 2712-2723, 2006.

  1. Z. Feng, W. Dai*, R. Nassar and J. Palmer, A combined analytic and numerical method for predicting solid layer growth in a static melt crystallizer, Numerical Heat Transfer, Part A, vol. 49, pp. 831-850, 2006.

  1. W. G. Besio*, K. Koka, R. Aakula, and W. Dai, Tri-polar concentric ring electrode - development for Laplacian electroencephalography, IEEE Transaction on Biomedical Engineering, vol. 53, pp. 926-933, 2006.

  1. W. G. Besio*, R. Aakula, K. Koka and W. Dai, Tri-polar concentric ring electrode - a highly accurate method to estimate Laplacian body surface potentials, Annals of Biomedical Engineering, vol. 34, pp. 426-435, 2006.

  1. W. Dai*, G. Li, R. Nassar and S. Su, On the stability of the FDTD method for solving a time dependent Schrodinger equation, Numerical Methods for Partial Differential Equations, vol. 21, pp. 1140-1154, 2005.

  1. S. Su, W. Dai*, D. Haynie, and N. Simicevic, Use of the z-transform to investigate nanopulse penetration of biological matter,  Bioelectromagnetics , vol. 26, pp. 389-397, 2005.

  1. L. Zhang, W. Dai* and R. Nassar, A numerical method for optimizing laser power in the irradiation of a 3D triple layered cylindrical skin structure, Numerical Heat Transfer, Part A, vol. 48, pp. 21-41, 2005.

  1. I. Kaba and W. Dai*, A stable three-level finite difference scheme for solving the parabolic two-step model in a 3D micro-sphere heated by ultrashort-pulsed lasers, Journal of Computational and Applied Mathematics, vol. 181, pp. 125-147, 2005.

  1. S. Su, W. Dai*, P.M. Jordan, and R. E. Mickens, Comparison of the solutions of a phase-lagging heat transport equation and damped wave equations, International Journal of Heat and Mass Transfer, vol. 48, pp. 2233-2241, 2005.

  1. S. Su, W. Dai*, D. Haynie, R. Nassar, and N. Simicevic, Numerical simulation of nanopulse penetration of biological matter using the z-transform, Journal of Mathematical Modelling and Algorithms, vol. 4, pp. 99-110, 2005.

  1. T. Zhu, W. Dai*, and L. Shen, Comparison of the solutions of a 1D dual-phase-lagging heat transport equation and its approximations, Far East Journal of Applied Mathematics, vol. 17, pp. 47-58, 2004.  

  1. W. Dai*, H. Yu, and R. Nassar, A fourth-order compact finite difference scheme for solving a 1-D Pennes' bioheat transfer equation in a triple-layered skin structure, Numerical Heat Transfer, Part B, vol. 46, pp. 447-461, 2004.

  1. W. Dai*, L. Shen, and T. Zhu, A stable three-level finite difference scheme for solving a three-dimensional dual-phase-lagging heat transport equation in spherical coordinates, Numerical Heat Transfer, Part B, vol. 46, pp. 121-139, 2004.

  1. W. Dai* and S. Su, A nonstandard finite difference scheme for solving one dimensional nonlinear heat transfer, Journal of Difference Equations and Applications, vol. 10, pp. 1025-1032, 2004.

  1. W. Dai*, L. Shen, R. Nassar, and T. Zhu, A stable and convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinates, International Journal of Heat and Mass Transfer, vol. 47, pp. 1817-1825, 2004.

  1. W. Dai*, G. Li, R. Nassar, and L. Shen, An unconditionally stable three level finite difference scheme for solving parabolic two-step micro heat transport equations in a three-dimensional double-layered thin film, International Journal for Numerical Methods in Engineering, vol. 59, pp. 493-509, 2004.

  1. W. Dai*, L. Shen and R. Nassar, A convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinates, Numerical Methods for Partial Differential Equations, vol. 20, pp. 60-71, 2004.

  1. W. Dai*, Z. Feng, R. Nassar and J. Palmer, A combined analytic and numerical method for predicting the solid layer growth from melt crystallization, Numerical Heat Transfer, Part A, vol. 44, pp. 577-590, 2003.

