## Elman, Howard C.

Compute Distance To:
 Author ID: elman.howard-c Published as: Elman, Howard C.; Elman, Howard; Elman, H. C.; Elman, H. more...less
 Documents Indexed: 99 Publications since 1983, including 2 Books 7 Contributions as Editor Co-Authors: 91 Co-Authors with 93 Joint Publications 2,370 Co-Co-Authors
all top 5

### Co-Authors

 12 single-authored 15 Silvester, David J. 8 Wathen, Andrew John 7 Shadid, John N. 7 Tuminaro, Ray S. 6 Golub, Gene Howard 5 Lee, Kookjin 5 O’Leary, Dianne P. 5 Ramage, Alison 4 Babuška, Ivo 4 Ernst, Oliver G. 4 Howle, Victoria E. 4 Sousedík, Bedřich 4 Walker, Homer F. 3 Benzi, Michele 3 Duff, Iain S. 3 Freund, Roland W. 3 Kelley, Tim 3 Kilmer, Misha Elena 3 Phillips, Edward G. 3 Powell, Catherine Elizabeth 3 Saylor, Paul E. 3 Schultz, Martin H. 3 Shuttleworth, Robert R. 3 Su, Tengfei 3 Xue, Fei 2 Ashby, Steve 2 Bui, Quan M. 2 Cai, Xiao-Chuan 2 Chernesky, Michael P. 2 Cyr, Eric C. 2 Eisenstat, Stanley C. 2 Forstall, Virginia 2 Furnival, Darran G. 2 Greenbaum, Anne 2 Jordan, Kirk E. 2 Kay, David A. 2 Leyffer, Sven 2 Loghin, Daniel 2 Manteuffel, Thomas A. 2 McCormick, Steve Fahrney 2 Miller, Christopher W. 2 Parter, Seymour V. 2 Pawlowski, Roger P. 2 Shih, Yintzer 2 Widlund, Olof B. 2 Woodward, Carol S. 2 Wu, Minghao 2 Yavneh, Irad 1 Agrón, Elvira 1 Bai, Zhaojun 1 Bourne, David P. 1 Carlberg, Kevin T. 1 Chan, Tony Fan-Cheong 1 Cho, Heyrim 1 Freund, Ronal 1 Guo, Xianzhong 1 Higham, Nicholas J. 1 Keyes, David Elliot 1 Knoll, Dana A. 1 Lee, Dennis K.-Y. 1 Lee, Dongeun 1 Liang, Jiaxing 1 Liao, Qifeng 1 Livshits, Irene 1 Long, Kevin R. 1 Lott, P. Aaron 1 Markley, K. 1 Meerbergen, Karl 1 Mehrman, Volker 1 Mihajlović, Milan D. 1 Moulton, David J. 1 Naiman, Aaron E. 1 Olson, Luke N. 1 Osborn, John E. 1 Phipps, Eric T. 1 Price, Randy 1 Rostami, Minghao W. 1 Saad, Yousef 1 Sánchez-Vizuet, Tonatiuh 1 Sherman, Andrew H. 1 Spence, Alastair 1 Starke, Gerhard 1 Stewart, Michael 1 Streit, Roy L. 1 Templeton, Jeremy A. 1 Tuminaro, Raymond S. 1 Ullmann, Elisabeth 1 Van der Vorst, Henk Albertus 1 Wu, Chin-Tien 1 Zavorin, Ilya 1 Zhang, Xuejun
all top 5

### Serials

 20 SIAM Journal on Scientific Computing 8 Journal of Computational Physics 6 SIAM Journal on Matrix Analysis and Applications 5 Computer Methods in Applied Mechanics and Engineering 5 Mathematics of Computation 5 SIAM Journal on Numerical Analysis 4 IMA Journal of Numerical Analysis 4 BIT 4 Numerische Mathematik 4 SIAM Journal on Scientific and Statistical Computing 4 SIAM/ASA Journal on Uncertainty Quantification 3 International Journal for Numerical Methods in Fluids 3 Linear Algebra and its Applications 2 Journal of Computational and Applied Mathematics 2 Parallel Computing 2 SIAM Review 2 International Journal for Uncertainty Quantification 2 Numerical Mathematics and Scientific Computation 1 Computer Physics Communications 1 ACM Transactions on Mathematical Software 1 International Journal for Numerical Methods in Engineering 1 Applied Numerical Mathematics 1 Numerical Methods for Partial Differential Equations 1 Journal of Scientific Computing 1 Applications of Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Communications on Pure and Applied Analysis
all top 5

