Howard Elman / Publications

Reports

Kayla D. Davie and Howard C. Elman
An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models
arXiv:2303.06101v2, May 2023.

Howard C. Elman and Akwum Onwunta
Reduced-Order Modeling for Nonlinear Bayesian Statistical Inverse Problems
arXiv:1909.02539v1, August 2019.

Papers published 2016 -

• Howard C. Elman, Jiaxing Liang and Tonatiuh Sánchez-Vizuet
  Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem
  Computer Physics Communications 298, May 2024, 109099
  DOI: https://doi.org/10.1016/j.cpc.2024.109099
  Preprint: arXiv:2306.13249v2, June 2023.
  
  
• Harbir Antil, Howard C. Elman, Akwum Onwunta and Deepanshu Verma
  A deep neural network approach for parameterized PDEs and Bayesian inverse problems
  Machine Learning: Science and Technology 4 035015, 2023.
  DOI 10.1088/2632-2153/ace67c
  
  
• Bedřich Sousedík, Howard Elman, Kookjin Lee and Randy Price
  On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity
  Applications of Mathematics Online first, 2022.
  DOI: 10.21136/AM.2022.0046-21.
  Preprint: arXiv:2103.00622, February 2021.
  
  
• Kookjin Lee, Howard C. Elman, Catherine E. Powell and Dongeun Lee
  Enhanced alternating energy minimization methods for stochastic Galerkin matrix equations
  BIT Numerical Mathematics 2022/01/03, 2022.
  DOI: https://link.springer.com/article/10.1007/s10543-021-00903-x
  
  
• Howard C. Elman, Jiaxing Liang and Tonatiuh Sánchez-Vizuet
  Surrogate approximation of the Grad-Shafranov free boundary problem via stochastic collocation on sparse grids
  Journal of Computational Physics 448, 2021.
  DOI: https://doi.org/10.1016/j.jcp.2021.110699
  Preprint: https://arxiv.org/abs/2105.12217v3, May 2021.
  
  
• Howard C. Elman and Tengfei Su
  A low-rank solver for the stochastic unsteady Navier-Stokes problem
  Computer Methods in Applied Mechanics and Engineering 364, 2020.
  DOI: 10.1016/j.cma.2020.112948
  Preprint: arXiv:1906.06785v1
  
  
• Quan Bui and Howard C. Elman
  Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media
  Journal of Computational Physics 407, 2020.
  DOI: 10.1016/j.jcp.2019.109163
  Preprint: arXiv:1805.05801v1
  
  
• Kookjin Lee, Howard C. Elman and Bedřich Sousedík
  A low-rank solver for the Navier-Stokes equations with uncertain viscosity
  SIAM/ASA Journal on Uncertainty Quantification 7:1275-1300, 2019.
  DOI: 10.1137/17M1151912
  
  
• Howard C. Elman and Tengfei Su
  Low-rank solution methods for stochastic eigenvalue problems
  SIAM Journal on Scientific Computing 41:A2657-S2680, 2019.
  DOI: https://doi.org/10.1137/18M122100X
  
  
• Howard C. Elman and David J. Silvester
  Collocation methods for exploring perturbations in linear stability analysis
  SIAM Journal on Scientific Computing 40:A2667-A2693, 2018.
  DOI: 10.1137/17M1117689
  
  
• Heyrim Cho and Howard C. Elman
  An adaptive reduced basis collocation method based on PCM ANOVA decomposition for anisotropic stochastic PDEs
  International Journal for Uncertainty Quantification 8:193-210, 2018.
  DOI: 10.1615/Int.J.UncertaintyQuantification.2018024436
  
  
• Kookjin Lee, Kevin Carlberg and Howard C. Elman
  Stochastic least-squares Petrov-Galerkin method for parameterized linear systems
  SIAM/ASA Journal on Uncertainty Quantification 6:374-396, 2018.
  DOI. 10.1137/17M1110729
  
  
• Howard C. Elman and Tengfei Su
  A low-rank multigrid method for the stochastic steady-state diffusion problem
  SIAM Journal on Matrix Analysis and Applications 39:492-509, 2018.
  DOI: 10.1137/17M1125170
  
  
• Kookjin Lee and Howard C. Elman
  A preconditioned low-rank projection method with a rank-reduction scheme for stochastic partial differential equations
  SIAM Journal on Scientific Computing 39:S828-S850, 2017.
  DOI: 10.1137/16M1075582
  