  1. W. Dai* and R. Nassar, A three level finite difference scheme for solving micro heat transport equations with temperature-dependent thermal properties, Numerical Heat Transfer, Part B, vol. 45, pp. 509-523, 2003 .

  1. W. Dai* and R. Nassar, An unconditionally stable hybrid FE-FD scheme for solving a 3-D heat transport equation in a cylindrical thin film with sub-microscale thickness, Journal of Computational Mathematics, vol. 21, pp. 555-568, 2003.

  1. R. Nassar*, W. Dai, and Q. Chen, An axisymmetric numerical model for simulating kinetically limited growth of a cylindrical rod in 3D laser-induced chemical vapor deposition, Journal of Material Science and Technology, vol. 18, pp. 127-132, 2002.

  1. W. Dai* and R. Nassar, An unconditionally stable finite difference scheme for solving 3-D heat transport equation in a sub-microscale thin film, Journal of Computational and Applied Mathematics, vol. 145, pp. 247-260, 2002.

  1. W. Dai* and R. Nassar, An approximate analytic method for solving dual-phase-lagging heat transfer equations, International Journal of Heat and Mass Transfer, vol. 45, pp. 1585-1593, 2002.

  1. W. Dai* and R. Nassar, Compact ADI scheme for solving parabolic differential equations, Numerical Methods for Partial Differential Equations, vol. 18, pp. 129-142, 2002.

  1. R. Nassar*, C. Zhang, W. Dai, H. Lan and J. Maxwell, Mathematical modeling of three-dimensional laser chemical vapor deposition, Microelectronic Engineering, vol. 60, pp. 395-408, 2002.

  1. W. Dai*, R. Nassar and L. Mo, A domain decomposition method for solving 3-D heat transfer equations in double layered cylindrical thin film with microscale thickness and nonlinear interfacial conditions, Numerical Heat Transfer, Part A, vol. 40, pp. 619-638, 2001.

  1. W. Dai* and R. Nassar, A finite difference method for solving 3-D heat transfer equations in double layered thin film with micro-scale thickness and nonlinear interfacial conditions, Numerical Heat Transfer, Part A, vol. 39, pp. 21-33, 2001.

  1. W. Dai* and R. Nassar, A finite difference scheme for solving a three dimensional heat transport equation in a thin film with micro-scale thickness, International Journal for Numerical Methods in Engineering, vol. 50, pp. 1665-1680, 2001.

  1. W. Dai* and R. Nassar, A compact finite difference scheme for solving a one-dimensional heat transport equation at the micro-scale, Journal of Computational and Applied Mathematics, vol. 132, pp. 431-441, 2001.

  1. W. Dai* and R. Nassar, A hybrid finite element-finite difference method for solving three dimensional heat transport equations in double layered thin films with micro-scale thickness, Numerical Heat Transfer, Part A, vol. 38, pp. 573-588, 2000.

  1. W. Dai* and R. Nassar, A preconditioned Richardson method for solving three dimensional thin film elliptic problems with first order derivatives and variable coefficients, International Journal of Numerical Methods for Heat & Fluid Flow, vol.10, pp. 477-487, 2000.

  1. W. Dai* and R. Nassar, A domain decomposition method for solving three-dimensional heat transport equations in double layered thin films with micro-scale thickness, Numerical Heat Transfer, Part A, vol. 38, pp. 243-256, 2000.

  1. W. Dai* and R. Nassar, A compact finite difference scheme for solving a three dimensional heat transport equation in a thin film, Numerical Methods for Partial Differential Equations, vol. 16, pp. 441-458, 2000.

  1. W. Dai* and R. Nassar, A finite difference scheme for the generalized nonlinear Schrodinger equation with variable coefficients, Journal of Computational Mathematics, vol. 18, no.2, pp. 123-132, 2000. 

  1. W. Dai* and R. Nassar, A new ADI scheme for solving three dimensional parabolic equations with first-order derivatives and variable coefficients, Journal of Computational Analysis and Applications, vol. 2, pp. 293-308, 2000.

