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Weizhang Huang's research

Research topics:

• Adaptive moving mesh methods (see pictures and animations) • Anisotropic mesh adaptation and generation • Spectral methods, collocation methods • Geometric integration, numerical solution of Hamiltonian systems • Computational fluid dynamics

Book:


    W. Huang and R. D. Russell, Adaptive Moving Mesh Methods (Springer, New York). 2011, XVII, 432p. 121 illus., 7 in color., Hardcover. ISBN: 978-1-4419-7915-5. (ebook version)

    Click here for Matlab programs for 1D moving mesh finite difference and finite element methods and some examples in Chapters 1 and 2 of the book.

    Errata (last updated on July 13, 2016).

Software:


  1. MMPDElab: A MATLAB package for adaptive mesh movement and finite element computation. The code is also availabel at github.com/weizhanghuang/MMPDElab

  2. Matlab codes for 1D moving mesh methods

  3. MOVCOL : 1D Moving collocation method (fortran77)

Research articles:

(Research listings in: Google Scholar, MathSciNet, Web of Science, ResearchGate

  1. Jinye Shen, Bowen Shi, and Weizhang Huang, Meshfree finite difference solution of homogeneous Dirichlet problems of the fractional Laplacian, Communications on Applied Mathematics and Computation (to appear) (arXiv:2404.04407)

  2. Jinye Shen, Heng Dai, and Weizhang Huang, A moving mesh finite element method for Bernoulli free boundary problems, Comm. Comput. Phys. (to appear) (arXiv:2404.04418)

  3. Weizhang Huang and Jinye Shen, A grid-overlay finite difference method for the fractional Laplacian on arbitrary bounded domains, SIAM Journal on Scientific Computing, 46 (2024), A744-A769. (arXiv:2307.14437) (DOI: 10.1137/23M1558562)

  4. Jinye Shen, Weizhang Huang, and Jingtang Ma, An efficient and provable sequential quadratic programming method for American and swing option pricing, European Journal of Operational Research, 316 (2024), 19-35. (DOI: 10.1016/j.ejor.2023.11.012)

  5. Weizhang Huang, Ruo Li, Jianxian Qiu, and Min Zhang, A well-balanced moving mesh discontinuous Galerkin method for the Ripa model on triangular meshes, J. Comput. Phys. 487 (2023), 112147. (arXiv:2205.14560) (DOI: 10.1016/j.jcp.2023.112147)

  6. Yinnian He and Weizhang Huang, Mesh sensitivity analysis for finite element solution of linear elliptic partial differential equations, (arXiv:2111.10935)

  7. Min Zhang, Weizhang Huang, and Jianxian Qiu, A study on CFL conditions for the DG solution of conservation laws on adaptive moving meshes, Numer. Math. Theor. Meth. Appl. 16 (2023), 111-139. (arXiv:2106.08504) (DOI: 10.4208/nmtma.OA-2021-0169)

  8. Alexander Fulk, Weizhang Huang, and Folashade Agusto, Exploring the effects of prescribed fire on ticks spread and propagation in a spatial setting, Computational and Mathematical Methods in Medicine (2022) 5031806 (medRXiv: 10.1101/2022.01.12.22268825) (DOI: 10.1155/2022/5031806)

  9. Cassidy Krause, Weizhang Huang, David Mechem, Erik Van Vleck, and Min Zhang, A metric tensor approach to data assimilation with adaptive moving meshes, J. Comput. Phys. 466 (2022), 111407. (arXiv:2109.05990) (DOI: 10.1016/j.jcp.2022.111407)

  10. Fei Zhang, Weizhang Huang, Xianping Li, and Shicheng Zhang, A study on phase-field models for brittle fracture Int. J. Numer. Anal. Modeling 19 (2022), 791-819. (arXiv:1805.07357)

  11. Maurin Lopez, Suzanne Shontz, and Weizhang Huang, A parallel variational mesh quality improvement method for tetrahedral meshes based on the MMPDE method, Computer-Aided Design 148 (2022), 103242. (DOI: 10.1016/j.cad.2022.103242)