  
• Quan M. Bui, Howard C. Elman and David J. Moulton
  Algebraic multigrid preconditioners for multiphase flow in porous media
  SIAM Journal on Scientific Computing 39:S662-S680, 2017.
  DOI: 10.1137/16M1082652
  
  
• Howard C. Elman and Virginia Forstall
  Numerical solution of the steady-state Navier-Stokes equations using empirical interpolation methods
  Computer Methods in Applied Mechanics and Engineering 317:380-399, 2017.
  DOI: https://doi.org/10.1016/j.cma.2016.12.011
  Preprint: https://arxiv.org/abs/1605.06138
  
  
• Edward G. Phillips, John N. Shadid, Eric C. Cyr, Howard C. Elman, and Roger P. Pawlowski
  Block preconditioners for stable mixed nodal and edge finite element representations of incompressible resistive MHD
  SIAM Journal on Scientific Computing 38:B1009-B1031, 2016.
  DOI: 10.1137/16M1074084
  
  
• Bedřich Sousedík and Howard C. Elman
  Stochastic Galerkin methods for the steady-state Navier-Stokes equations
  Journal of Computational Physics 316:435-452, 2016.
  DOI: 10.1016/j.jcp.2016.04.013
  Preprint: https://arxiv.org/pdf/1506.08899.pdf
  
  
• Bedřich Sousedík and Howard C. Elman
  Inverse subspace iteration for spectral stochastic finite element methods
  SIAM/ASA Journal on Uncertainty Quantification 4:163-189, 2016
  DOI:10.1137/140999359
  
  
• Howard C. Elman and Minghao W. Rostami
  Efficient iterative algorithms for linear stability analysis of incompressible flows
  IMA Journal of Numerical Analysis 36:296-316, 2016.
  DOI:10.1093/imanum/drv003
  
  

Papers published 2011 - 2015

• Howard C. Elman and Virginia Forstall
  Preconditioning techniques for reduced basis methods for parameterized partial differential equations
  SIAM Journal on Scientific Computing 37:S177-S194, 2015.
  DOI: 10.1137/140970859
  
  
• Edward G. Phillips and Howard C. Elman
  A stochastic approach to uncertainty in the equations of MHD kinematics
  Journal of Computational Physics 284:334-350, 2015.
  DOI: 10.1016/j.jcp.2014.12.002
  
  
• Edward G. Phillips, Howard C. Elman, Eric C. Cyr, John N. Shadid and Roger P. Pawlowski
  A block preconditioner for an exact penalty formulation for stationary MHD
  SIAM Journal on Scientific Computing 36:B930-B951, 2014.
  DOI: 10.1137/140955082
  
  
• Howard C. Elman, Alison Ramage and David J. Silvester
  IFISS: A computational laboratory for investigating incompressible flow problems
  SIAM Review 56:261-273, 2014.
  DOI: 10.1137/120891393  
• Howard C. Elman and Minghao Wu
  Lyapunov inverse iteration for computing a few rightmost eigenvalues of large generalized eigenvalue problems
  SIAM Journal on Matrix Analysis and Applications 34:1685-1707, 2013.
  DOI: 10.1137/120897468  
• Howard C. Elman and Qifeng Liao
  Reduced basis collocation methods for partial differential equations with random coefficients
  SIAM/ASA Journal on Uncertainty Quantification 1:192-217, 2013.
  DOI: 10.1137/120881841  
• Howard C. Elman and Christopher W. Miller
  Stochastic collocation with kernel density estimation
  Computer Methods in Applied Mechanics and Engineering 245-246:36-46, 2012.
  DOI: 10.1016/j.cma.2012.06.020.  
• Howard C. Elman, Karl Meerbergen, Alastair Spence and Minghao Wu
  Lyapunov inverse iteration for identifying Hopf bifurcations in models of incompressible flow
  SIAM Journal on Scientific Computing 34:A1584-A1606, 2012.
  DOI: 10.1137/110827600.  
• Fei Xue and Howard C. Elman
  Fast inexact implicitly restarted Arnoldi method for generalized eigenvalue problems with spectral transformation
  SIAM Journal on Matrix Analysis and Applications 33:433-459, 2012. DOI: 10.1137/100786599.  
• Elisabeth Ullmann, Howard C. Elman and Oliver G. Ernst
  Efficient iterative solvers for stochastic Galerkin discretizations of log-transformed random diffusion problems
  SIAM Journal on Scientific Computing 34:A659-A682, 2012.
  DOI: 10.1137/110836675.  
• Howard Elman, Milan Mihajlović and David Silvester
  Fast iterative solvers for buoyancy driven flow problems
  Journal of Computional Physics 230:3900-3914, 2011.
  DOI: 10.1016/j.jcp.2011.02.014.  
• Fei Xue and Howard C. Elman
  Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation
  Linear Algebra and Its Applications 435:601-622, 2011.
  DOI: 10.1016/j.laa.2010.06.021.  
• Robert R. Shuttleworth, Howard C. Elman, Kevin R. Long and Jeremy A. Templeton
  Fast solvers for models of ICEO microfluidic flows
  International Journal for Numerical Methods in Fluids 65:383-404, 2011.  
• Howard C. Elman, Christopher W. Miller, Eric T. Phipps and Ray S. Tuminaro
  Assessment of collocation and Galerkin approaches to linear diffusion equations with random data
  International Journal for Uncertainty Quantification 1:19-34, 2011.  
• P. Aaron Lott and Howard Elman
  Fast iterative solver for convection-diffusion systems with spectral elements
  Numerical Methods for Partial Differential Equations 27:231-254, 2011.  
  

