RESEARCH

Research Interests

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

  2. Artificial neural network method for solving partial differential equations.

  3. Simulations for micro/nano scale heat transfer, bio-heat transfer.

Awards and Honors

  1. Ranked #4 Highly Ranked Scholar in Finite Difference Method (Lifetime and top 0.05% of all scholars worldwide) by ScholarGPS (2024); Listed in Top 2% Scientists (2022) worldwide by Top2percentscientists.com based on Stanford/Elsevier's data.

  2. CARE Milestone Award, Louisiana Tech University (2021).

  3. Education Award, College of Engineering & Science, Louisiana Tech University (2017).

  4. Louisiana Tech University Senate Chair Award (2012).

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

  6. Louisiana Board of Regents Endowed Professorship with Title: McDermott International Professor (since 2004).

Professional Services

  1. Guest Editor for a special issue of Mathematical and Computational Applications. Extended deadline for manuscript submission: 15 October 2024.

  2. Editorial Board Member for two SCI journals: Processes and Electronic Research Archive

  3. Reviewer for Mathematical Reviews, American Mathematical Society; and Zentrablatt MATH, European Mathematical Society.

  4. Reviewer for numerous international journals, such as SIAM Journal on Numerical Analysis, Applied Mathematics Letters, Journal of Computational and Applied Mathematics, Numerical Methods for Partial Differential Equations, Journal of Computational Physics, International Journal of Heat and Mass Transfer, International Journal of Thermal Sciences.

  5. Reviewer for book proposals related to the finite difference method for publishers De Gruyter and Elsevier.

  6. Reviewer for research proposals for the National Science Foundation.

  7. Member of a Fulbright U.S. Scholar Discipline Peer Review Math Committee (2018).

  8. Invited Participant by Times Higher Education for ranking the best research universities and the best teaching universities in the world in 2020, 2021, 2022, 2023, 2024. Invited participant by U.S. News & World Report for ranking doctoral programs in mathematics in 2022, 2023. Invited participant by QS for the QS World University Rankings in 2023.

Ph.D. Dissertation Advisees

  1. Teng Zhu (deseased), Ph.D. in CAM (May 2000) Title: A hybrid finite element-finite difference method for thermal analysis in a double-layered thin film.

  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.

  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.

  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.

  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.

  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.

  7. Shengjun Su, Ph.D. in CAM (May 2005) Title: Numerical simulation of nanopulse penetration of biological matter using the z-transform.

  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.

  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.

  10. Haojie Wang, Ph.D. in Engineering (May 2007) Title: A numerical method for studying thermal deformation in 2D thin films exposed to ultrashort-pulsed lasers.

  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.

  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.

  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.

  15. Di Zhao, Ph.D. in CAM (May 2010) Title: Accurate and stable numerical methods for solving micro heat transfer models in an N-carrier system in spherical coordinates.

  16. Abdul Khaliq, Ph.D. in Engineering (August 2010) Title: Modeling and its numerical method for micro-scaled diffusion-reaction systems in the neuromuscular junction.

  17. Xiaoqi Zeng, Ph.D. in CAM (February 2011) Title: Vascular countercurrent network for 3D triple-layered skin structure with radiation heating.

  18. Runzhou Liu, Ph.D. in CAM (August 2011) Title: A numerical method for studying thermal deformation in 3D double-layered thin films with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers.

  19. James J. Elliott, III, Ph.D. in CAM (August 2011) Title: Improving the accuracy of the generalized FDTD-Q scheme for solving the linear time-dependent Schrodinger equation.

  20. Fei Zhu, Ph.D. in CAM (May 2012) Title: Numerical simulation of nanopulse penetration of biological matters using the ADI-FDTD method.

  21. Frederick I. Moxley III, Ph.D. in Engineering (August 2013) Title: A generalized finite-difference time-domain scheme for solving nonlinear Schrodinger equations.

  22. Liwei Shi, Ph.D. in CAM (August 2013) Title: A mathematical model and numerical method for thermoelectric DNA sequencing.

  23. Fei Han, Ph.D. in CAM (May 2014) Title: Numerical simulation of hydrogen absorption/desorption processes in cylindrical metal-hydrogen reactors for hydrogen storage.

  24. Casey O. Orndorff, Ph.D. in CAM (August 2016) Title: Thermal analysis in a triple-layered skin structure with embedded vasculature, tumor, and gold nanoshells.

