Howard Elman

Professor
4210 Iribe Center
(301) 405-2694
(301)405-6707
Academic Web Page
Education: 
Ph.D., Yale University (Computer Science)
Biography: 

Howard Elman is a professor in the Department of Computer Science.

Elman's research focus is numerical solution of partial differential equations, computational fluid dynamics, sparse matrix methods, and uncertainty quantification.

He has held visiting positions at Stanford University, the University of Manchester Institute of Science and Technology, and the University of Oxford. Elman has been selected as a SIAM Fellow and serves on the SIAM Committee on Science Policy and SIAM Financial Management Committee.

He has been designated a "highly cited researcher" by Thomson Reuters. In addition, he has served on the editorial boards of SIAM Journal on Scientific Computing, where he was editor-in-chief from 1998-2004, as well as Mathematics of Computation and Numerical Linear Algebra with Applications. Elman's book, "Finite Elements and Fast Iterative Solvers," co-authored with D. J. Silvester and A. J. Wathen, was published by Oxford University Press.

He received his doctorate in computer science from Yale University in 1982.

Go here to view Elman's academic publications on Google Scholar.

Publications

2011


Shuttleworth RR, Elman H, Long KR, Templeton JA.  2011.  Fast solvers for models of ICEO microfluidic flows. International Journal for Numerical Methods in Fluids. 65(4):383-404.

2009


Powell CE, Elman H.  2009.  Block-diagonal preconditioning for spectral stochastic finite-element systems. IMA Journal of Numerical Analysis. 29(2):350-350.

2008


Elman H, Furnival DG, Powell CE.  2008.  H (div) preconditioning for a mixed finite element formulation of the stochastic diffusion problem.

Xue F, Elman H.  2008.  Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration. CONVERGENCE. 31(3):877-899.

2007


Ramage A, Elman H.  2007.  Some observations on multigrid convergence for convection–diffusion equations. Computing and Visualization in Science. 10(1):43-56.

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, Ramage A, Silvester DJ.  2007.  IFISS: A Matlab toolbox for modelling incompressible flow. ACM Transactions on Mathematical Software. 33(2)

Elman H, Furnival D.  2007.  Solving the stochastic steady-state diffusion problem using multigrid. IMA journal of numerical analysis. 27(4):675-675.

2006


Wu CT, Elman H.  2006.  Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations. ANALYSIS. 28(6):2208-2228.

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, Howle VE, Shadid J, Shuttleworth R, Tuminaro R.  2006.  Block preconditioners based on approximate commutators. SIAM Journal on Scientific Computing. 27(5):1651-1668.

2005


Elman H, Ernst OG, O’Leary DP, Stewart M.  2005.  Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering. Computer Methods in Applied Mechanics and Engineering. 194(9–11):1037-1055.

Elman H, Silvester DJ, Wathen AJ.  2005.  Finite Elements and Fast Iterative Solvers : with Applications in Incompressible Fluid Dynamics. :416.

Elman H.  2005.  Preconditioning strategies for models of incompressible flow. Journal of Scientific Computing. 25(1):347-366.

2003


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.

Zavorin I, O'Leary DP, Elman H.  2003.  Complete stagnation of. Linear Algebra and its Applications. 367:165-183.

Elman H, Ramage A.  2003.  A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation. Mathematics of computation. 72(241):263-288.

Zavorin I, O’Leary DP, Elman H.  2003.  Complete stagnation of GMRES. Linear Algebra and its Applications. 367:165-183.

2002


Elman H, Silvester DJ, Wathen AJ.  2002.  Block preconditioners for the discrete incompressible Navier–Stokes equations. International Journal for Numerical Methods in Fluids. 40(3‐4):333-344.

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, 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, Silvester DJ, Wathen AJ.  2002.  Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations. Numerische Mathematik. 90(4):665-688.

2001


Elman H.  2001.  Preconditioners for Saddle Point Problems Arising in Computational Fluid Dynamics. UMIACS-TR-2001-88

2000


Shih YT, Elman H.  2000.  Iterative methods for stabilized discrete convection-diffusion problems. IMA journal of numerical analysis. 20(3):333-333.

1999


Elman H.  1999.  Preconditioning for the steady-state Navier-Stokes equations with low viscosity. SIAM Journal on Scientific Computing. 20(4):1299-1316.

Shih Y-T, Elman H.  1999.  Modified streamline diffusion schemes for convection-diffusion problems. Computer Methods in Applied Mechanics and Engineering. 174(1-2):137-151.

