Publications

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Elman H, Ramage A, Silvester DJ.  2007.  IFISS: A Matlab toolbox for modelling incompressible flow. ACM Transactions on Mathematical Software. 33(2)
Elman H.  1981.  Preconditioned Conjugate-Gradient Methods for Nonsymmetric Systems of Linear Equations..
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, Golub GH.  1994.  Inexact and Preconditioned Uzawa Algorithms for Saddle Point Problems. SIAM Journal on Numerical Analysis. 31(6):1645-1661.
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, 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.  2005.  Preconditioning strategies for models of incompressible flow. Journal of Scientific Computing. 25(1):347-366.
Elman H, Howle VE, Shadid J, Tuminaro R.  2002.  A Parallel Block Multi-level Preconditioner for the 3D Incompressible Navier--Stokes Equations. UMIACS-TR-2002-95
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.  1997.  Iterative Methods for Linear and Nonlinear Equations.. 66
Elman H, Silvester DJ, Wathen AJ.  2005.  Finite Elements and Fast Iterative Solvers : with Applications in Incompressible Fluid Dynamics. :416.
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, Lee DK-Y.  1995.  Use of linear algebra kernels to build an efficient finite element solver. Parallel Computing. 21(1):161-173.
Elman H, Streit R.  1986.  Polynomial iteration for nonsymmetric indefinite linear systems. Numerical Analysis. :103-117.
Elman H, O'Leary DP.  1999.  Eigenanalysis of Some Preconditioned Helmholtz Problems. Numerische Mathematik. 83:231-257.
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, Silvester DJ, Wathen AJ.  1997.  Iterative methods for problems in computational fluid dynamics. Iterative Methods in Scientific Computing. :271-327.
Elman H, Schultz MH.  1986.  Preconditioning by Fast Direct Methods for Nonself-Adjoint Nonseparable Elliptic Equations. SIAM Journal on Numerical Analysis. 23(1):44-57.
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, 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, 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, Ramage A.  2003.  A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation. Mathematics of computation. 72(241):263-288.

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