  25. Yun Yan, Ph.D. in CAM (August 2018) Title: Higher-order accurate finite difference method for thermal analysis in double-layered solid structures--Gradient preserved method.

  26. Joshua P. Wilson, Ph.D. in CAM (May 2020) Title: ABC method and fractional momentum layer for the FDTD method to solve the Schrödinger equation on unbounded domains.

  27. Yu-Shan Lin, Ph.D. in CAM (May 2021) Title: An accurate numerical method for solving the model of American options with regimes switching.

  28. Aniruddha Bora, Ph.D. in CAM (November 2021) Title: Gradient preserved method and artificial neural network method for solving heat conduction equations in double layered structures.

GRANTS

  1. PI, A generalized finite-difference time-domain method for solving the complex Ginzburg-Landau equation, granted by LaSPACE, $33,263, 07/01/2013-09/30/2014.

  2. PI, Computational model and experimental verification for the development of drug-eluting stent coatings for arterial pharmacokinetics, granted by NSF-Louisiana Pfund, $10,000, 01/01/2013-12/31/2013.

  3. PI, A generalized finite-difference time-domain method for solving time-dependent non-linear Schrödinger equation, granted by LaSPACE, $46,280, 01/01/2012-01/31/2013.

  4. Senior Investigator, Louisiana Alliance for Simulation-Guided Materials Applications (LA-SiGMA), granted by NSF-EPSCOR, $20,000,000, 10/1/2010-11/30/2015.

  5. Co-PI, DNA image segmentation methods and statistical modeling, granted by BoRSF (Louisiana Board of Regents Support Fund), $113,554, 7/1/2010-9/1/2013.

  6. PI, Development of a higher-order finite difference time domain method for solving Schrödinger equation, granted by Louisiana SPACE, $16,504, 11/01/2010-10/31/2011.

  7. Co-PI, A hybrid method for solving inverse medium and obstacle problems with limited or synthetic aperture, granted by BoRSF, $116,394, 7/1/2008-9/1/2011.

  8. Co-PI, An efficient method for simulating diffusion inside nano-tubes for drug delivery systems, granted by BoRSF, $83,793, 7/1/2007-9/1/2010.

  9. PI, 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, 6/1/2005-9/15/2005.

  10. Co-PI, An approximate analytic method for solving a dual-phase-lagging heat transport equation in microscale thin films, granted by BoRSF, $108,315, 6/01/2002-6/30/2005.

  11. Senior Investigator, Bioeffects of electromagnetic nanopulses, granted by Air Force Office of Scientific Research, $2,221,000, 3/1/2002 - 9/30/2004.

  12. Senior Investigator, Development of a center for advanced mold/mask process and applications, granted by Army Research Office, $1,994,501, 03/15/1996 - 03/14/2001.

  13. Co-PI, High pressure, convectively-enhanced laser chemical vapor deposition for rapid prototyping and automated part manufacture, granted by BoRSF, $199,068, 06/01/1997 - 06/30/2000.

  14. PI, Three-dimensional numerical method for thermal analysis in X-ray lithography, granted by Louisiana BoRSF, $29,682, 06/01/1996 - 06/30/1998.

  15. Co-PI, Computational Analysis and Modeling Doctoral Graduate Fellows, granted by Louisiana BoRSF, $108K, 2018-2022.

  16. PI, Computational Analysis and Modeling Doctoral Graduate Fellows, granted by Louisiana BoRSF, $100K, 2015-2019.

  17. Co-PI, Computational Analysis and Modeling Doctoral Graduate Fellows, granted by Louisiana BoRSF, $200K, 2012-2016.

  18. Co-PI, Computational Analysis and Modeling Doctoral Graduate Fellows, granted by Louisiana BoRSF, $200K, 2011-2015.

PUBLICATIONS

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 (deseased). Xiamen University, Xiamen, P. R. China, 1986.

  2. Ph.D. dissertation "A numerical solution of unsteady incompressible Navier-Stokes equations using the explicit finite analytic method". Advisor: Professor Ching-Jen Chen (deseased). University of Iowa , Iowa, 1994.

Book / Book Chapter

  1. R. Nassar and W. Dai, Modeling of Microfabrication Systems, Springer-Verlag, Berlin, 2003. ISBN 3-540-00252-9, Library of Congress Classification: TK7836 .N35 2003.

    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.

