Howard C. Elman

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All published works

Action	Title	Year	Authors
+ PDF Chat	Surrogate-based multilevel Monte Carlo methods for uncertainty quantification in the Grad-Shafranov free boundary problem	2025	Howard C. Elman Jiaxing Liang Tonatiuh Sánchez-Vizuet
+ PDF Chat	Transformed Physics-Informed Neural Networks for The Convection-Diffusion Equation	2024	Jiajing Guan Howard C. Elman
+ PDF Chat	Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem	2024	Howard C. Elman Jiaxing Liang Tonatiuh Sánchez-Vizuet
+	An Assessment of the Supremizer and Aggregation Methods of Stabilization for Reduced-Order Models	2023	Kayla D. Davie Howard C. Elman
+	Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem	2023	Howard C. Elman Jiaxing Liang Tonatiuh Sánchez-Vizuet
+ PDF Chat	Multilevel Monte Carlo Methods for the Grad-Shafranov Free Boundary Problem	2023	Howard C. Elman Jiaxing Liang Tonatiuh Sánchez-Vizuet
+ PDF Chat	On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity	2022	Bedřich Sousedík Howard C. Elman Kookjin Lee Randy Price
+ PDF Chat	Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids	2021	Howard C. Elman Jiaxing Liang Tonatiuh Sánchez-Vizuet
+	Surrogate Approximation of the Grad-Shafranov Free Boundary Problem via Stochastic Collocation on Sparse Grids	2021	Howard C. Elman Jiaxing Liang Tonatiuh Sánchez-Vizuet
+	Novel Deep neural networks for solving Bayesian statistical inverse.	2021	Harbir Antil Howard C. Elman Akwum Onwunta Deepanshu Verma
+	Novel Deep neural networks for solving Bayesian statistical inverse	2021	Harbir Antil Howard C. Elman Akwum Onwunta Deepanshu Verma
+ PDF Chat	Fast Computational Algorithms for Partial Differential Equations and Uncertainty Quantifications	2020	Howard C. Elman
+ PDF Chat	A low-rank solver for the stochastic unsteady Navier–Stokes problem	2020	Howard C. Elman Tengfei Su
+	Alternating Energy Minimization Methods for Multi-term Matrix Equations	2020	Kookjin Lee Howard C. Elman Catherine E. Powell Dong‐Eun Lee
+	Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media	2019	Quan M. Bui Howard C. Elman
+	Reduced-order modeling for nonlinear Bayesian statistical inverse problems	2019	Howard C. Elman Akwum Onwunta
+ PDF Chat	A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity	2019	Kookjin Lee Howard C. Elman Bedřich Sousedík
+	Low-Rank Solution Methods for Stochastic Eigenvalue Problems	2019	Howard C. Elman Tengfei Su
+	Reduced-order modeling for nonlinear Bayesian statistical inverse problems	2019	Howard C. Elman Akwum Onwunta
+	A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem	2018	Howard C. Elman Tengfei Su
+ PDF Chat	Collocation Methods for Exploring Perturbations in Linear Stability Analysis	2018	Howard C. Elman David J. Silvester
+	Low-Rank Solution Methods for Stochastic Eigenvalue Problems	2018	Howard C. Elman Tengfei Su
+	Stochastic Least-Squares Petrov--Galerkin Method for Parameterized Linear Systems	2018	Kookjin Lee Kevin Carlberg Howard C. Elman
+ PDF Chat	AN ADAPTIVE REDUCED BASIS COLLOCATION METHOD BASED ON PCM ANOVA DECOMPOSITION FOR ANISOTROPIC STOCHASTIC PDES	2018	Heyrim Cho Howard C. Elman
+	Stochastic Least-Squares Petrov-Galerkin Method for Parameterized Linear Systems	2017	Kookjin Lee Kevin Carlberg Howard C. Elman
+	Algebraic Multigrid Preconditioners for Multiphase Flow in Porous Media	2017	Quan M. Bui Howard C. Elman D. Moulton
+	A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations	2017	Kookjin Lee Howard C. Elman
+	Stochastic Least-Squares Petrov-Galerkin Method for Parameterized Linear Systems	2017	Kookjin Lee Kevin Carlberg Howard C. Elman