Papers published 2009 - 2010

• Howard C. Elman, Darran G. Furnival and Catherine E. Powell
  H(div) Preconditioning for a mixed finite element formulation of the diffusion problem with random data
  Mathematics of Computation 79:733-760, 2010.  
• Howard C. Elman and Ray S. Tuminaro
  Boundary conditions in approximate commutator preconditioners for the Navier-Stokes equations
  Electronic Transactions on Numerical Analysis 35:257-280, 2009.  
• Fei Xue and Howard C. Elman
  Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration
  SIAM Journal on Matrix Analysis and Applications 31:877-899, 2009.
  
  
• Catherine E. Powell and Howard C. Elman
  Block-diagonal preconditioning for spectral stochastic finite element systems
  IMA Journal of Numerical Analysis 29:350-375, 2009.

Papers published 2007 - 2008

• Howard Elman, V. E. Howle, John Shadid, Robert Shuttleworth and Ray Tuminaro
  A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations
  Journal of Computational Physics 227:1790-1808, 2008.
  
  
• Howard Elman, Victoria E. Howle, John Shadid, David Silvester and Ray Tuminaro
  Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations
  SIAM Journal on Scientific Computing 30:290-311, 2007.
  
  
• Kouroush Sadegh Zadeh, Howard C. Elman, Hubert J. Montas and Adel Shirmohammadi
  A finite element model for protein transport in vivo
  Biomedical Engineering Online 6: Article No. 24 June 28, 2007.
  
  
• Howard Elman and Darran Furnival
  Solving the stochastic steady-state diffusion problem using multigrid
  IMA Journal of Numerical Analysis 27:675-688, 2007.
  
  
• Howard C. Elman, Alison Ramage and David J. Silvester
  IFISS: A Matlab toolbox for modelling incompressible flow
  ACM Transactions on Mathematical Software 33:14:1-14:18, 2007.

Papers published 2005 - 2006

• Howard C. Elman and Alison Ramage
  Fourier analysis of multigrid for the two-dimensional convection-diffusion equation
  BIT Numerical Mathematics 46:283-306, 2006.
  
  
• Chin-Tien Wu and Howard C. Elman
  Analysis and comparison of geometric and algebraic aultigrid for convection-diffusion equations
  SIAM Journal on Scientific Computing 28:2208-2228, 2006.
  
  
• Howard Elman, Victoria E. Howle, John Shadid, Robert Shuttleworth and Ray Tuminaro
  Block preconditioners based on approximate commutators
  SIAM Journal on Scientific Computing 27:1651-1055, 2006.
  
  
• Howard C. Elman,
  Preconditioning strategies for models of incompressible flow
  Journal of Scientific Computing 25:347-366, 2005.
  
  
• Howard C. Elman, Oliver G. Ernst, Dianne P. O'Leary and Michael Stewart,
  Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering
  Computer Methods in Applied Mechanics and Engineering 18:1037-1055, 2005.

Papers published 2003 - 2004

• Howard C. Elman and Alison Ramage
  A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation
  Mathematics of Computation 72:263-288, 2003.  
• Ilya Zavorin, Dianne P. O'Leary and Howard C. Elman
  Stagnation of GMRES
  Linear Algebra and its Applications 367:165-183, 2003.  
• Howard C. Elman, Victoria E. Howle, John N. Shadid and Ray S. Tuminaro
  A parallel block multi-level preconditioner for the 3D incompressible Navier-Stokes equations
  Journal of Computational Physics 187:504-523, 2003.  
• H. C. Elman, D. Loghin and A. J. Wathen
  Preconditioning techniques for Newton's method for the incompressible Navier-Stokes equations
  BIT 43:961-974, 2003.