  3. W. Dai, Constructal Theory Applied to Vascular Countercurrent Networks, Chapter 9 in the Book “Constructal Law and the Unifying Pronciple of Design” edited by Luiz A. O. Rocha, Sylvie Lorente, and Adrian Bejan, Springer, 2013, pp. 143-160. ISBN 978-1-4614-5048-1

  4. F. I. Moxley III, D. T. Chuss, and W. Dai, An Implicit Generalized Finite-Difference Time-Domain Scheme for Solving Nonlinear Schrödinger Equations, in the Book “Contemporary Mathematics: Mathematics of Continuous and Discrete Dynamical Systems”, edited by Abba B. Gumel, American Mathematical Society, vol. 618, pp. 181-194, 2014. ISBN-13: 978-0-8218-9862-8

  5. W. Dai, A. Khaliq, and R. Nassar, An Introduction to Finite Element Method, Van-Griner Learning, Cincinnati, Ohio, 2021. ISBN 978-1-61740-847-2

  6. C. Ji and W. Dai, A Fractional-Order Equation and Its Finite Difference Scheme for Approximating a Delay Equation, in the Book “Contemporary Mathematics: Mathematical and Computational Modeling of Phenomena Arising in Population Biology and Nonlinear Oscillations”, edited by Abba B. Gumel, in celebrating the 80th birthday of Professor Ronald E. Mickens, American Mathematical Society, vol. 793, pp. 141-166, 2024.

 

Encyclopedia

  1. W. Dai, Finite Difference Simulation of Thermal Deformation in Ultrashort-Pulsed Laser Material Processing, in the “Encyclopedis of Thermal Stresses”, edited by Richard Hetnarski, Springer, ISBN 978-94-007-2738-0, 2014, pp. 1594-1600.

  2. W. Dai, Skin Burn Injury Prediction, in the “Encyclopedis of Thermal Stresses”, edited by Richard Hetnarski, Springer, ISBN 978-94-007-2738-0, 2014, pp. 4421-4427.

 

Papers in Refereed Journals (Asterisk indicates the corresponding author, publications in MathSciNet)

  1. J. P. Wilson, C. Ji, and W. Dai*, A new variable-order fractional momentum operator for wave absorption when solving Schrödinger equations, Journal of Computational Physics, vol. 511, 113123, 2024.

  1. C. Nwankwo*, T. Ware, and W. Dai, Ensemble deep neural network method for solving free boundary American style stochastic volatility models, accepted by Applied Intelligence.

  1. E. Awad*, W. Dai, and S. Sobolev, Thermal oscillations and resonance in electron-phonon interaction process, Zeitschrift für angewandte Mathematik und Physik, vol. 75, 143, 2024.

  1. C. Nwankwo*, T. Ware, and W. Dai, A fast and enhanced shallow learning framework for solving free boundary options pricing problems, Neural Computing and Applications, vol. 36, pp. 12327-12356, 2024.

  1. C. Nwankwo* and W. Dai, Sixth-order compact differencing with staggered boundary schemes and 3 (2) Bogacki-Shampine pairs for pricing free-boundary options, International Journal of Numerical Analysis and Modeling, vol. 21, pp. 793-821, 2024.

  1. F. Guo and W. Dai*, Model and numerical method for soliton propagation through thermal meduim based on nonlinear Schrodinger and heat transfer equations, Communications in Nonlinear Science and Numerical Simulation, vol. 131, 107790, 2024.

  1. C. Nwankwo*, N. Umeorah, T. Ware, and W. Dai, Deep learning and American options via free boundary framework, accepted by Computational Economics.

  1. Y. He, X. Wang*, W. Dai, and Y. Deng , A new high-order accurate conservative finite difference scheme for the coupled nonlinear Schrodinger equations, accepted by Mathematical Methods in the Applied Sciences.

  1. C. Nwankwo* and W. Dai, Efficient adaptive strategies with fourth-order compact scheme for a fixed-free boundary regime-switching model, Decisions in Economics and Finance, vol. 47, pp. 43-82, 2024.

  1. M. Cui, C. Ji*, and W. Dai, Afinite difference method for solving the wave equation with fractional damping, Mathematical and Computational Applications, vol. 29, 2, 2024.

  1. Z. Weng, S. Zhai*, W. Dai, Y. Yang, and Y. Mo, Splitting method for the nonlocal ternary conservative Allen-Cahn model, Journal of Computational and Applied Mathematics, vol. 441, 115668, 2024.