+	Collocation Methods for Exploring Perturbations in Linear Stability Analysis	2017	Howard C. Elman David J. Silvester
+ PDF Chat	Numerical solution of the parameterized steady-state Navier–Stokes equations using empirical interpolation methods	2016	Howard C. Elman Virginia Forstall
+	A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations	2016	Kookjin Lee Howard C. Elman
+ PDF Chat	Stochastic Galerkin methods for the steady-state Navier–Stokes equations	2016	Bedřich Sousedík Howard C. Elman
+	Block Preconditioners for Stable Mixed Nodal and Edge finite element Representations of Incompressible Resistive MHD	2016	Edward Geoffrey Phillips John N. Shadid Eric C. Cyr Howard C. Elman Roger P. Pawlowski
+	A Low-Rank Multigrid Method for the Stochastic Steady-State Diffusion Problem	2016	Howard C. Elman Tengfei Su
+ PDF Chat	Inverse Subspace Iteration for Spectral Stochastic Finite Element Methods	2016	Bedřich Sousedík Howard C. Elman
+	A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations	2016	Kookjin Lee Howard C. Elman
+	Preconditioning Techniques for Reduced Basis Methods for Parameterized Elliptic Partial Differential Equations	2015	Howard C. Elman Virginia Forstall
+	Optimization with PDE Constraints	2014	Howard C. Elman David J. Silvester Andrew J. Wathen
+	Solution of Discrete Navier–Stokes Problems	2014	Howard C. Elman David J. Silvester Andrew J. Wathen
+ PDF Chat	Lyapunov Inverse Iteration for Computing a Few Rightmost Eigenvalues of Large Generalized Eigenvalue Problems	2013	Howard C. Elman Minghao Wu
+	The solution of two-parameter eigenvalue problems arising from the determination of Hopf bifurcations of dynamical systems	2012	Karl Meerbergen A. Spence Howard C. Elman Minghao Wu
+ PDF Chat	Fast iterative solvers for buoyancy driven flow problems	2011	Howard C. Elman Milan Mihajlović David J. Silvester
+	Recent Progress in Nonlinear and Linear Solvers	2011	P. Aaron Lott Howard C. Elman Katherine J. Evans X S Li Andy Salinger Carol S. Woodward
+	Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation	2010	Fei Xue Howard C. Elman
+ PDF Chat	Convergence Analysis of Iterative Solvers in Inexact Rayleigh Quotient Iteration	2009	Fei Xue Howard C. Elman
+	BOUNDARY CONDITIONS IN APPROXIMATE COMMUTATOR PRECONDITIONERS FOR THE NAVIER-STOKES EQUATIONS ∗	2009	Howard C. Elman Ray Tuminaro
+	Fast iterative solver for convection-diffusion systems with spectral elements	2009	P. Aaron Lott Howard C. Elman
+	Preconditioners Boundary Conditions for the Navier-Stokes Equations Based on Commutators.	2008	Raymond S. Tuminaro Howard C. Elman
+ PDF Chat	Least Squares Preconditioners for Stabilized Discretizations of the Navier–Stokes Equations	2007	Howard C. Elman Victoria E. Howle John N. Shadid David J. Silvester Ray Tuminaro
+	A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier–Stokes equations	2007	Howard C. Elman Victoria E. Howle John N. Shadid Robert Shuttleworth Ray Tuminaro
+	Algorithm 866	2007	Howard C. Elman Alison Ramage David J. Silvester
+	Some observations on multigrid convergence for convection–diffusion equations	2007	Alison Ramage Howard C. Elman
+	Fourier Analysis of Multigrid for a Model Two-Dimensional Convection-Diffusion Equation	2006	Howard C. Elman Alison Ramage
+ PDF Chat	Analysis and Comparison of Geometric and Algebraic Multigrid for Convection‐Diffusion Equations	2006	Chin‐Tien Wu Howard C. Elman
+ PDF Chat	Preconditioning Strategies for Models of Incompressible Flow	2005	Howard C. Elman
+	Solution of Discrete Navier-Stokes Problems	2005	Howard C. Elman David J. Silvester Andrew J. Wathen
