Publications

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Elman H, Golub GH.  1994.  Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems. SIAM Journal on Numerical Analysis. 31(6):1645-1661.
Elman H, Howle VE, Shadid J, Shuttleworth R, Tuminaro R.  2006.  Block preconditioners based on approximate commutators. SIAM Journal on Scientific Computing. 27(5):1651-1668.
Elman H, Ernst OG, O'Leary DP, others.  2002.  A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations. SIAM Journal on scientific computing. 23(4):1291-1315.
Elman H, Ramage A.  2003.  A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation. Mathematics of computation. 72(241):263-288.
Elman H, Chernesky MP.  1993.  Ordering Effects on Relaxation Methods Applied to the Discrete One- Dimensional Convection-Diffusion Equation. SIAM Journal on Numerical Analysis. 30(5):1268-1290.
Elman H, Furnival DG, Powell CE.  2008.  H (div) preconditioning for a mixed finite element formulation of the stochastic diffusion problem.
Elman H, O'Leary DP.  1999.  Eigenanalysis of Some Preconditioned Helmholtz Problems. Numerische Mathematik. 83:231-257.
Elman H, Zhang X.  1995.  Algebraic Analysis of the Hierarchical Basis Preconditioner. SIAM Journal on Matrix Analysis and ApplicationsSIAM. J. Matrix Anal. & Appl.. 16(1):192-192.
Elman H, Howle VE, Shadid J, Silvester D, Tuminaro R.  2007.  Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations. SIAM J. Sci. Comput. 30(1):290-311.
Elman H, Furnival D.  2007.  Solving the stochastic steady-state diffusion problem using multigrid. IMA journal of numerical analysis. 27(4):675-675.
Elman H, Golub GH.  1990.  Iterative methods for cyclically reduced non-self-adjoint linear systems. Math. Comp. 54(190):671-700.
Elman H.  1989.  Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems. BIT Numerical Mathematics. 29(4):890-915.
Elman H.  1989.  Approximate Schur Complement Preconditioners on Serial and Parallel Computers. SIAM Journal on Scientific and Statistical ComputingSIAM J. Sci. and Stat. Comput.. 10(3):581-581.
Elman H, Ramage A.  2006.  Fourier analysis of multigrid for a model two-dimensional convection-diffusion equation. BIT Numerical Mathematics. 46(2):283-306.
Elman H, Ramage A.  2003.  An Analysis of Smoothing Effects of Upwinding Strategies for the Convection-Diffusion Equation. SIAM Journal on Numerical Analysis. 40(1):254-281.
Elman H, O'Leary DP.  1998.  Efficient Iterative Solution of the Three-Dimensional Helmholtz Equation. Journal of Computational Physics. 142(1):163-181.
Elman H.  2001.  Preconditioners for Saddle Point Problems Arising in Computational Fluid Dynamics. UMIACS-TR-2001-88
Elman H, Silvester DJ, Wathen AJ.  2005.  Finite Elements and Fast Iterative Solvers : with Applications in Incompressible Fluid Dynamics. :416.
Elman H, Ramage A, Silvester DJ.  2007.  IFISS: A Matlab toolbox for modelling incompressible flow. ACM Transactions on Mathematical Software. 33(2)
Elman H, Golub GH, Starke G.  1994.  On the convergence of line iterative methods for cyclically reduced non-symmetrizable linear systems. Numerische Mathematik. 67(2):177-190.
Elman H.  1994.  Iterative methods for linear systems. Large-Scale Matrix Problems and the Numerical Solution of Partial Differential Equations. 3:69-177.
Elman H, Guo X-Z.  1993.  Performance Enhancements and Parallel Algorithms for Two Multilevel Preconditioners. SIAM Journal on Scientific ComputingSIAM J. Sci. Comput.. 14(4):890-890.
Elman H.  1996.  Multigrid and Krylov subspace methods for the discrete Stokes equations. International journal for numerical methods in fluids. 22(8):755-770.
Elman H.  1999.  Preconditioning for the steady-state Navier-Stokes equations with low viscosity. SIAM Journal on Scientific Computing. 20(4):1299-1316.
Elman H, Silvester D.  1996.  Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM Journal on Scientific Computing. 17(1):33-46.

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