  1. J. L. Lage*, et al., Professor Adrian Bejan on his 75th birthday, International Communications in Heat and Mass Transfer, vol. 149, 107162, 2023. Click here to link the article.

  1. C. Nwankwo*, W. Dai, and R. Liu, Compact finite difference scheme with Hermite interpolation for pricing American put options based on regime switching model, Computational Economics, vol. 62, pp. 817-854, 2023.

  1. C. Nwankwo* and W. Dai, Efficiency of some predictor-corrector methods with fourth-order compact scheme for a system of free boundary options, Axioms, vol. 12, 762, 2023.

  1. C. Ji and W. Dai*, Sub-diffusion two-temperature model and accurate numerical scheme for heat conduction induced by ultrashort-pulsed laser heating, Fractal and Fractional, vol. 7, 319, 2023.

  1. C. Nwankwo * and W. Dai, Local refinement and adaptive strategy for a system of free boundary power options with high order compact differencing, Axioms, vol. 12, 602, 2023.

  1. F. Guo* and W. Dai, A new absorbing layer approach for solving the nonlinear Schrödinger equation, Applied Numerical Mathematics, vol. 189, pp. 88-106, 2023.

  1. Y-S. Lin, W. Dai*, and R. Liu, An accurate compact finite difference scheme for solving the American option with M-regime switching model, International Journal of Applied and Computational Mathematics, vol. 9. 17, 2023.

  1. C. Ji, W. Dai*, and R. E. Mickens, A fractional-order alternative for phase-lagging equation, International Journal of Numerical Analysis and Modeling, vol. 20, pp. 391-406, 2023.

  1. J. Chen and W. Dai*, A compact finite difference scheme with absorbing boundary condition for forced KdV equation, MethodsX, vol. 10, 102036, 2023.

  1. S. Shen, W. Dai*, Q. Liu, and P. Zhuang, Accurate numerical scheme for solving fractional diffusion-wave two-step model for nanoscale heat conduction, Journal of Computational and Applied Mathematics, vol. 419, 114721, 2023.

  1. C. Ji* and W. Dai, Numerical algorithm with fourth-order spatial accuracy for solving the time-fractional dual-phase-lagging nanoscale heat conduction equation, Numerical Mathematics: Theory, Methods and Applications, vol. 16, pp. 511-540, 2023.

  1. F. Guo* and W. Dai, Arbitrarily high-order accurate and energy-stable schemes for solving the conservative Allen-Cahn equation, Numerical Methods for Partial Differential Equations , vol. 39, pp. 187-212, 2023.

  1. X. Wang*, H. Cheng, and W. Dai, Conservative and fourth-order compact difference schemes for the generalized Rosenau-Kawahara-RLW equation, Engineering with Computers, vol. 38, pp. 1491-1514, 2022.

  1. J. P. Wilson, W. Dai*, A. Bora, and J. C. Boyt, A new artificial neural network method for solving Schrodinger equations on unbounded domains, Communications in Computational Physics, vol. 32, pp. 1039-1060, 2022.

  1. A. Bora, W. Dai*, J. P. Wilson, J. C. Boyt, and S. L. Sobolev, Neural network method for solving nonlocal two-temperature nanoscale heat conduction in gold films exposed to ultrashort-pulsed lasers, International Journal of Heat and Mass Transfer, vol. 190, 122791, 2022.

  1. C. Nwankwo* and W. Dai, On the efficiency of 5(4) RK-embedded pairs with high order compact scheme and Robin boundary condition for options valuation, Japan Journal of Industrial and Applied Mathematics, vol. 39, pp. 753-775, 2022.

  1. S. L. Sobolev* and W. Dai, Heat transport on ultrashort time and space scales in nanosized systems: diffusive or wave-like? Materials, vol. 15, 4287, 2022.

  1. Y. He, X. Wang*, and W. Dai, Coupled and decoipled high-order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations, Numerical Methods for Partial Differential Equations, vol. 38, pp. 1112-1143, 2022.

  1. F. Guo* and W. Dai, A new absorbing layer for simulation of wave propagation based on a KdV model on unbounded domain, Applied Numerical Mathematics, vol. 174, pp. 46-70, 2022.

  1. A. Bora, W. Dai*, J. P. Wilson, and J. C. Boyt, Neural network method for solving parabolic two-temperature microscale heat conduction in double-layered thin films exposed to ultrashort-pulsed lasers, International Journal of Heat and Mass Transfer, vol. 178, 121616, 2021.

