Shaun Lui

Profile

Select Publications

Name: Shaun Lui

Position Title: Head/Professor

Office Phone Number: (204) 474-9693

Email: Shaun.Lui@umanitoba.ca

Research and Teaching Interests

Numerical analysis, spectral methods, scientific computing, partial differential equations

Education

B.Sc. Toronto
M.Sc. Toronto
Ph.D. California Institute of Technology

Links

http://home.cc.umanitoba.ca/~luish/

https://mathscinet.ams.org/mathscinet/MRAuthorID/367996

Aghajani, A.; Cowan, C. and Lui, S. H. (2018). Existence and regularity of nonlinear advection problems. Nonlinear Anal. 166, 19–47.
Aghajani, A.; Cowan, C. and Lui, S. H. (2018). Singular solutions of elliptic equations involving nonlinear gradient terms on perturbations of the ball. J. Differential Equations 264 (4), 2865–2896.
Kotovshchikova, Marina; Firsov, Dmitry K. and Lui, Shiu Hong (2018). A third order finite volume WENO scheme for Maxwell’s equations on tetrahedral meshes. Commun. Appl. Math. Comput. Sci. 13(1), 87–106.
Lui, S. H. (2017). Legendre spectral collocation in space and time for PDEs. Numer. Math. 136 (1), 75–99.
Dahlke, Stephan; Lellek, Dominik and Lui, Shiu Hong and Stevenson, Rob (2016). Adaptive wavelet Schwarz methods for the Navier-Stokes equation. Numer. Funct. Anal. Optim. 37 (10), 1213–1234.
Krishna Kumar, G. and Lui, S. H. (2015). Pseudospectrum and condition spectrum. Oper. Matrices 9 (1), 121–145.
Kumar, G. Krishna and Lui, S. H. (2014). On some properties of the pseudospectral radius. Electron. J. Linear Algebra 27, 342–353.
Lui, S. H. (2013). A numerical study of the Dirichlet and Neumann eigenvalue problem of the Laplacian on cusp domains. J. Comput. Methods Sci. Eng. 13 (5-6), 433–437.
Lui, S. H. (2011). Numerical analysis of partial differential equationsPure and Applied Mathematics (Hoboken). John Wiley & Sons, Inc., Hoboken, NJ.
Lui, S. H. (2011). Pseudospectral mapping theorem II. Electron. Trans. Numer. Anal. 38, 168–183.
Lui, Shiu Hong. Optimized Schwarz methods for domains with an arbitrary interface. In Domain decomposition methods in science and engineering XIX 109–116. Springer, Heidelberg, 2011.
Lui, S. H. (2010). Convergence estimates for an higher order optimized Schwarz method for domains with an arbitrary interface. J. Comput. Appl. Math. 235 (1), 301–314.
Dubois, O. and Lui, S. H. (2009). Convergence estimates for an optimized Schwarz method for PDEs with discontinuous coefficients. Numer. Algorithms 51 (1), 115–131.
Lui, S. H. (2009). A Lions non-overlapping domain decomposition method for domains with an arbitrary interface. IMA J. Numer. Anal. 29 (2), 332–349.
Lui, S. H. (2009). Spectral domain embedding for elliptic PDEs in complex domains. J. Comput. Appl. Math. 225 (2), 541–557.
Firsov, D. and Lui, S. H. (2006). A fast deblurring algorithm. Appl. Math. Comput. 183 (1), 285–291.
Firsov, D. and Lui, S. H. (2006). Domain decomposition methods in image denoising using Gaussian curvature. J. Comput. Appl. Math. 193 (2), 460–473.
Lui, S. H. and Shivakumar, P. N. (2005). Spectral decomposition of a finite-difference operator. Int. J. Comput. Math. 82 (10), 1275–1286.
Xu, Xuejun; Chow, C. O. and Lui, S. H. (2005). On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations. M2AN Math. Model. Numer. Anal. 39 (6), 1251–1269.