  12. Dongmi Luo, Shiyi Li, Weizhang Huang, Jianxian Qiu, and Yibing Chen, A quasi-conservative DG-ALE method for multi-component flows using the non-oscillatory kinetic flux, J. Sci. Comput. 90 (2022) 46. (arXiv:2101.04897) (DOI: 10.1007/s10915-021-01732-4)

  13. Min Zhang, Weizhang Huang, and Jianxian Qiu, A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations, Comm. Comput. Phys. 31 (2022), 94-130. (arXiv:2008.11594) (DOI: 10.4208/cicp.OA-2021-0127)

  14. Bowen Lin, Shujun Fu, Yuting Lin, Ronny Rotondo, Weizhang Huang, Harold Li, Ronald Chen, and Hao Gao, An adaptive spot placement method on Cartesian grid for pencil beam scanning proton therapy, Physics in Medicine and Biology, 66 (2021), 235012. (DOI: 10.1088/1361-6560/ac3b65)

  15. Min Zhang, Weizhang Huang, and Jianxian Qiu, A high-order well-balanced positivity-preserving moving mesh DG method for the shallow water equations with non-flat bottom topography, J. Sci. Comput. 87 (2021) 88. (arXiv:2006.15187) (DOI: 10.1007/s10915-021-01490-3)

  16. Mohamed Sulman, Truong B. Nguyen, Ronald D. Haynes, and Weizhang Huang, Domain decomposition parabolic Monge-Ampere approach for fast generation of adaptive moving meshes, Comput. Math. Appl. 84 (2021), 97-111. (arXiv:2006.14602) (DOI: 10.1016/j.camwa.2020.12.007)

  17. Weizhang Huang, Weishi Liu, and Yufei Yu, Permanent charge effects on ionic flow: a numerical study of flux ratios and their bifurcation, Comm. Comput. Phys. 30 (2021), 486-514. (arXiv:2003.11223) (DOI: 10.4208/cicp.OA-2020-0057)

  18. W. Huang, L. Kamenski, and J. Lang, Conditioning of implicit Runge-Kutta integration for finite element approximation of linear diffusion equations on anisotropic meshes, J. Comput. Appl. Math. 387 (2021), 112497. (arXiv:1703.06463) (DOI: 10.1016/j.cam.2019.112497)

  19. Min Zhang, Weizhang Huang, and Jianxian Qiu, High-order conservative positivity-preserving DG-interpolation for deforming meshes and application to moving mesh DG simulation of radiative transfer, SIAM J. Sci. Comput. 42 (2020), A3109-A3135. (arXiv:1910.11931) (DOI: 10.1137/19M1297907)

  20. W. Huang and Y. Wang, Anisotropic mesh quality measures and adaptation for polygonal meshes, J. Comput. Phys. 410 (2020), 109368 (arXiv:1507.08243) (DOI: 10.1016/j.jcp.2020.109368)

  21. Weizhang Huang, An introduction to MMPDElab, (arXiv:1904.05535)

  22. Min Zhang, Juan Cheng, Weizhang Huang, and Jianxian Qiu, An adaptive moving mesh discontinuous Galerkin method for the radiative transfer equation, Comm. Comput. Phys. 27 (2020), 1140-1173. (arXiv:1809.09052) (DOI: 10.4208/cicp.OA-2018-0317)

  23. A Ram Kim, Shawn Keshmiri, Aaron Blevins, Daksh Shukla, and Weizhang Huang, Control of multi-agent collaborative fixed-wing UASs in unstructured environment, Journal of Intelligent and Robotics Systems 97 (2020), 205-225. (DOI: 10.1007/s10846-019-01057-3)

  24. Avary Kolasinski and Weizhang Huang, A surface moving mesh method based on equidistribution and alignment, J. Comput. Phys. 403 (2020), 109097. (arXiv:1901.09081) (DOI: 10.1016/j.jcp.2019.109097)