  1. C. Nwankwo* and W. Dai, An adaptive and explicit fourth order Runge-Kutta-Fehlberg method coupled with compact finite differencing for pricing American put options, Japan Journal of Industrial and Applied Mathematics, vol. 38, pp. 921-946, 2021.

  1. X. Wang*, W. Dai, and Y. Yan, Numerical analysis of a new conservative scheme for the 2D generalized Rosenau-RLW equation, Applicable Analysis, vol. 100, pp. 2564-2580, 2021.

  1. W. Li*, J. Huang, J. Li, and W. Dai, Matrix representation of optimal scale for generalized multi-scale decision table, Journal of Ambient Intelligence and Humanized Computing, vol. 12, pp. 8549-8559, 2021.

  1. X. Wang*, W. Dai, and M. Usman, A high-order accurate finite difference for the KdV equation with time-periodic boundary forcing, Applied Numerical Mathematics, vol. 160, pp. 102-121, 2021.

  1. W. Li*, J. Li, J. Huang, W. Dai, and X. Zhang, A new rough set model based on multi-scale covering, International Journal of Machine Learning and Cybernetics, vol. 12, pp. 243-256, 2021.

  1. A. Bora and W. Dai*, Gradient preserved method for solving heat conduction equation with variable coefficients in double layers, Applied Mathematics and Computation, vol. 386, 125516, 2020.

  1. X. Wang* and W. Dai, A new conservative finite difference scheme for the generalized Rosenau-KdV-RLW equation, Computational and Applied Mathematics, vol. 39, pp. 1-19, 2020.

  1. S. Shen, W. Dai*, and J. Cheng, Fractional parabolic two-step model and its accurate numerical scheme for nanoscale heat conduction, Journal of Computational and Applied Mathematics, vol. 375, 112812, 2020.

  1. J. Cheng* and W. Dai, Adjoint difference equation for the Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on non-uniform lattices, The Ramanujan Journal, vol. 53, pp. 285-318, 2020.

  1. S. Zhai, L. Huang, Z. Weng, and W. Dai*, Parabolic two-step model and accurate numerical scheme for nanoscale heat conduction induced by ultrashort-pulsed laser, Journal of Computational and Applied Mathematics, vol. 369, 112591, 2020.

  1. J. Cheng* and W. Dai, Fractional vector Taylor and Cauchy mean value formulas, Journal of Fractional Calculus and Applications, vol. 11, pp. 130-147, 2020.

  1. Z. Huang*, J. Li, W. Dai, and R. Lin, Generalized multi-scale decision tables with multi-scale decision attributes, International Journal of Approximate Reasoning, vol. 115, pp. 194-208, 2019.

  1. C. Ji, W. Dai, and Z.Z. Sun*, Numerical schemes for solving the time-fractional dual-phase-lagging heat conduction model in a double-layered nanoscale thin film, Journal of Scientific Computing, vol. 81, pp. 1167-1800, 2019.

  1. Y. Yan, W. Dai*, L. Wu, and S. Zhai, Accurate gradient preserved method for solving heat conduction equations in double layers, Applied Mathematics and Computation, vol. 354, pp. 58-85, 2019.

  1. X. Wang* and W. Dai, Numerical investigation into natural convection of nanofluids in an inclined square enclosure with non-uniform heated walls, Scientia Iranica B, vol. 26, pp. 2311-2328, 2019.

  1. X. Wang* and W. Dai, A conservative fourth-order stable finite difference scheme for the generalized Rosenau-KdV equation in both 1D and 2D, Journal of Computational and Applied Mathematics, vol. 355, pp. 310-331, 2019.

  1. X. Wang*, W. Dai, and S. Guo, A conservative linear difference scheme for the 2D regularized long-wave equation, Applied Mathematics and Computation, vol. 342, pp. 55-70, 2019.

  1. J. L. Lage*, et al., Celebration of Professor Adrian Bejan on his 70th birthday, International Journal of Heat and Mass Transfer, vol. 126, pp. 1377-1378, 2018. Click here to link the article.

  1. X. Wang* and W. Dai, A new implicit energy conservative difference scheme with fourth-order accuracy for the generalized Rosenau-Kawahara-RLW equation, Computational and Applied Mathematics, vol. 37, pp. 6560-6581, 2018.