  1. W. Dai*, Y. Zhang and R. Nassar, A hybrid finite element-alternating direction implicit method for solving parabolic differential equations on multi-layers with irregular geometry, Journal of Computational and Applied Mathematics, vol. 117, pp. 1-16, 2000.  (Ei)

  1. W. Dai*, Y. Zhang and R. Nassar, A three-dimensional numerical algorithm for predicting temperature rise in resist with arbitrary geometry of pattern during X-ray exposure, Microelectronic Engineering, vol. 49, pp. 216-231, 1999.  (Ei)

  1. W. Dai* and R. Nassar, A finite difference method for solving the heat transport equation at the micro-scale, Numerical Methods for Partial Differential Equations, vol. 15, pp. 697-708, 1999. 

  1. W. Dai*, R. Nassar, C. Zhang, S. Shabanian, and J. Maxwell, A numerical model for simulating axisymmetric rod growth in three-dimensional laser chemical vapor deposition, Numerical Heat Transfer, Part A, vol. 36, pp. 251-262, 1999.  (Sci) (Ei)

  1. W. Dai* and R. Nassar, A domain decomposition method for solving thin film elliptic interface problems with variable coefficients, International Journal for Numerical Methods in Engineering , vol. 46, pp. 747-756, 1999. (Ei)

  1. W. Dai* and R. Nassar, A hybrid finite element-finite difference for thermal analysis in X-ray lithography, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 9, pp. 660-676, 1999. (Ei)

  1. W. Dai* and R. Nassar, A preconditioned Richardson numerical method for thermal analysis in X-ray lithography with cylindrical geometry, Numerical Heat Transfer, Part A, vol. 34, pp. 599-616, 1998.  (Sci) (Ei)

  1. H. Hegab*, B. Shen, W. Dai and T. Ameel, Three-dimensional numerical transient model for thermal analysis in X-ray lithography, Numerical Heat Transfer, Part A, vol. 34, pp. 805-819, 1998.  (Sci) (Ei)

  1. W. Dai* and C. J. Chen, Explicit finite analytic method for unsteady three-dimensional Navier-Stokes equations, Numerical Heat Transfer, Part B , vol. 33, pp. 339-354, 1998.  (Sci) (Ei)

  1. W. Dai* and R. Nassar, A second-order ADI scheme for three-dimensional parabolic differential equations, Numerical Methods for Partial Differential Equations, vol. 14, pp. 159-168, 1998.  (Sci) (Ei)

  1. W. Dai* and R. Nassar, A three-dimensional numerical method for thermal analysis in X-ray lithography, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 8, pp. 409-423, 1998. (Sci)

  1. W. Dai*, A new ADI scheme for solving three-dimensional parabolic differential equations, Journal of Scientific Computing, vol. 12, pp. 361-369, 1997.

  1. W. Dai*, A generalized Peaceman-Rathford ADI scheme for solving two-dimensional parabolic differential equations, Journal of Scientific Computing, vol. 12, pp. 353-360, 1997.

  1. W. Dai* and R. Nassar, A three-dimensional numerical model for thermal analysis in X-ray irradiated photo-resists with cylindrical domain, Numerical Heat Transfer, Part A , vol. 32, pp. 517-530, 1997. (Sci) (Ei)

  1. W. Dai* and R. Nassar, A generalized two-cycle component-wise splitting method for solving three-dimensional parabolic differential equations with variable coefficients on multi-layers, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 7, pp. 863-879, 1997. (Sci)

  1. W. Dai*, R. Nassar, R. Warrington, and B. Shen, Three-dimensional numerical model for thermal analysis in x-ray irradiated photo-resists, Numerical Heat Transfer, Part A, vol. 31, pp. 585-595, 1997.  (Sci) (Ei)

  1. W. Dai* and R. Nassar, A generalized Douglas ADI method for solving three-dimensional parabolic differential equations on multi-layers, International Journal of Numerical Methods for Heat and Fluid Flow, vol. 7, pp. 659-674, 1997. (Sci)

  1. W. Dai*, An unconditionally stable three level explicit difference scheme for the Schrodinger's equation with a variable coefficient, SIAM Journal on Numerical Analysis, 29(1992), pp. 174-181.  (Mathematical Reviews 93a:65112) (Sci) (Ei)

  1. W. Dai* and C. D. Chen, A three level difference schemes for two dimensional nonlinear parabolic differential equations, Mathematica Numerica Sinica, vol. 11, pp. 1-9, 1989. (Chinese) (Mathematical Reviews 90c:65162)