  25. Suzanne Shontz, Lopez Maurin, and Weizhang Huang, A parallel variational mesh quality improvement method for tetrahedral meshes, the 28th International Meshing Roundtable (2019) (pdf) (DOI: 10.5281/zenodo.3653361)

  26. Dongmi Luo, Weizhang Huang, and Jianxian Qiu, A quasi-Lagrangian moving mesh discontinuous Galerkin method for hyperbolic conservation laws, J. Comput. Phys. 396 (2019), 544-578. (DOI: 10.1016/j.jcp.2019.06.061) (arXiv:1812.00530)

  27. Xiang Wang, Weizhang Huang, and Yonghai Li, Conditioning of the finite volume element method for diffusion problems with general simplicial meshes, Math. Comput. 88 (2019), 2665-2696. (DOI: 10.1090/mcom/3423) (arXiv:1802.01416)

  28. Xiaobo Yang, Weizhang Huang, and Jianxian Qiu, Moving mesh finite difference solution of non-equilibrium radiation diffusion equations, Numerical Algorithms 82 (2019), 1409-1440. (DOI: 10.1007/s11075-019-00662-5) (arXiv:1802.09521)

  29. Cuong Ngo and Weizhang Huang, Adaptive finite element solution of the porous medium equation in pressure formulation, Numer. Meth. P.D.E. 35 (2019), 1224-1242. (DOI: 10.1002/num.22347) (arXiv:1801.01566)

  30. Kelsey DiPietro, Ronald Haynes, Weizhang Huang, Alan Lindsay, and Yufei Yu, Moving mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems, J. Comput. Phys. 375 (2018), 763-782. (DOI: 10.1016/j.jcp.2018.08.053) (arXiv:1805.00160)

  31. W. Huang and L. Kamenski, On the mesh nonsingularity of the moving mesh PDE method, Math. Comput. 87 (2018), 1887-1911. (DOI: 10.1090/mcom/3271) (arXiv:1512.04971) (WIAS Preprint No. 2218 (2016))

  32. A. Kolasinski and W. Huang, A new functional for variational mesh generation and adaptation based on equidistribution and alignment conditions, Comput. Math. Appl. 75 (2018), 2044-2058. (DOI: 10.1016/j.camwa.2017.06.043) (arXiv:1612.04347)

  33. Y. Yu and W. Huang, Selection of the Regularization Parameter in the Ambrosio-Tortorelli Approximation of the Mumford-Shah Functional for Image Segmentation, Numer. Math. Theor. Meth. Appl. 11 (2018), 211-234. (DOI: 10.4208/nmtma.OA-2017-0074) (arXiv:1706.06459)

  34. F. Zhang, W. Huang, X. Li, and S. Zhang, Moving Mesh Finite Element Simulation for Phase-Field Modeling of Brittle Fracture and Convergence of Newton's Iteration, J. Comput. Phys. 356 (2018), 127-149. (DOI: 10.1016/j.jcp.2017.11.033) (arXiv:1706.05449)

  35. C. Lu, W. Huang, and J. Qiu, An adaptive moving mesh finite element solution of the Regularized Long Wave equation, J. Sci. Comput. 74 (2018), 122-144. (DOI: 10.1007/s10915-017-0427-6) (arXiv:1606.06541)

  36. X. Li and W. Huang, Anisotropic mesh adaptation for 3D anisotropic diffusion problems with application to fractured reservoir simulation, Numer. Math. Theor. Meth. Appl. 10 (2017), 913-940. (DOI: 10.4208/nmtma.2017.m1625) (arXiv:1509.06604)

  37. J. Cheng, W. Huang, S. Jiang, and B. Tian, A third-Order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows, J. Comput. Phys. 349 (2017), 137-153. (DOI: 10.1016/j.jcp.2017.08.018) (arXiv:1701.00433)

  38. X. Li and W. Huang, A study on nonnegativity preservation in finite element approximation of Nagumo-type nonlinear differential equations, Appl. Math. Comput. 309 (2017), 49-67. (DOI: 10.1016/j.amc.2017.03.038) (arXiv:1610.02741)