+	Complete stagnation of gmres	2003	Ilya Zavorin Dianne P. O’Leary Howard C. Elman
+	A new preconditioner for the Oseen equations	2003	Andy Wathen Daniel Loghin David Kay Howard C. Elman David J. Silvester
+ PDF Chat	Preconditioning Techniques for Newton's Method for the Incompressible Navier–Stokes Equations	2003	Howard C. Elman Daniel Loghin Andy Wathen
+ PDF Chat	Preconditioners for saddle point problems arising in computational fluid dynamics	2002	Howard C. Elman
+ PDF Chat	A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation	2001	Howard C. Elman Alison Ramage
+ PDF Chat	Efficient preconditioning of the linearized Navier–Stokes equations for incompressible flow	2001	David J. Silvester Howard C. Elman David Kay Andrew J. Wathen
+ PDF Chat	Efficient preconditioning of the linearized Navier—Stokes equations for incompressible flow	2001	David J. Silvester Howard C. Elman David Kay Andrew J. Wathen
+	Iterative Methods for Problems in Computational Fluid Dynamics	1998	Howard C. Elman David J. Silvester Andrew J. Wathen
+	Introduction to the Special Issue on Iterative Methods for Solving Systems of Algebraic Equations	1998	Howard C. Elman
+	Upwind finite element solutions for convection-diffusion problems	1998	Howard C. Elman Yin-Tzer Shih
+	Perturbation of Eigenvalues of Preconditioned Navier--Stokes Operators	1997	Howard C. Elman
+ PDF Chat	A note on conjugate gradient convergence	1997	Aaron E. Naiman Ivo Babuška Howard C. Elman
+ PDF Chat	Fast Nonsymmetric Iterations and Preconditioning for Navier–Stokes Equations	1996	Howard C. Elman David J. Silvester
+	Fast non-symmetric iterations and efficient preconditioning for Navier-Stokes equations	1994	David J. Silvester Howard C. Elman
+	On the convergence of line iterative methods for cyclically reduced non-symmetrizable linear systems	1994	Howard C. Elman Gene H. Golub Gerhard Starke
+	Iterative Methods for Linear Systems	1994	Howard C. Elman
+	Ordering Effects on Relaxation Methods Applied to the Discrete Convection-Diffusion Equation	1994	Howard C. Elman Michael P. Chernesky
+	Ordering Effects on Relaxation Methods Applied to the Discrete One-Dimensional Convection-Diffusion Equation	1993	Howard C. Elman Michael P. Chernesky
+	Parallel sparse Cholesky factorization on a shared memory multiprocessor	1992	G. Zhang Howard C. Elman
+ PDF Chat	Line Iterative Methods for Cyclically Reduced Discrete Convection-Diffusion Problems	1992	Howard C. Elman Gene H. Golub
+ PDF Chat	Iterative methods for cyclically reduced nonselfadjoint linear systems. II	1991	Howard C. Elman Gene H. Golub
+	Iterative Methods for Cyclically Reduced Non-Self-Adjoint Linear Systems. II	1991	Howard C. Elman Gene H. Golub
+	Iterative Methods for Cyclically Reduced Non-Self-Adjoint Linear Systems	1990	Howard C. Elman Gene H. Golub
+	Block Iterative Methods for Cyclically Reduced Non-Self-Adjoint Elliptic Problems	1990	Howard C. Elman Gene H. Golub
+	Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems	1989	Howard C. Elman
+	Ordering techniques for the preconditioned conjugate gradient method on parallel computers	1989	Howard C. Elman Elvira Agrón
+	Block-Preconditioned Conjugate-Gradient-Like Methods for Numerical Reservoir Simulation	1988	Stanley C. Eisenstat Howard C. Elman Martin H. Schultz
+	A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations	1986	Howard C. Elman Yousef Saad Paul E. Saylor
+	Preconditioning by Fast Direct Methods for Nonself-Adjoint Nonseparable Elliptic Equations	1986	Howard C. Elman Martin H. Schultz
+	Polynomial iteration for nonsymmetric indefinite linear systems	1986	Howard C. Elman Roy L. Streit