### Fields

 95 Numerical analysis (65-XX) 46 Partial differential equations (35-XX) 34 Fluid mechanics (76-XX) 14 Probability theory and stochastic processes (60-XX) 7 General and overarching topics; collections (00-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Mechanics of deformable solids (74-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

90 Publications have been cited 2,821 times in 1,870 Documents Cited by Year
Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Zbl 1083.76001
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2005
Variational iterative methods for nonsymmetric systems of linear equations. Zbl 0524.65019
Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H.
1983
Finite elements and fast iterative solvers. With applications in incompressible fluid dynamics. 2nd ed. Zbl 1304.76002
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2014
Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041
Elman, Howard C.; Golub, Gene H.
1994
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow. Zbl 1365.65326
Elman, Howard C.; Ramage, Alison; Silvester, David J.
2007
Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations. Zbl 1143.76531
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2002
Preconditioning for the steady-state Navier–Stokes equations with low viscosity. Zbl 0935.76057
Elman, Howard C.
1999
Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. Zbl 0843.65080
Elman, Howard; Silvester, David
1996
A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations. Zbl 1004.65134
Elman, Howard C.; Ernst, Oliver G.; O’Leary, Dianne P.
2001
Block-diagonal preconditioning for spectral stochastic finite-element systems. Zbl 1169.65007
Powell, Catherine E.; Elman, Howard C.
2009
Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. Zbl 0983.76051
Silvester, David; Elman, Howard; Kay, David; Wathen, Andrew
2001
IFISS: A computational laboratory for investigating incompressible flow problems. Zbl 1426.76645
Elman, Howard C.; Ramage, Alison; Silvester, David J.
2014
Block preconditioners based on approximate commutators. Zbl 1100.65042
Elman, Howard; Howle, Victoria E.; Shadid, John; Shuttleworth, Robert; Tuminaro, Ray
2006
Preconditioners for saddle point problems arising in computational fluid dynamics. Zbl 1168.76348
Elman, Howard C.
2002
A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations. Zbl 1290.76023
Elman, Howard; Howle, V. E.; Shadid, John; Shuttleworth, Robert; Tuminaro, Ray
2008
Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021
Elman, Howard C.; Golub, Gene H.
1990
A stability analysis of incomplete LU factorizations. Zbl 0621.65024
Elman, Howard C.
1986
Preconditioning by fast direct methods for nonself-adjoint nonseparable elliptic equations. Zbl 0619.65093
Elman, Howard C.; Schultz, Martin H.
1986
Fourier analysis of iterative methods for elliptic problems. Zbl 0684.65092
Chan, Tony F.; Elman, Howard C.
1989
Preconditioning strategies for models of incompressible flow. Zbl 1203.76098
Elman, H. C.
2005
Reduced basis collocation methods for partial differential equations with random coefficients. Zbl 1282.35424
Elman, Howard C.; Liao, Qifeng
2013
Multigrid and Krylov subspace methods for the discrete Stokes equations. Zbl 0865.76078
Elman, Howard C.
1996
A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations. Zbl 0613.65031
Elman, Howard C.; Saad, Youcef; Saylor, Paul E.
1986
Modified streamline diffusion schemes for convection-diffusion problems. Zbl 0957.76035
Shih, Yin-Tzer; Elman, Howard C.
1999
Boundary conditions in approximate commutator preconditioners for the Navier-Stokes equations. Zbl 1391.76539
Elman, Howard C.; Tuminaro, Ray S.
2009