  39. C. Ngo and W. Huang, A study on moving mesh finite element solution of the porous medium equation, J. Comput. Phys. 331 (2017) 357-380. (DOI: 10.1016/j.jcp.2016.11.045) (arXiv:1605.03570)

  40. A. Kim, S. Keshmiri, W. Huang, and G. Garcia, Guidance of multi-agent fixed-wing aircraft using a moving mesh method. Unmanned Systems 4 (2016), 227-244. (DOI: 10.1142/S2301385016500084)

  41. W. Huang, L. Kamenski, and J. Lang, Stability of explicit Runge--Kutta methods for finite element approximation of linear parabolic equations on anisotropic meshes. SIAM J. Numer. Anal. 54 (2016), 1612-1634. (WIAS Preprint No. 1869 (2013)) (DOI: 10.1137/130949531)

  42. J. Wang and W. Huang, Image segmentation with eigenfunctions of an anisotropic diffusion operator. IEEE Transactions on Image Processing 25 (2016), 2155-2167. (DOI: 10.1109/TIP.2016.2541924) (arXiv:1404.0723)

  43. D. Luo, W. Huang, and J. Qiu, A hybrid LDG-HWENO scheme for KdV-type equations, J. Comput. Phys. 313 (2016), 754-774. (DOI: 10.1016/j.jcp.2016.02.064) (arXiv:1511.04505)

  44. C. Ngo and W. Huang, Monotone finite difference schemes for anisotropic diffusion problems via nonnegative directional splittings, Comm. Comput. Phys. 19 (2016), 473-495. (DOI: 10.4208/cicp.280315.140815a) (arXiv:1503.08177)

  45. Y. He and W. Huang, A posteriori error analysis for finite element solution of elliptic differential equations using equidistributing meshes, J. Comput. Appl. Math. 299 (2016), 101-126. (DOI: 10.1016/j.cam.2015.10.033) (arXiv:0911.0065)

  46. W. Huang, L. Kamenski, and H. Si, Mesh smoothing: An MMPDE approach. Procedia Engineering (2015) (Research Note of 24th International Meshing Roundtable (IMR24)) (WIAS Preprint No. 2130 (2015))

  47. J. Wang and W. Huang, A study on anisotropic mesh adaptation for finite element approximation of eigenvalue problems with anisotropic diffusion operators, SIAM J. Sci. Comput. 37 (2015), A2924-A2946. (DOI: 10.1137/140958554) (arXiv:1402.6001)

  48. W. Huang and L. Kamenski, A geometric discretization and a simple implementation for variational mesh generation and adaptation, J. Comput. Phys. 301 (2015), 322-337. (DOI: 10.1016/j.jcp.2015.08.032) (arXiv:1410.7872; WIAS Preprint No. 2035 (2014))

  49. W. Huang, L. Kamenski, and R. D. Russell, A comparative numerical study of meshing functionals for variational mesh adaptation, J. Math. Study 48 (2015), 168-186. (DOI: 10.4208/jms.v48n2.15.04) (arXiv:1503.04709; WIAS Preprint No. 2086 (2015))

  50. W. Huang and Y. Wang, Discrete maximum principle for the weak Galerkin method for anisotropic diffusion problems, Comm. Comput. Phys. 18 (2015), 65-90. (DOI: 10.4208/cicp.180914.121214a) (arXiv:1401.6232)

  51. W. Huang, Computation of eigenvalue problems with anisotropic diffusion operators, AIP Conf. Proc. 1648, 020008 (2015); (DOI: 10.1063/1.4912312) (Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 -- ICNAAM-2014).