  1. C. Ji, W. Dai, and Z. Z. Sun*, Numerical method for solving the time-fractional dual-phase-lagging heat conduction equation with the temperature-jump boundary condition, Journal of Scientific Computing, vol. 75, pp. 1307-1336, 2018.

  1. J. Cheng and W. Dai*, Higher-order fractional Green and Gauss formulas, Journal of Mathematical Analysis and Applications, vol. 462, pp. 157-171, 2018.

  1. X. Wang* and W. Dai, A three-level linear implicit conservative scheme for the Rosenau-KdV-RLW equation, Journal of Computational and Applied Mathematics, vol. 330, pp. 295-306, 2018.

  1. X. Wang*, J. Wang, and W. Dai, Effects of heat flux on natural convection of water-based nanofluids in a trapezoidal enclosure, Heat Transfer Research, vol. 49, pp. 1299-1321, 2018.

  1. X. Wang* and W. Dai, Heatline analysis on heat transfer and convective flow of nanofluids in an inclined enclosure, Heat Transfer Engineering, vol. 39, pp. 843-860, 2018.

  1. C. Orndorff, S. Ponomarev, W. Dai*, and A. Bejan, Thermal analysis in a triple-layered skin structure with embedded vasculature, tumor, and gold nanoshells, International Journal of Heat and Mass Transfer, vol. 111, pp. 677-695, 2017.

  1. F. I. Moxley*, J. P. Dowling, W. Dai, and T. Byrnes, Sagnac interferometer with coherent vortex superposition states in exciton-polariton condensates, Physical Review A, vol. 93, 053603, 2017.

  1. H. Sun, Z. Z. Sun, and W. Dai*, A second-order difference scheme for the dual-phase-lagging equation in a double-layered thin film, Numerical Methods for Partial Differential Equations, vol. 33, pp. 142-173, 2017.

  1. J. Ren, Z. Z. Sun, and W. Dai*, New approximations for solving the Caputo-Type fractional partial differential equations, Applied Mathematical Modelling, vol. 40, pp. 2625-2636, 2016.

  1. C. Orndorff and W. Dai*, Numerical hyperthermia simulation for a 3-D triple-layered skin structure with embedded vascular countercurrent network and nanoparticles, International Journal of Heat and Technology, vol. 34, pp. S179-S184, 2016.

  1. F. I. Moxley, T. Byrnes, B. Ma, Y. Yan, and W. Dai*, A G-FDTD scheme for solving multi-dimensional open dissipative Gross-Pitaevskii equations, Journal of Computational Physics, vol. 282, pp. 303-316, 2015.

  1. Y. Yan, F. I. Moxley, and W. Dai*, A new compact finite difference scheme for solving the complex Ginzburg-Landau equation, Applied Mathematics and Computation, vol. 260, pp. 269-287, 2015.

  1. H. Sun, R. Du, W. Dai, and Z. Z. Sun*, A high order accurate numerical method for solving two-dimensional dual-phase-lagging equation with temperature jump boundary condition in nano heat conduction, Numerical Methods for Partial Differential Equations, vol. 31, pp. 1742-1768, 2015.

  1. R. K. Mohanty*, W. Dai, and F. Han, Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations, Applied Mathematics and Computation, vol. 256, pp. 381-393, 2015.

  1. R. K. Mohanty*, W. Dai, and D. Liu, Compact operator method of accuracy two in time and four in space for the the solution of time dependent Burgers-Huxley equation, Numerical Algorithms, vol. 70, pp. 591-605, 2015.

  1. R. K. Mohanty*, W. Dai, and F. Han, A new high accuracy method for 2D biharmonic equation with nonlinear third derivative terms: application to Navier-Stokes equations of motion, International Journal of Computer Mathematics, vol. 92, pp. 1574-1590, 2015.

  1. B. Jiang, W. Dai, A. Khaliq, X. Zhou and L. Zhang*, Novel 3D GPU based numerical parallel diffusion algorithms in cylindrical coordinates for health care simulation, Mathematics and Computers in Simulation, vol. 109, pp. 1-19, 2015.

  1. Z. Z. Sun* and W. Dai, A new accurate numerical method for solving heat conduction in a double-layered film with the Neumann boundary condition, Numerical Methods for Partial Differential Equations, vol. 30, pp. 1291-1314, 2014.