Assessment of collocation and Galerkin approaches to linear diffusion equations with random data. Zbl 1229.65026
Elman, Howard C.; Miller, Christopher W.; Phipps, Eric T.; Tuminaro, Raymond S.
2011
Efficient iterative solvers for stochastic Galerkin discretizations of log-transformed random diffusion problems. Zbl 1251.35200
Ullmann, Elisabeth; Elman, Howard C.; Ernst, Oliver G.
2012
Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations. Zbl 1166.65326
Elman, Howard; Howle, Victoria E.; Shadid, John; Silvester, David; Tuminaro, Ray
2007
Iterative methods for problems in computational fluid dynamics. Zbl 0957.76071
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
1997
Block preconditioners for stable mixed nodal and edge finite element representations of incompressible resistive MHD. Zbl 1349.76903
Phillips, Edward G.; Shadid, John N.; Cyr, Eric C.; Elman, Howard C.; Pawlowski, Roger P.
2016
A block preconditioner for an exact penalty formulation for stationary MHD. Zbl 1308.76333
Phillips, Edward G.; Elman, Howard C.; Cyr, Eric C.; Shadid, John N.; Pawlowski, Roger P.
2014
Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering. Zbl 1091.76032
Elman, Howard C.; Ernst, Oliver G.; O’Leary, Dianne P.; Stewart, Michael
2005
Efficient iterative solution of the three-dimensional Helmholtz equation. Zbl 0929.65089
Elman, Howard C.; O’Leary, Dianne P.
1998
Complete stagnation of GMRES. Zbl 1025.65022
Zavorin, Ilya; O’Leary, Dianne P.; Elman, Howard
2003
A parallel block multi-level preconditioner for the 3D incompressible Navier-Stokes equations. Zbl 1061.76058
Elman, Howard C.; Howle, Victoria E.; Shadid, John N.; Tuminaro, Ray S.
2003
Solving the stochastic steady-state diffusion problem using multigrid. Zbl 1141.65004
Elman, Howard; Furnival, Darran
2007
Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems. Zbl 0694.65011
Elman, Howard C.
1989
Fast iterative solvers for buoyancy driven flow problems. Zbl 1369.76040
Elman, Howard; Mihajlović, Milan; Silvester, David
2011
Iterative methods for cyclically reduced non-self-adjoint linear systems. II. Zbl 0716.65096
Elman, Howard C.; Golub, Gene H.
1991
Line iterative methods for cyclically reduced discrete convection- diffusion problems. Zbl 0752.65067
Elman, Howard C.; Golub, Gene H.
1992
Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation. Zbl 1253.65059
Xue, Fei; Elman, Howard C.
2011
Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration. Zbl 1201.65060
Xue, Fei; Elman, Howard C.
2010
Eigenanalysis of some preconditioned Helmholtz problems. Zbl 0934.65119
Elman, Howard C.; O’Leary, Dianne P.
1999
Preconditioning techniques for Newton’s method for the incompressible Navier-Stokes equations. Zbl 1244.76023
Elman, H. C.; Loghin, D.; Wathen, A. J.
2003
An analysis of smoothing effects of upwinding strategies for the convection-diffusion equation. Zbl 1017.65090
Elman, Howard C.; Ramage, Alison
2002
Some aspects of parallel implementation of the finite-element method on message passing architectures. Zbl 0693.65077
Babuška, I.; Elman, H. C.
1989
Iterative methods for stabilized discrete convection-diffusion problems. Zbl 0980.65127
Shih, Yin-Tzer; Elman, Howard C.
2000
Lyapunov inverse iteration for identifying Hopf bifurcations in models of incompressible flow. Zbl 1247.65047
Elman, Howard C.; Meerbergen, Karl; Spence, Alastair; Wu, Minghao
2012
Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations. Zbl 1133.65102
Wu, Chin-Tien; Elman, Howard C.
2006
Algebraic multigrid preconditioners for multiphase flow in porous media. Zbl 1392.65024
Bui, Quan M.; Elman, Howard C.; Moulton, David J.
2017