  52. W. Huang, L. Kamenski, and J. Lang, Stability of explicit Runge-Kutta methods for high order finite element approximation of linear parabolic equations, Numerical Mathematics and Advanced Applications 103 (2015), 165--173. (Proceedings of The 2013 European Numerical Mathematics and Advanced Applications Conference ENUMATH-2013, Lausanne, Switzerland, August 26 - 30, 2013) (DOI: 10.1007/978-3-319-10705-9_16) (WIAS Preprint No. 1904 (2013))

  53. X. Yang, W. Huang, and J. Qiu, A moving mesh finite difference method for equilibrium radiation diffusion equations, J. Comput. Phys. 298 (2015), 661-677. (DOI: 10.1016/j.jcp.2015.06.014)

  54. W. Huang, Unconditionally stable high-order time integration for moving mesh finite difference solution of linear convection-diffusion equations, Int. J. Comput. Math. 92 (2015), 1180-1203. (DOI: 10.1080/00207160.2014.927447) (arXiv:1310.4215)

  55. L. Kamenski and W. Huang, How a nonconvergent recovered Hessian works in mesh adaptation, SIAM J. Numer. Anal. 52 (2014), 1692-1708. (DOI: 10.1137/120898796) (arXiv:1211.2877)

  56. L. Kamenski and W. Huang, A study on the conditioning of finite element equations with arbitrary anisotropic meshes via a density function approach, Journal of Mathematical Study 47 (2014), 151-172. (DOI: 10.4208/jms.v47n2.14.02) (arXiv:1302.6868; WIAS Preprint No. 1903 (2013))

  57. L. Kamenski, W. Huang, and H. Xu, Conditioning of finite element equations with arbitrary anisotropic meshes, Math. Comput. 83 (2014), 2187-2211. (DOI: 10.1090/S0025-5718-2014-02822-6) (arXiv:1201.3651)

  58. W. Huang, Sign-preserving of principal eigenfunctions in P1 finite element approximation of eigenvalue problems of second-order elliptic operators, J. Comput. Phys. 274 (2014), 230-244. (DOI: 10.1016/j.jcp.2014.06.012) (arXiv:1306.1987)

  59. C. Lu, W. Huang, and J. Qiu, Maximum principle in linear finite element approximations of anisotropic diffusion-convection-reaction problems, Numer. Math. 127 (2014), 515-537. (DOI: 10.1007/s00211-013-0595-8) (arXiv:1201.3564)

  60. X. Li and W. Huang, Maximum principle for the finite element solution of time dependent anisotropic diffusion problems, Numer. Meth. P.D.E. 29 (2013), 1963-1985. (DOI: 10.1002/num.217847) (arXiv:1209.5657)

  61. R. D. Haynes, W. Huang, and P. A. Zegeling, A numerical study of blowup in the harmonic map heat flow using the MMPDE moving mesh method, Numer. Math. Theor. Meth. Appl. 6 (2013), 364-383.

  62. W. Huang, L. Kamenski, and J. Lang, Adaptive finite elements with anisotropic meshes, Numerical Mathematics and Advanced Applications 2011 (2013), pp. 33-42. (Proceedings of The 2011 European Numerical Mathematics and Advanced Applications Conference ENUMATH-2011, University of Leicester, U.K., September 5-9, 2011) (DOI: 10.1007/978-3-642-33134-3_4) (arXiv:1201.4090)

  63. C. Lu, W. Huang, and E. S. Van Vleck, The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations, J. Comput. Phys. 242 (2013), 24-36. (arXiv:1206.6312)

  64. X. Yang, W. Huang, and J. Qiu, A moving mesh WENO method for one-dimensional conservation laws, SIAM J. Sci. Comput. 34 (2012), A2317-A2343.

  65. W. Huang and F. Schaeffer, An $L^\infty$ stability analysis for the finite difference solution of one dimensional linear convection-diffusion equations on moving meshes, J. Comput. Appl. Math. 236 (2012), 3338-3348.

  66. J. Ma, W. Huang, and R. D. Russell, Analysis of a moving collocation method for one-dimensional partial differential equations, Science China Mathematics 55 (2012), 827-840.