  1. W. Dai*, Absolutely stable explicit and semi-explicit schemes for Schrodinger equation, Mathematica Numerica Sinica, vol. 11, pp. 128-131, 1989. (Chinese) (Mathematical Reviews 91c:65060)

  1. W. Dai*, Linearized difference scheme for a kind of nonlinear parabolic equations, Journal of Xiamen University (Natural Science), vol. 28, pp. 222-226, 1989. (Chinese) (Mathematical Reviews 91h:65136)

  1. W. Dai*, Stability and convergence for generalized Du Fort-Frankel's scheme with variable coefficients, Journal of Xiamen University (Natural Science), vol. 28, pp. 563-567, 1989. (Chinese) (Mathematical Reviews 91h:65137)

  1. W. Dai*, Stable explicit and semi-explicit three level difference schemes for the dispersive equation, Journal of Xiamen University (Natural Science), vol. 27, pp. 116-118, 1988. (Chinese)

  1. W. Dai* and C. Chen, The general three level explicit difference schemes for solving parabolic equations with variable coefficients and mixed derivatives, Chinese Universities on Journal of Numerical Mathematics, vol. 6, pp. 235-242, 1987. (Chinese) (Mathematical Reviews 89i:65086)

  1. W. Dai*, The general two level difference schemes for nonlinear parabolic equations, Journal of Xiamen University (Natural Science), vol. 26, pp. 161-165, 1987. (Chinese) (Mathematical Reviews 88h:65163)

  1. C. Chen* and W. Dai, The stability of the explicit difference schemes for solving parabolic equations with mixed derivatives and variable coefficients, Journal of Xiamen University (Natural Science), vol. 25, pp. 386-393, 1986. (Chinese)

Papers in International Conference Proceedings (Asterisk indicates the presenter)

  1. D. Liu* and W. Dai, Spectral element simulation of flow past an ellipsoid at different Reynolds numbers, Proceedings of the FLUCOME 2007, Tallahassee, Florida, September 17-20, 2007, 8 pages.

  1. R. Nassar*, J. Hu, J. Palmer and W. Dai, Statistical modeling of an open flow microroreactor system, Proceedings of the First International Conference on Experiments/Process/ System Modelling/Simulation/Optimization, CD-ROM, Athens, Greece, July 6-9, 2005, 5 pages.

  1. W.Dai* and T. Zhu, A nonlinear finite difference scheme for solving two-step nonlinear parabolic model, Lecture Notes in Computer Science, vol. 3314, Springer-Verlag, Heidelberge, 2004, pp. 304-309. ISBN: 0302-9743. (Proceedings of the International Symposium on Computational and Information Sciences, Shanghai, China, December 16-18, 2004)

  1. W.G. Besio*, R. Aakula and W. Dai, Comparison of bipolar vs. tripolar concentric ring electrode Laplacian estimate, Proceedings of the 26th Annual International Conference of the IEEE EMB, San Francisco, CA, 2004, pp. 2255-2258.

  1. L. Zhang*, X. Tang and W. Dai, High dimension Web cluster algorithm, Proceedings of the IC-AI 04 International Conference, Las Vegas, Nevada, June 21-24, 2004, pp. 964-970.

  1. W. Dai*, H. Yu, R. Nassar and T. Zhu, A fourth-order compact finite difference scheme for solving a 1-D Pennes' bioheat transfer equation in a uniform tissue, Proceedings of the 2003 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, Las Vegas, Nevada, June 23-26, 2003, pp. 336-339.

  1. R. Nassar*, J. Palmer, W. Dai, M. J. Mcshane, N. Gupta and Y. M. L'vov, Modeling of FITC-dextran release in polyelectrolyte nanocapsules, Proceedings of Hawaii International Conference on Statistics and Related Fields (CD-ROM), Hawaii, June 5-8, 2003. (4 pages)

  1. W. Dai*, G. Li, R. Nassar and T. Zhu, A domain decomposition method for solving the Pennes' bioheat transfer in a 3D triple-layered skin structure, Proceedings of the Second M.I.T. Conference on Computational Fluid and Solid Mechanics, MIT, Boston, June 17-20, 2003, vol. 2, pp. 1650-1659.