  1. L. Shi, E. J. Guilbeau, G. Nestorova, and W. Dai*, A mathematical model and numerical method for thermoelectric DNA sequencing, Heat and Mass Transfer, vol. 50, pp. 693-709, 2014.

  1. Y. Yan* and W. Dai, Generalized finite-difference time-domain compact schemes for solving a nonlinear Schrödinger equation, Chinese Universities on Journal of Numerical Mathematics, vol. 36, pp. 49-57, 2014.

  1. C. V. Falke, A. Khaliq, T. R. Dugas, J. J. Kleinedler, and W. Dai*, Mathematical model for predicting arterial drug diffusion from drug-eluting stents, International Journal of Computer Science and Application, vol. 3, pp. 34-37, 2014.

  1. L. Cui, F. Han, W. Dai, and E. P. Murray*, Influence of microstructure on the sensing behavior of NOx exhaust gas sensors, Journal of The Electrochemical Socirty, vol. 161, pp. B34-B38, 2014.

  1. W. Dai*, F. Han, and Z. Z. Sun, Accurate numerical method for solving dual-phase-lagging equation with temperature jump boundary condition in nano heat conduction, International Journal of Heat and Mass Transfer, vol. 64, pp. 966-975, 2013.

  1. F. I. Moxley III, D. T. Chuss, and W. Dai*, A generalized finite-difference time-domain scheme for solving nonlinear Schrodinger equations, Computer Physics Communications, vol. 184, pp. 1834-1841, 2013.

  1. F. Han and W. Dai*, New higher-order compact finite difference schemes for 1D heat conduction equations, Applied Mathematical Modelling. vol. 37, pp. 7940-7953, 2013.

  1. R. Liu, F. Han, and W. Dai*, A numerical method for studying thermal deformation in 3D double-layered thin films with imperfect thermal contact exposed to ultrashort-pulsed lasers, Numerical Heat Transfer, Part A, vol. 63, pp. 643-665, 2013.

  1. W. Dai*, F. Han, and D. Hui, A numerical method for simulating hydrogen absorption in metal-H2 reactors for hydrogen storage, World Journal of Engineering, vol. 10, pp. 29-38, 2013.

  1. F. I. Moxley III, T. Byrnes, F. Fujiwara, and W. Dai*, Generalized finite-difference time-domain quantum method for the N-body interacting Hamiltonian, Computer Physics Communications. vol. 183, pp. 2434-2440, 2012.

  1. F. I. Moxley III, F. Zhu, and W. Dai*, A generalized FDTD method with absorbing boundary condition for solving a time-dependent linear Schrödinger equation, American Journal of Computational Mathematics, vol. 2, pp. 163-172, 2012.

    Download the files to see PARTICLE MOTION and an APPLICATION of This Method

  1. W. Dai* and D. Y. Tzou, An accurate and stable numerical method for solving a micro heat transfer model in a 1D N-carrier system in spherical coordinates, ASME Journal of Heat Transfer. vol. 134, 051005, 2012.

    This paper was presented in the 2009 ASME Micro/Nanoscale Heat and Mass Transfer Conference in Shanghai, China, and was recommended for being included in a special issue of the journal.

  1. B. Jiang, A. Struthers, Z. Sun, Z. Feng, X. Zhao, K. Zhao, W. Dai, X. Zhou, M. E. Berens, and L. Zhang*, Employing graphic programming unit technology, alternating direction implicit method and domain decomposition to speed up the numerical diffusion solver for the biomedical engineering research, International Journal for Numerical Methods in Biomedical Engineering, vol. 27, pp. 1429-1449, 2011.

  1. A. Khaliq, F. Jenkins, M. DeCoster, and W. Dai*, A new 3D mass diffusion-reaction model in the neuromuscular junction, Journal of Computational Neuroscience, vol. 30, pp. 729-745, 2011.

  1. D. Liu*, Y. Lvov, and W. Dai, Joint simulations of confined diffusion inside nanotubules, Journal of Computational and Theoretical Nanoscience, vol. 8, pp. 1-11, 2011.

  1. W. Dai*, An improved compact finite difference scheme for solving an N-carrier system with Neumann boundary conditions, Numerical Methods for Partial Differential Equations, vol. 27, pp. 436-446, 2011.

  1. R. Nassar*, X. Wu, M. Paun, W. Dai, and J. Palmer, A mathematical model characterizing the diffusion properties of microcapsules, Chemical Engineering Communications, vol. 198, pp. 33-45, 2011.