  67. W. Huang, Discrete maximum principle and a Delaunay-type mesh condition for linear finite element approximations of two-dimensional anisotropic diffusion problems, Numerical Mathematics: Theory, Methods and Applications 4 (2011), 319-334. (arXiv:1008.0562)

  68. W. Huang, L. Kamenski, and X. Li, Anisotropic mesh adaptation for variational problems using error estimation based on hierarchical bases, Canadian Applied Mathematics Quarterly (Special issue for the 30th anniversary of CAIMS) 17 (2009), 501-522. (arXiv:1006.0191)

  69. X. Xu, W. Huang, R. D. Russell, and J. F. Williams, Convergence of De Boor's algorithm for generation of equidistributing meshes, IMA J. Numer. Anal. 31 (2011), 558-596.

  70. X. Li and W. Huang, An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems. J. Comput. Phys. 229 (2010), 8072-8094. (arXiv:1003.4530)

  71. W. Huang, L. Kamenski, and J. Lang, A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates, J. Comput. Phys. 229 (2010) 2179-2198.

  72. W. Huang and X. Li, An anisotropic mesh adaptation method for the finite element solution of variational problems, Finite Elements in Analysis and Design 46 (2010) 61-73.

  73. C. J. Budd, W. Huang, and R. D. Russell, Adaptivity with moving grids, Acta Numerica 18 (2009), 111-241.

  74. W. Huang, J. Ma, and R. D. Russell, A study of moving mesh PDE methods for numerical simulation of blowup in reaction diffusion equations, J. Comput. Phys. 227 (2008), 6532-6552.

  75. R. D. Haynes, W. Huang, and R. D. Russell, A moving mesh method for time-dependent problems based on Schwarz waveform relaxation, Proceedings of the 17th International Domain Decomposition Methods Meeting, Lecture Notes in Computational Science and Engineering (LNCSE), Springer--Verlag, Vol. 60, pages 229--236, 2008.

  76. W. Huang, Chapter 3: Anisotropic mesh adaptation and movement, in Adaptive computations: Theory and Algorithms (edited by T. Tang and J. Xu, Science Press, Beijing 2007), Pages 68 -- 158.

  77. W. Huang, Mathematical principles of anisotropic mesh adaptation, Communications in Computational Physics 1 (2006), 276 -- 310. ( full text in PDF )

  78. W. Huang and X. Y. Zhan, Adaptive moving mesh modeling for two dimensional groundwater flow and transport, in AMS Contemporary Mathematics series, Vol. 383, 2005, pages 283 -- 296. ( full text in PDF )

  79. Y. He, W. Huang, K. Camarda, and K. Bishop, Preconditioning for the dynamic simulation of reaction-transport systems, Ind. Eng. Chem. Res. 44 (2005), 5680 -- 5690. ( full text in PDF )

  80. W. Huang, "Anisotropic mesh adaptation and movement", Lecture notes for Peking Univ. Workshop on Adaptive mesh methods June -- August, 2005. ( full text in PDF )

  81. W. Huang, Metric tensors for anisotropic mesh generation, J. Comput. Phys. 204 (2005) 633 -- 665. ( full text in PDF )

  82. W. Huang, Measuring Mesh Qualities and Application to Variational Mesh Adaptation, SIAM J. Sci. Comput. 26 (2005), 1643 -- 1666. ( full text in PDF )

  83. W. Huang, Convergence analysis of finite element solution of one-dimensional singularly perturbed differential equations on equidistributing meshes, Int. J. Numer. Anal. Modeling 2 (2005), 57 -- 74. ( full text in PDF )

  84. W. Huang, H. Ma, and W. Sun, Convergence analysis of spectral collocation methods for a singular differential equation, SIAM J. Numer. Anal. 41 (2003) 2333 -- 2349. ( full text in PDF )

  85. J. Lang, W. Cao, W. Huang and R. D. Russell, A Two--dimensional Moving Finite Element Method with Local Refinement Based on a Posteriori Error Estimates, Appl. Numer. Math. 46 (2003), 75 -- 94. ( full text in PDF )

  86. W. Huang and W. Sun, Variational mesh adaptation II: Error estimates and monitor functions, J. Comput. Phys. 184 (2003) 619 -- 648. ( full text in PDF )

  87. W. Cao, R. Carretero-Gonzalez, W. Huang, and R. D. Russell, Variational mesh adaptation methods for axisymmetrical problems, SIAM J. Numer. Anal. 41 (2003) 235 -- 257. ( full text in PDF )