Silvester D, Elman H, Kay D, Wathen A.  1999.  Efficient preconditioning of the linearized Navier-Stokes equations.

Elman H, O'Leary DP.  1999.  Eigenanalysis of Some Preconditioned Helmholtz Problems. Numerische Mathematik. 83:231-257.

1998


Elman H, O'Leary DP.  1998.  Efficient Iterative Solution of the Three-Dimensional Helmholtz Equation. Journal of Computational Physics. 142(1):163-181.

1997


Naiman AE, Babuška IM, Elman H.  1997.  A note on conjugate gradient convergence. Numerische Mathematik. 76(2):209-230.

Elman H.  1997.  Iterative Methods for Linear and Nonlinear Equations.. 66

Elman H, Silvester DJ, Wathen AJ.  1997.  Iterative methods for problems in computational fluid dynamics. Iterative Methods in Scientific Computing. :271-327.

Elman H.  1997.  Perturbation of eigenvalues of preconditioned Navier-Stokes operators. SIAM Journal on Matrix Analysis and Applications. 18(3):733-751.

1996


Elman H, Silvester D.  1996.  Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. SIAM Journal on Scientific Computing. 17(1):33-46.

Elman H.  1996.  Multigrid and Krylov subspace methods for the discrete Stokes equations. International journal for numerical methods in fluids. 22(8):755-770.

1995


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, Lee DK-Y.  1995.  Use of linear algebra kernels to build an efficient finite element solver. Parallel Computing. 21(1):161-173.

1994


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, 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.

1993


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, 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.

Chernesky MP, Elman H.  1993.  Costs of Solving the Discrete Convection-diffusion Equation by Relaxation Methods.

1992


Zhang G, Elman H.  1992.  Parallel sparse Cholesky factorization on a shared memory multiprocessor. Parallel Computing. 18(9):1009-1022.

1991


Elman H, Golub GH.  1991.  Iterative methods for cyclically reduced non-self-adjoint linear systems II. Math. Comp. 56(193):215-242.

1990


Elman H, Golub GH.  1990.  Iterative methods for cyclically reduced non-self-adjoint linear systems. Math. Comp. 54(190):671-700.

Elman H, Golub GH.  1990.  Line iterative methods for cyclically reduced discrete convection-diffusion problems.

1989


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.

Babuska I, Elman H.  1989.  Some aspects of parallel implementation of the finite-element method on message passing architectures. Journal of Computational and Applied Mathematics. 27(1-2):157-187.

Chan TF, Elman H.  1989.  Fourier Analysis of Iterative Methods for Elliptic Problems. SIAM Review. 31(1):20-49.

Elman H.  1989.  Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems. BIT Numerical Mathematics. 29(4):890-915.

Elman H, Agrón E.  1989.  Ordering techniques for the preconditioned conjugate gradient method on parallel computers. Computer Physics Communications. 53(1-3):253-269.

1988


Eisenstat S, Elman H, Schlutz M.  1988.  Block-Preconditioned Conjugate-Gradient-Like Methods for Numerical Reservoir Simulation. SPE Reservoir EngineeringSPERE. 3(1)

1986


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.  1986.  A Stability Analysis of Incomplete LU Factorizations. Mathematics of Computation. 47(175):191-217.

Elman H, Streit R.  1986.  Polynomial iteration for nonsymmetric indefinite linear systems. Numerical Analysis. :103-117.

Elman H, Saad Y, Saylor PE.  1986.  A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations. SIAM Journal on Scientific and Statistical ComputingSIAM J. Sci. and Stat. Comput.. 7(3):840-840.

1983


Eisenstat SC, Elman H, Schultz MH.  1983.  Variational Iterative Methods for Nonsymmetric Systems of Linear Equations. SIAM Journal on Numerical Analysis. 20(2):345-357.

Eisenstat SC, Elman H, Schultz MH, Sherman AH.  1983.  The (new) Yale sparse matrix package. Elliptic problem solvers II. :45-52.

1982


Elman H.  1982.  Iterative methods for large, sparse, nonsymmetric systems of linear equations.. Dissertation Abstracts International Part B: Science and Engineering[DISS. ABST. INT. PT. B- SCI. & ENG.],. 43(5):1982-1982.

1981


Elman H.  1981.  Preconditioned Conjugate-Gradient Methods for Nonsymmetric Systems of Linear Equations..