Xu, Xuejun; Lui, S. H. and Rahman, T. (2004). A two-level additive Schwarz method for the Morley nonconforming element approximation of a nonlinear biharmonic equation. IMA J. Numer. Anal. 24(1), 97–122.
Lui, S. H.. Nonlinearly preconditioned Newton’s method. In Domain decomposition methods in science and engineering 95–105. Natl. Auton. Univ. Mex., México, 2003.
Lui, S.-H. (2003). A pseudospectral mapping theorem. Math. Comp. 72 (244), 1841–1854.
Lui, S.-H. (2003). On monotone iteration and Schwarz methods for nonlinear parabolic PDEs. J. Comput. Appl. Math. 161 (2), 449–468.
Xu, Xuejun and Lui, S. H. (2003). A two-level Schwarz method for a finite element approximation of a nonlinear biharmonic equation. Appl. Math. Comput. 145 (2-3), 683–700.
Lui, S. H. (2002). On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs.Numer. Math. 93 (1), 109–129.
Lui, S. H. (2002). On Schwarz alternating methods for the subsonic full potential equation. Numer. Algorithms 30 (1), 59–69.
Lui, S. H. (2001). On accelerated convergence of nonoverlapping Schwarz methods. J. Comput. Appl. Math. 130 (1-2), 309–321.
Lui, S. H.. On Schwarz methods for monotone elliptic PDEs. In Domain decomposition methods in sciences and engineering (Chiba, 1999) 55–62. DDM.org, Augsburg, 2001.
Lui, Shiu-Hong (2001). On monotone and Schwarz alternating methods for nonlinear elliptic PDEs.M2AN Math. Model. Numer. Anal. 35 (1), 1–15.
Lui, Shiu Hong and Xu, Kun (2001). Entropy analysis of kinetic flux vector splitting schemes for the compressible Euler equations. Z. Angew. Math. Phys. 52 (1), 62–78.
Lui, S. H. (2000). Domain decomposition methods for eigenvalue problems. J. Comput. Appl. Math. 117 (1), 17–34.
Lui, S. H. (2000). On Schwarz alternating methods for the incompressible Navier-Stokes equations.SIAM J. Sci. Comput. 22 (6), 1974–1986.
Lui, S. H. (1999/00). On Schwarz alternating methods for nonlinear elliptic PDEs. SIAM J. Sci. Comput. 21 (4), 1506–1523.
Elliott, Robert J.; Tsoi, Allanus H. and Lui, Shiu Hong (1999). Short rate analysis and marked point processes. Math. Methods Oper. Res. 50 (1), 149–160.
Lui, S. H. (1999). Multiple bifurcation from “simple” eigenvalues. Appl. Math. Comput. 100 (2-3), 111–130.
Lui, S. H.. On Schwarz alternating methods for the incompressible Navier-Stokes equations in Ndimensions. In Eleventh International Conference on Domain Decomposition Methods (London, 1998)65–72. DDM.org, Augsburg, 1999.
Lui, S. H. (1998). Kron’s method for symmetric eigenvalue problems. J. Comput. Appl. Math. 98 (1), 35–48.
Lui, Shiu Hong. On Schwarz alternating methods for nonlinear elliptic problems. In Domain decomposition methods, 10 (Boulder, CO, 1997) 447–452. Amer. Math. Soc., Providence, RI, 1998.
Lui, S. H. (1997). An interview with Vladimir Arnolp̧rime d. Notices Amer. Math. Soc. 44 (4), 432–438.
Lui, S. H. (1997). Computation of pseudospectra by continuation. SIAM J. Sci. Comput. 18 (2), 565–573.
Lui, S. H.; Keller, H. B. and Kwok, T. W. C. (1997). Homotopy method for the large, sparse, real nonsymmetric eigenvalue problem. SIAM J. Matrix Anal. Appl. 18 (2), 312–333.
Lui, S. H. and Golub, G. H. (1995). Homotopy method for the numerical solution of the eigenvalue problem of self-adjoint partial differential operators. Numer. Algorithms 10 (3-4), 363–378.
Lui, Shiu-Hong (1992). Part I. Multiple bifurcations. Part II. Parallel homotopy method for the real nonsymmetric eigenvalue problem. ProQuest LLC, Ann Arbor, MI.