  88. W. Cao, W. Huang, and R. D. Russell, Approaches for generating moving adaptive meshes: location versus velocity, Appl. Numer. Math. 47 (2003), 121 -- 138. ( full text in PDF )

  89. W. Huang, X. Zhan, and L. Zheng, Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts, Int. J. Numer. Meth. Eng. 54 (2002), 1579 -- 1603. ( full text in PDF ) ( full text in gzipped PostScript )

  90. W. Cao, W. Huang, and R. Russell, A moving mesh method based on the geometric conservation law, SIAM J. Sci. Comput. 24 (2002), 118 -- 142. ( full text in PDF )

  91. W. Huang, Variational mesh adaptation: isotropy and equidistribution J. Comput. Phys. 174 (2001), 903 -- 924. ( full text in PDF )

  92. W. Huang, Practical aspects of formulation and solution of moving mesh partial differential equations, J. Comput. Phys. 171 (2001), 753 -- 775. ( full text in PDF )

  93. W. Cao, W. Huang, and R.D. Russell, An error indicator monitor function for an r-adaptive finite-element method, J. Comput. Phys. 170 (2001), 871 -- 892.

  94. W. Huang and R. D. Russell, Adaptive mesh movement -- the MMPDE approach and its applications, J. Comput. Appl. Math. 128 (2001), 383 -- 398.

  95. W. Cao, W. Huang, and R.D. Russell, Comparison of two-dimensional r-adaptive finite element methods using various error indicators, Math. Comput. Simulation 56 (2001), 127 -- 143.

  96. W. Huang and T. Tang, Pseudospectral solutions for steady motion of a viscous fluid inside a circular boundary, Appl. Numer. Math. 33 (2000), 167 -- 173.

  97. C. J. Budd, G. J. Collins, W. Huang, and R. D. Russell, Self-similar numerical solutions of the porous-medium equation using moving mesh methods, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 357 (1999), 1047 -- 1077.

  98. W. Cao, W. Huang, and R.D. Russell, A moving mesh method in multi-block domains with application to combustion problems, Numer. Meth. PDEs 15 (1999), 449 -- 467.

  99. W. Cao, W. Huang, and R.D. Russell, An r-adaptive finite element method based upon moving mesh PDEs, J. Comput. Phys. 149 (1999), 221 -- 244.

  100. W. Cao, W. Huang, and R.D. Russell, A study of monitor functions for two dimensional adaptive mesh generation, SIAM J. Sci. Comput. 20 (1999), 1978 -- 1994. ( full text in PDF )

  101. W. Huang and R.D. Russell, Moving mesh strategy based upon a gradient flow equation for two dimensional problems, SIAM J. Sci. Comput. 20 (1999), 998 -- 1015. ( full text in PDF )

  102. L.S. Mulholland, W. Huang, and D.M. Sloan, Pseudospectral solution of near-singular problems using numerical coordinate transformations based on adaptivity, SIAM J. Sci. Comput. 19 (1998), 1261 -- 1289. ( full text in PDF )

  103. W. Huang and A. Kappen, A study of cell-center finite volume methods for diffusion equations, Mathematics Research Report 98-10-01, the University of Kansas, Lawrence, KS 66045. ( full text in PDF )

  104. W. Huang and R.D. Russell, A high dimensional moving mesh strategy, Appl. Numer. Math. 26 (1998), 63 -- 76.

  105. W. Huang and R.D. Russell, Analysis of moving mesh partial differential equations with spatial smoothing, SIAM J. Numer. Anal. 34 (1997), 1106 -- 1126. ( full text in PDF )

  106. J. Frank, W. Huang, and B. Leimkuhler, Geometric integrators for classical spin systems, J. Comput. Phys. 133 (1997), 160 -- 172.