+ PDF Chat	A stability analysis of incomplete 𝐿𝑈 factorizations	1986	Howard C. Elman
+	The (New) Yale Sparse Matrix Package11The work presented in this paper was supported in part by the Office of Naval Research under contract N00014-82-K-0184 and by the National Science Foundation under grant MCS-81-04874.	1984	Stanley C. Eisenstat Howard C. Elman Martin H. Schultz Andrew H. Sherman
+	Variational Iterative Methods for Nonsymmetric Systems of Linear Equations	1983	Stanley C. Eisenstat Howard C. Elman Martin H. Schultz
+	Iterative methods for large, sparse, nonsymmetric systems of linear equations	1982	Howard C. Elman
+	Solving Approximations To The Convection Diffusion Equation	1979	Stanley C. Eisenstat Howard C. Elman Martin H. Schultz Andrew H. Sherman

Common Coauthors

Coauthor	Papers Together
David J. Silvester	14
Kookjin Lee	9
Tonatiuh Sánchez-Vizuet	6
Jiaxing Liang	6
Gene H. Golub	6
Andrew J. Wathen	6
Martin H. Schultz	5
Tengfei Su	5
Alison Ramage	4
Bedřich Sousedík	4
Stanley C. Eisenstat	4
Akwum Onwunta	4
David Kay	3
John N. Shadid	3
Kevin Carlberg	3
Ray Tuminaro	3
Fei Xue	2
Deepanshu Verma	2
Virginia Forstall	2
Minghao Wu	2
Victoria E. Howle	2
Harbir Antil	2
P. Aaron Lott	2
Andrew H. Sherman	2
A. J. Wathen	2
Daniel Loghin	2
Quan M. Bui	2
Michael P. Chernesky	2
Dong‐Eun Lee	1
A. Spence	1
Randy Price	1
Roy L. Streit	1
Chin‐Tien Wu	1
Robert Shuttleworth	1
Yousef Saad	1
Aaron E. Naiman	1
Carol S. Woodward	1
Ilya Zavorin	1
Roger P. Pawlowski	1
Andy Salinger	1
Jiajing Guan	1
Eric C. Cyr	1
Dianne P. O’Leary	1
Raymond S. Tuminaro	1
G. Zhang	1
Gerhard Starke	1
Yin-Tzer Shih	1
Catherine E. Powell	1
Ivo Babuška	1
Edward Geoffrey Phillips	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems	1986	Yousef Saad Martin H. Schultz	22
+	Solution of Sparse Indefinite Systems of Linear Equations	1975	Christopher C. Paige Michael A. Saunders	10
+	Variational Iterative Methods for Nonsymmetric Systems of Linear Equations	1983	Stanley C. Eisenstat Howard C. Elman Martin H. Schultz	10
+ PDF Chat	Efficient preconditioning of the linearized Navier–Stokes equations for incompressible flow	2001	David J. Silvester Howard C. Elman David Kay Andrew J. Wathen	9
+ PDF Chat	A projection method to solve linear systems in tensor format	2012	Jonas Ballani Lars Grasedyck	9
+	A class of first order factorization methods	1978	Ivar Gustafsson	8
+	Numerical Methods for Singularly Perturbed Differential Equations	1996	Hans‐Görg Roos Martin Stynes Lutz Tobiska	8
+ PDF Chat	Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems	2011	Daniel Kreßner Christine Tobler	8
+	Methods of conjugate gradients for solving linear systems	1952	Magnus R. Hestenes Eduard Stiefel	7
+	Convergence analysis of a multigrid method for convection–diffusion equations	2002	Arnold Reusken	7
+ PDF Chat	An iterative solution method for linear systems of which the coefficient matrix is a symmetric 𝑀-matrix	1977	J. A. Meijerink H.A. van der Vorst	7
+	Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods	1980	David M. Young Kang C. Jea	7
+ PDF Chat	Fast Nonsymmetric Iterations and Preconditioning for Navier–Stokes Equations	1996	Howard C. Elman David J. Silvester	7
+ PDF Chat	QMR: a quasi-minimal residual method for non-Hermitian linear systems	1991	Roland W. Freund No�l M. Nachtigal	7
+	Numerical Solution of Convection-Diffusion Problems	2019	K. W. Morton	6
+	An Analysis of Block Successive Overrelaxation for a Class of Matrices with Complex Spectra	1988	R. C. Y. Chin Thomas A. Manteuffel	6
+	Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations	1994	J.C. Simo F. Armero	6
