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
Shaun Lui
Profile
Select Publications
- 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.
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