  107. W. Huang and B. Leimkuhler, The adaptive Verlet method, SIAM J. Sci. Comput. 18 (1997), 239 -- 256. ( full text in PDF )

  108. W. Huang and R.D. Russell, A moving collocation method for solving time dependent partial differential equations, Appl. Numer. Math. 20 (1996), 101 -- 116.

  109. C.J. Budd, J. Chen, W. Huang, and R.D. Russell, Moving mesh methods with applications to blow-up problems for PDEs, Numerical Analysis 1995: Proceedings of 1995 Biennial Conference on Numerical Analysis (Ed. by D. F. Griffiths and G. A. Watson, Pitman Research Notes in Mathematics, Longman Scientific and Technical, 1996), 1 -- 17.

  110. W. Sun, W. Huang, and R.D. Russell, Finite difference preconditioning for solving orthogonal collocation equations of boundary value problems, SIAM J. Numer. Anal. 33 (1996), 2268 -- 2285.

  111. C.J. Budd, W. Huang, and R.D. Russell, Moving mesh methods for problems with blow-up, SIAM J. Sci. Comput. 17 (1996), 305 -- 327.

  112. W. Huang, Y. Ren and R.D. Russell, Moving mesh partial differential equations (MMPDEs) based upon the equidistribution principle, SIAM J. Numer. Anal. 31 (1994), 709 -- 730. ( full text in PDF )

  113. W. Huang, Y. Ren and R.D. Russell, Moving mesh methods based on moving mesh partial differential equations, J. Comput. Phys. 113 (1994), 279 -- 290.

  114. W. Huang and D.M. Sloan, A simple adaptive grid method in two dimensions, SIAM J. Sci. Comput. 15 (1994), 776 -- 797.

  115. W. Huang and D.M. Sloan, The pseudospectral method for solving differential eigenvalue problems, J. Comput. Phys. 111 (1994), 399 -- 409.

  116. W. Huang and D.M. Sloan, Pole condition for singular problems : the pseudospectral approximation, J. Comput. Phys. 107 (1993), 254 -- 261.

  117. W. Huang and D.M. Sloan, A new pseudospectral method with upwind features, IMA J. Numer. Anal. 13 (1993), 413 -- 430.

  118. Jia-chun Li, W. Huang, Zuo-heng Xie, and Suo-chun Zhang, Controlling the hot-capillary convection in a floating zone under micro-gravity condition, Science in China (Series A) 23, 2 (1993), 162 -- 170.

  119. W. Huang, The mini-package HIMEC for Hermite interpolation with multiple end conditions, Mathematics and Statistics Research Report No. 93-19, Simon Fraser University, B.C. Canada.

  120. W. Huang, The convergence of the multigrid method using the symmetric Kaczmarz iteration as its smoothing method, Acta Mathematicae Applicatae Sinica 16 (1993), 100 -- 106.

  121. W. Huang and D.M. Sloan, The pseudospectral method for third-order differential equations, SIAM J. Numer. Anal. 29 (1992), 1626 -- 1647. ( full text in PDF )

  122. W. Huang, S.C. Zhang, Z.H. Xie, and J.C. Li, On the application of ADI method to numerical simulation of the Marangoni convection controlling in liquid bridge model, Appl. Math. Mech. 13 (1992), 393 -- 400.

  123. W. Huang, Convergence of algebraic multigrid methods (AMG) for symmetric and positive definite matrices with weak diagonal dominance, Appl. Math. Comput. 46 (1991), 145 -- 164.

  124. W. Huang, Existence of globally smooth solutions of quasilinear hyperbolic systems in diagonal form under large initial data, Acta Mathematicae Applicatae Sinica 14 (1991), 229 -- 233.

  125. W. Huang, Y.R. Wang, S.C. Zhang, and T.S. Zhang, Stellar core collapse and equation of state (I) -- Inputting factor of collapse calculation, Chinese J. Comput. Phys. 4 (1987), 317 -- 328.

  126. Y.R. Wang, W. Huang, S.C. Zhang, and T.S. Zhang, Stellar core collapse and equation of state (II) -- Computer simulation of stellar collapse, Chinese J. Comput. Phys. 4 (1987), 329 -- 338.