Papers published 2001 - 2002

• David Silvester, Howard Elman, David Kay and Andrew Wathen,
  Efficient preconditioning of the linearized Navier-Stokes equations
  Journal of Computational and Applied Mathematics 128:261-279, 2001.  
• Howard C. Elman, Oliver G. Ernst and Dianne P. O'Leary,
  A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations
  SIAM Journal on Scientific Computing 23:1291-1315, 2001.  
• Howard C. Elman and Alison Ramage
  An analysis of smoothing effects of upwinding strategies for the convection-diffusion equation
  SIAM Journal on Numerical Analysis 40:254-281, 2002.  
• Howard C. Elman, David J. Silvester, and Andrew J. Wathen
  Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
  Numerische Mathematik 90:641-664, 2002.  
• H. C. Elman, D. J. Silvester and A. J. Wathen
  Block preconditioners for the discrete incompressible Navier-Stokes equations
  International Journal for Numerical Methods in Fluids 40:333-344, 2002.  
• Howard C. Elman,
  Preconditioners for saddle point problems arising in computational fluid dynamics
  Applied Numerical Mathematics 43:75-89, 2002.

Papers published prior to 2001

• Yin-Tzer Shih and Howard C. Elman,
  Iterative methods for stabilized discrete convection-diffusion problems
  IMA Journal of Numerical Analysis 20:333-358, 2000.  
• Yin-Tzer Shih and Howard C. Elman, UMIACS-TR-97-71, 1997,
  Modified streamline diffusion schemes for convection-diffusion problems
  Computer Methods in Applied Mechanics and Engineering 174:137-151, 1999.  
• Howard C. Elman
  Preconditioning for the steady-State Navier-Stokes equations with low viscosity
  SIAM Journal on Scientific Computing 20:1299-1316, 1999.  
• Howard C. Elman and Dianne P. O'Leary,
  Eigenanalysis of some preconditioned Helmholtz problems
  Numerische Mathematik 83:231-257, 1999.  
• Howard C. Elman and Dianne P. O'Leary,
  Efficient iterative solution of the three-dimensional Helmholtz equation
  Journal of Computational Physics 142:163-181, 1998.  
• Howard C. Elman, David. J. Silvester and Andrew J. Wathen,
  Iterative Methods for Problems in Computational Fluid Dynamics
  Iterative Methods in Scientific Computing, R. Chan, T. Chan and G. Golub, Eds., Springer-Verlag, Singapore, 1997, pp. 271-327.  
• Howard C. Elman,
  Perturbation of eigenvalues of preconditioned Navier-Stokes operators
  SIAM Journal on Matrix Analysis and Applications 18:733-751, 1997.  
• Aaron E. Naiman, Ivo M. Babuska and Howard C. Elman,
  A note on conjugate gradient convergence
  Numerische Mathematik 76:209-230, 1997.  
• Howard Elman and David Silvester
  Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations
  SIAM Journal on Scientific Computing 17:33-46, 1996.  
• Howard C. Elman
  Multigrid and Krylov subspace methods for the discrete Stokes equations
  International Journal for Numerical Methods in Fluids 22:755-770, 1996.  
• Howard C. Elman and Gene H. Golub
  Inexact and preconditioned Uzawa algorithms for saddle point problems
  SIAM Journal on Numerical Analysis 31:1645-1661, 1994.  
• Howard C. Elman and Gene H. Golub
  Line iterative methods for cyclically reduced discrete convection-diffusion problems
  SIAM Journal on Scientific and Statistical Computing 13:339-363, 1992.
  
  
• Howard C. Elman and Gene H. Golub
  Iterative methods for cyclically reduced non-self-adjoint linear systems
  Mathematics of Computation 54:671-700, 1990.
  
  
• Tony F. Chan and Howard C. Elman,
  Fourier analysis of iterative methods for elliptic problems
  SIAM Review 31:20-49, 1989.
  
  
• Howard C. Elman,
  A stibility analysis of incomplete LU factorizations
  Mathematics of Computation 47:191-217, 1986.
  
  
• Howard C. Elman, Stanley C. Eisenstat and Martin H. Schultz,
  Variational methods for nonsymmetric systems of linear equations
  SIAM Journal on Numerical Analysis 20:345-357, 1983.