  1. C. Zhang, W. Dai*, R. Nassar and H. Lan, Inverse model for optimizing the process of fabricating a microstructure, Proceedings of the SPIE Symposia on Micromachining and Microfabrication, San Jose, California, January 25-31, 2003, vol. 4979, pp. 540-548.

  1. H. Lan, R. Nassar*, W. Dai and C. Zhang, Hybrid mathematical model for simulating axisymmetric rod growth with mass transport limited rates, Proceedings of the SPIE Symposia on Micromachining and Microfabrication, San Jose, California, January 25-31, 2003, vol. 4979, pp. 549-560.

  1. T. Zhu* and W. Dai, A domain decomposition method for solving three dimensional heat transport equations in a double layered cylindrical thin film with submicroscale thickness, Proceedings of the Sixth World Multiconference on Systemics, Cybernetics and Informatics (SCI 2002), vol. XVII, pp. 120-124, Orlando, USA, July 14-18, 2002.

  1. R. Nassar*, W. Dai, C. Zhang, and M. Boman, Modeling of microstructures grown by laser assisted chemical vapor deposition, Fourth International Workshop on High-Aspect-Ratio Micro-Structure Technology, Baden-Baden, Germany, June 17-19, 2001, pp. 53-54.

  1. H. Black, R. Nassar* and W. Dai, Fluid flow in microchannels: a Stochastic approach, Pro. SPIE, vol. 4557, Micromachining and Microfabrications, 2001, pp. 233-241.

  1. W. Dai* and R. Nassar, A fourth-order compact finite difference scheme for solving a biharmonic equation, Proceedings of the IMACS International Conference on Scientific Computing and Mathematical Modeling, Milwaukee, Wisconsin, May 25-27, 2000.

(4 pages)

  1. R. Nassar*, W. Dai, C. Zhang, H. Lan and J. Maxwell, A mathematical model for process control in laser chemical vapor deposition, Proceedings of the Third International Conference on Modeling and Simulation of Microsystems, San Diego, California, March 27-29, 2000, pp. 517-519.

  1. W. Dai* and R. Nassar, A domain decomposition algorithm for thermal analysis in x-ray lithography with cylindrical geometry, Proceedings of Parallel Computing, 1998 International Mechanical Engineering Congress & Exposition (IMECE), ASME, Anaheim, California, November 15-20, 1998, vol. 247, pp. 95-99. (Ei)

  1. W. Dai* and R. Nassar, A preconditioned Richardson method for solving micro-scale thin film elliptic interface problem with variable coefficients, Proceedings of the Fourth IMACS International Symposium on Iterative Methods in Scientific Computation, Austin, Texas, USA, October 18-20, 1998, pp. 357-362.

  1. R. Nassar, W. Dai* and J. Maxwell, A numerical simulation for laser chemical vapor deposition, Proceedings of the 7th International Symposium on Flow Modeling and Turbulence Measurements (ISFMTM 98'), Taiwan, R.O.C., October 5-7, 1998, pp. 133-140.

  1. R. Nassar* and W. Dai, Stochastic models for dispersion in a two-phase flow of a bubble column reactor, Proceedings of the 13th International Workshop on Statistical Modeling, New Orleans, July 27-31, 1998, pp. 461-465.

  1. W. Dai and R. Nassar*, A preconditioned Richardson method for thermal analysis in Xray lithography, Proceedings of the Third IMACS International Symposium on Iterative Methods in Scientific Computation, Wyoming, USA, July 9-12, 1997, pp. 357-362.

  1. W. Dai*, R. Nassar and D. Jiang, Domain decomposition method for solving three dimensional parabolic differential equations arising in thermal analysis in X-ray lithograph, Proceedings of the 8th SIAM Conference on Parallel Processing for Scientific Computing (CD-ROM), SIAM, Minneapolis, Minnesota, March, 1997, 8 pages. (Ei)

  1. W. Dai* and C. J. Chen, Explicit finite analytic method for unsteady incompressible laminar two-dimensional Navier-Stokes equations, Proceedings of the 6th International Symposium on Flow Modeling and Turbulence Measurements, Tallahassee, Florida, September, 1996, pp. 457-464.

  1. W. Dai*, A parallel algorithm for direct solution of five-diagonal linear systems, Proceedings of the 7th SIAM Conference on Parallel Processing for Scientific Computing, SIAM, San Francisco, California, February, 1995, pp. 498-499.

