Huang's Research (Last updated on Nov, 2009)

Keywords: Numerical analysis, Scientific computing, Numerical solution of partial differential equations, Mesh generation and adaptation, moving mesh methods, variational mesh generation, anisotropic mesh generation, spectral methods, collocation methods, geometric integration, numerical solution of Hamiltonian systems

Moving Mesh Methods are a type of adaptive mesh methods which are designed for the numerical solution of time dependent partial differential equations. With this type methods, a mesh equation is employed to move the mesh around in an orderly fashion. Ideally, the mesh equation is formulated so that the mesh qualities such as smoothness and orthogonality can be controlled while a sufficient number of mesh points are concentrated in regions of rapid variation in the physical solution. Pictures: Airfoil Analysis Mesh Laminar flame propagation Temperature Mesh Wave equation Solution Mesh

Weizhang Huang's web of science listing

Weizhang Huang's MathSciNet listing

Research Publications:

  1. W. Huang, L. Kamenski, and J. Lang, A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates, J. Comput. Phys. (to appear).
  2. W. Huang and X. Li, An anisotropic mesh adaptation method for the finite element solution of variational problems, Finite Elements in Analysis and Design (to appear).
  3. C. J. Budd, W. Huang, and R. D. Russell, Adaptivity with moving grids, Acta Numerica 18 (2009), 111-241.
  4. 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.
  5. 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.
  6. 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.
  7. W. Huang, Mathematical principles of anisotropic mesh adaptation, Communications in Computational Physics 1 (2006), 276 -- 310. ( full text in PDF )
  8. 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 )
  9. Y. He, W. Huang, K. Camarda, and K. Bishop, "Preconditioning for the dynamic simulation of reaction-tranport systems", Ing. Eng. Chem. Res. 44 (2005), 5680 -- 5690. ( full text in PDF )
  10. W. Huang, "Anisotropic mesh adaptation and movement", Lecture notes for Peking Univ. Workshop on Adaptive mesh methods June -- August, 2005. ( full text in PDF )
  11. W. Huang, Metric tensors for anisotropic mesh generation, J. Comput. Phys. 204 (2005) 633 -- 665. ( full text in PDF )
  12. W. Huang, Measuring Mesh Qualities and Application to Variational Mesh Adaptation, SIAM J. Sci. Comput. 26 (2005), 1643 -- 1666. ( full text in PDF )
  13. 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 )
  14. 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 )
  15. 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 )
  16. 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 )
  17. 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 )
  18. 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 )
  19. 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 )
  20. 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 )
  21. W. Huang, Variational mesh adaptation: isotropy and equidistribution J. Comput. Phys. 174 (2001), 903 -- 924. ( full text in PDF )
  22. 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 )
  23. 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.
  24. W. Huang and R. D. Russell, Adaptive mesh movement -- the MMPDE approach and its applications, J. Comput. Appl. Math. 128 (2001), 383 -- 398.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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 )
  31. 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 )
  32. 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 )
  33. 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.
  34. W. Huang and R.D. Russell, A high dimensional moving mesh strategy, Appl. Numer. Math. 26 (1997), 63 -- 76.
  35. 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 )
  36. J. Frank, W. Huang, and B. Leimkuhler, Geometric integrators for classical spin systems, J. Comput. Phys. 133 (1997), 160 -- 172.
  37. W. Huang and B. Leimkuhler, The adaptive Verlet method, SIAM J. Sci. Comput. 18 (1997), 239 -- 256. ( full text in PDF )
  38. W. Huang and R.D. Russell, A moving collocation method for solving time dependent partial differential equations, Appl. Numer. Math. 20 (1996), 101 -- 116.
  39. 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.
  40. 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.
  41. 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.
  42. 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 )
  43. 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.
  44. W. Huang and D.M. Sloan, A simple adaptive grid method in two dimensions, SIAM J. Sci. Comput. 15 (1994), 776 -- 797.
  45. W. Huang and D.M. Sloan, The pseudospectral method for solving differential eigenvalue problems, J. Comput. Phys. 111 (1994), 399 -- 409.
  46. W. Huang and D.M. Sloan, Pole condition for singular problems : the pseudospectral approximation, J. Comput. Phys. 107 (1993), 254 -- 261.
  47. W. Huang and D.M. Sloan, A new pseudospectral method with upwind features, IMA J. Numer. Anal. 13 (1993), 413 -- 430.
  48. 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.
  49. 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.
  50. 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.
  51. 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 )
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  56. 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.