  1. D. Zhao and W. Dai*, Accurate finite difference schemes for solving a 3D micro heat transfer model in an N-carrier system with Neumann boundary condition in spherical coordinates, Journal of Computational and Applied Mathematics, vol. 235, pp. 850-869, 2010.

  1. W. Dai* and C. Johnson, A new accurate finite difference scheme for thermal analysis in 1D micro-spheres exposed to ultrashort-pulsed lasers, Numerical Heat Transfer, Part B, vol. 57, pp. 241-259, 2010.

  1. X. Zeng, W. Dai*, and A. Bejan, Vascular countercurrent network for 3D triple-layered skin structure with radiation heating, Numerical Heat Transfer, Part A, vol. 57, pp. 369-391, 2010.

  1. W. Dai*, A compact LOD scheme for solving a 3D N-carrier system with Neumann boundary conditions, Numerical Methods for Partial Differential Equations, vol. 26, pp. 1079-1098, 2010.

  1. W. Dai*, A new accurate finite difference scheme for Neumann (insulated) boundary condition of heat conduction, International Journal of Thermal Sciences. vol. 49, pp. 571-579, 2010.

  1. W. Dai* and D. Y. Tzou, A fourth-order compact finite difference scheme for solving an N-carrier system with Neumann boundary conditions, Numerical Methods for Partial Differential Equations vol. 25, pp. 274-289, 2010.

  1. S. Ni, P. Wang, M. Paun, W. Dai, and A. Paun*, Spotted cDNA microarray image segmentation using ACWE, Romanian Journal of Information Science and Technology. vol. 12, pp. 249-263, 2009.

  1. W. Dai*, A hyperbolic microscopic model and its numerical scheme for thermal analysis in an N-carrier system, International Journal of Heat and Mass Transfer, vol. 52, pp. 2379-2389, 2009.

  1. W. Dai*, F. Zhu, and D. Y. Tzou, A stable finite difference scheme for thermal analysis in an N-carrier system, International Journal of Thermal Sciences, vol. 48, pp. 1530-1541, 2009.

  1. D. Y. Tzou* and W. Dai, Thermal lagging in multi-carrier systems, International Journal of Heat and Mass Transfer, vol. 52, pp. 1206-1213, 2009.

  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, Chemical Engineering Communications, vol. 196, pp. 812-823, 2009.

  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.

    The paper is listed as one of the Most Cited MRC Articles Since 2007.

  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.

  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.

  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. 

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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.

  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, vol. 29, pp. 174-181, 1992.

  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. F. Han and W. Dai*, A numerical method for simulating hydrogen desorption in metal-H2 reactors for hydrogen storage, Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, Texas, November 9-15, 2012, 10 pages.

  1. F. Zhu and W. Dai*, Numerical simulation of nanopulse penetration of biological matters using the ADI-FDTD method, Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition, Houston, Texas, November 9-15, 2012, 12 pages.

  1. W. Dai*, Applications of constructal theory to vascular countercurrent network, Proceedings of the Constructal Conference, Porto Alegre, Brazil, December 1-2, 2011, 10 pages. (This paper was selected by the conference for being included in an edited book published by Springer.)

  1. R. Liu and W. Dai*, A numerical method for studying thermal deformation in 3D double-layered thin films with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers, Proceedings of the 19th Annual International Conference on Composites or Nano Engineering, Shanghai, China, July 24-30, 2011, 2 pages.

  1. B. Mathew*, T. J. John, W. Dai, and H. Hegab, Performance of cross flow microchannel heat exchangers subjected to viscous dissipation, Proceedings of the ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting and 8th International Conference on Nanochannels, Microchannels, and Minichannels, Montreal, Canada, August 1-5, 2010, 8 pages.

  1. W. Dai* and D. Y. Tzou, An accurate and stable numerical method for solving a micro heat transfer model in a 1D N-carrier system in spherical coordinates, Proceedings of the ASME 2009 Micro/Nanoscale Heat and Mass Transfer, Shanghai, China, December 18-21, 2009, 10 pages.

  1. T. Chen, W. Besio*, and W. Dai, Comparison of the tripolar, bipolar, and spline Laplacian electrocardiogram based on computer simulation, Proceedings of the 31st Annual International IEEE EMBS Conference, Minneapolis, Minnesota, September 2-6, 2009, 10 pages.

  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.

  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.

  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, Ohio, pp. 549-553.