+	A Preconditioned Low-Rank Projection Method with a Rank-Reduction Scheme for Stochastic Partial Differential Equations	2017	Kookjin Lee Howard C. Elman	6
+	Multi-Grid Methods and Applications	1985	Wolfgang Hackbusch	6
+ PDF Chat	Least Squares Preconditioners for Stabilized Discretizations of the Navier–Stokes Equations	2007	Howard C. Elman Victoria E. Howle John N. Shadid David J. Silvester Ray Tuminaro	5
+ PDF Chat	Block Iterative Methods for Elliptic and Parabolic Difference Equations	1982	Seymour V. Parter Michael Steuerwalt	5
+	Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method	1984	Vance Faber Thomas A. Manteuffel	5
+	Convergence Analysis of a Multigrid Method for a Convection-Dominated Model Problem	2004	Maxim A. Olshanskii Arnold Reusken	5
+ PDF Chat	Multi-grid methods and applications.	1986	Wolfgang Hackbusch	5
+	Iterative methods for linear and nonlinear equations	1996	C. T. Kelley	5
+	Iterative methods for large, sparse, nonsymmetric systems of linear equations	1982	Howard C. Elman	5
+	Matrix-dependent prolongations and restrictions in a blackbox multigrid solver	1990	Paul M. de Zeeuw	5
+ PDF Chat	Stochastic Galerkin methods for the steady-state Navier–Stokes equations	2016	Bedřich Sousedík Howard C. Elman	5
+	None	1998	Thomas Gerstner Michael Griebel	5
+	Orthogonal Error Methods	1987	Vance Faber Thomas A. Manteuffel	5
+	Aspects of Numerical Methods for Elliptic Singular Perturbation Problems	1982	A. Śegal	5
+	An Approximate Factorization Procedure for Solving Self-Adjoint Elliptic Difference Equations	1968	Todd Dupont Richard P. Kendall H. H. Rachford	5
+	Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems	1992	H.A. van der Vorst	4
+ PDF Chat	A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation	2001	Howard C. Elman Alison Ramage	4
+	An inexact inverse iteration for large sparse eigenvalue problems	1997	Yu-Ling Lai Kun-Yi Lin Wen‐Wei Lin	4
+ PDF Chat	Preconditioning Techniques for Newton's Method for the Incompressible Navier–Stokes Equations	2003	Howard C. Elman Daniel Loghin Andy Wathen	4
+ PDF Chat	Nonlinear Model Reduction via Discrete Empirical Interpolation	2010	Saifon Chaturantabut Danny C. Sorensen	4
+	BOUNDARY CONDITIONS IN APPROXIMATE COMMUTATOR PRECONDITIONERS FOR THE NAVIER-STOKES EQUATIONS ∗	2009	Howard C. Elman Ray Tuminaro	4
+	Conjugate gradient methods for indefinite systems	1976	R. Fletcher	4
+ PDF Chat	Numerical solution of saddle point problems	2005	Michele Benzi Gene H. Golub Jörg Liesen	4
+	The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations	2003	Dongbin Xiu George Em Karniadakis	4
+ PDF Chat	Adaptive Time-Stepping for Incompressible Flow Part I: Scalar Advection-Diffusion	2008	Philip Gresho David F. Griffiths David J. Silvester	4
+	Mixed and Hybrid Finite Element Methods	2011	Franco Brezzi Michel Fortin	4
+	The numerical analysis of bifurcation problems with application to fluid mechanics	2000	K. A. Cliffe A. Spence Simon Tavener	4
+ PDF Chat	The reliability of local error estimators for convection-diffusion equations	2001	D. W. K. Kay David J. Silvester	4
+	The Uncoupling of Boundary Integral and Finite Element Methods for Nonlinear Boundary Value Problems	1995	Gabriel N. Gatica George C. Hsiao	4
+ PDF Chat	Adaptive Time-Stepping for Incompressible Flow Part II: Navier–Stokes Equations	2010	David Kay Philip Gresho David F. Griffiths David J. Silvester	4
+	Ordering Effects on Relaxation Methods Applied to the Discrete Convection-Diffusion Equation	1994	Howard C. Elman Michael P. Chernesky	4
+	An Analysis of the Fractional Step Method	1993	Blair Perot	4
+	Algorithm 866	2007	Howard C. Elman Alison Ramage David J. Silvester	4