  1. W. Dai and C. J. Chen*, Finite analytic explicit scheme for viscous Burger's equation, Proceedings of ASCE Engineering Mechanics Specialty Conference, May 20-22, 1991, Columbus, OH, USA, pp. 549-553. (Ei)

Invited Talks

  1. A hyperbolic model and its numerical scheme for thermal analysis in an N-carrier system, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana, October 10, 2008.

  1. A numerical method for studying thermal deformation in 3D micro structures exposed to ultrashort-pulsed lasers, Department of Mathematics, University of Texas at Arlington, February 8, 2008.

  1. 1) A hyperbolic two-step model based finite difference scheme for studying thermal deformation in a double-layered thin film exposed to ultrashort-pulsed lasers; 2) A numerical method for studying thermal deformation in 3D micro structures exposed to ultrashort-pulsed lasers, and 3) Solution methods for dual-phase-lagging heat transfer equations, First ASME Micro/Nanoscale Heat Transfer International Conference (MNHT08), Tainan, Taiwan, January 6-9, 2008.

  1. A hyperbolic two-step model based finite difference scheme for studying thermal deformation in a double-layered thin film exposed to ultrashort-pulsed lasers, 74th Annual Meeting of the American Physics Society Southeastern Section, Nashville, Tennessee, November 8-10, 2007.

  1. A numerical method for studying thermal deformation in 3D micro structures exposed to ultrashort-pulsed lasers, 1) Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, China, June 2007; 2) College of Mathematical Sciences, Xiamen University, Fujian, China, June 2007; 3) Department of Mathematics, Zhangzhou Normal University, Fujian, China, June 2007.

  1. A finite difference scheme for solving a nonlinear hyperbolic two-step model in a double-layered thin film exposed to ultrashort-pulsed lasers, Fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, Athens, Georgia , April 16-19, 2007

  1. On the stability of the FDTD method for solving a time-dependent Schrodinger equation, International Conference of Hybrid Systems and Applications, Lafayette, Louisiana , May 22-26, 2006

  1. A numerical method for obtaining an optimal temperature distribution in a 3D triple layered cylindrical skin structure, Department of Mathematical Sciences, University of Texas at Dallas, Texas, April, 2005

  1. Numerical modeling for optimizing laser power irradiating on a 3D triple layered skin structure, Proceedings of the 4th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields Honolulu, Hawaii, January 9-11, 2005.

  1. Finite difference schemes for solving parabolic two-step heat conduction equations in micro structures exposed to ultra-short pulsed lasers, Department of Mathematics & Statistics, Wright State University, Ohio, November, 2004

  1. A linear finite difference scheme for solving a nonlinear micro heat transport equation in symmetric thin film, Proceedings of the IUTAM Symposium on Complementary-Dual Variational Principles in Nonlinear Mechanics, Shanghai, CHINA, August 12-16, 2002.

  1. Approximate analytic method for solving dual-phase-lagging heat transport equations, SIAM Annual Meeting, San Diego, CA, July 8-13, 2001.

  1. Compact ADI methods for solving 2D and 3D heat equations, SIAM Conference in Computational Science and Engineering, Washington, D.C., September 21-24, 2000.

  1. A finite difference method for solving the heat transport equation in the microscale, American Mathematics Society, Special Session on Numerical Analysis and Mathematical Computations, Las Vegas, NV, April 10-12, 1999.

PRINCIPAL RESEARCH COLLABORATORS

 Adrian Bejan

 J. A. Jones Distinguished Professor, Duke University

 Walter Besio

 Assistant Professor, University of Rhode Island

 Zheng-fu Han

 Professor, University of Science and Technology of China

 Pedro M. Jordan

 Senior Scientist, Naval Research Laboratory at Mississippi

 Roderick V. N. Melnik

 Canada Tier-I Research Chair Professor, Wilfrid Laurier University

 Ronald E. Mickens

 Callaway Professor, Clark Atlanta University

 Raja Nassar

 Maxfield Professor, Louisiana Tech University

 Da Yu Tzou

 J. C. Dowell Professor and Chairman, University of Missouri at Columbia

 Jun Zhang

 Professor, University of Kentucky

 Jennifer Zhao

 Professor, University of Michigan at Dearborn