Parallel implementation of the $$hp$$-version of the finite element method on a shared-memory architecture. Zbl 0765.65101
Babuška, I.; Elman, H. C.; Markley, K.
1992
Fast inexact implicitly restarted Arnoldi method for generalized eigenvalue problems with spectral transformation. Zbl 1263.65041
Xue, Fei; Elman, Howard C.
2012
Polynomial iteration for nonsymmetric indefinite linear systems. Zbl 0605.65020
Elman, Howard C.; Streit, Roy L.
1986
Stochastic Galerkin methods for the steady-state Navier-Stokes equations. Zbl 1349.76268
Sousedík, Bedřich; Elman, Howard C.
2016
Performance of the $$h-p$$ version of the finite element method with various elements. Zbl 0780.73071
Babuška, I.; Elman, H. C.
1993
Ordering techniques for the preconditioned conjugate gradient method on parallel computers. Zbl 0798.65038
Elman, Howard C.; Agrón, Elvira
1989
A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation. Zbl 1008.65083
Elman, Howard C.; Ramage, Alison
2003
Block preconditioners for the discrete incompressible Navier-Stokes equations. Zbl 1019.76023
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2002
A low-rank multigrid method for the stochastic steady-state diffusion problem. Zbl 1390.35437
Elman, Howard C.; Su, Tengfei
2018
A note on conjugate gradient convergence. Zbl 0905.65047
Naiman, Aaron E.; Babuška, Ivo M.; Elman, Howard C.
1997
A preconditioned low-rank projection method with a rank-reduction scheme for stochastic partial differential equations. Zbl 1373.60126
Lee, Kookjin; Elman, Howard C.
2017
Ordering effects on relaxation methods applied to the discrete one- dimensional convection-diffusion equation. Zbl 0790.65027
Elman, Howard C.; Chernesky, Michael P.
1993
Ordering effects on relaxation methods applied to the discrete convection-diffusion equation. Zbl 0803.65033
Elman, Howard C.; Chernesky, Michael P.
1994
A stochastic approach to uncertainty in the equations of MHD kinematics. Zbl 1351.76310
Phillips, Edward G.; Elman, Howard C.
2015
Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations. Zbl 1457.65174
Elman, Howard C.; Forstall, Virginia
2015
Lyapunov inverse iteration for computing a few rightmost eigenvalues of large generalized eigenvalue problems. Zbl 1425.65053
Elman, Howard C.; Wu, Minghao
2013
$$H(\text{div})$$ preconditioning for a mixed finite element formulation of the diffusion problem with random data. Zbl 1216.65155
Elman, Howard C.; Furnival, Darran G.; Powell, Catherine E.
2010
Algebraic analysis of the hierarchical basis preconditioner. Zbl 0828.65032
Elman, Howard C.; Zhang, Xuejun
1995
A new preconditioner for the Oseen equations. Zbl 1268.76036
Wathen, A.; Loghin, D.; Kay, D.; Elman, H.; Silvester, D.
2003
A low-rank solver for the Navier-Stokes equations with uncertain viscosity. Zbl 1442.35568
Lee, Kookjin; Elman, Howard C.; Sousedík, Bedřich
2019
Multigrid and Krylov subspace methods for the discrete Stokes equations. Zbl 0814.65119
Elman, Howard C.
1994
A non-self-adjoint quadratic eigenvalue problemdescribing a fluid-solid interaction. II: Analysis of convergence. Zbl 1153.74015
Bourne, David; Elman, Howard; Osborn, John E.
2009
Approximate Schur complement preconditioners on serial and parallel computers. Zbl 0678.65018
Elman, Howard C.
1989
A low-rank solver for the stochastic unsteady Navier-Stokes problem. Zbl 1442.76065
Elman, Howard C.; Su, Tengfei
2020
Fast iterative solver for convection-diffusion systems with spectral elements. Zbl 1209.65130
Lott, P. Aaron; Elman, Howard
2011
Efficient iterative algorithms for linear stability analysis of incompressible flows. Zbl 1425.65052
Elman, Howard C.; Rostami, Minghao W.
2016
Inverse subspace iteration for spectral stochastic finite element methods. Zbl 1336.65060
Sousedík, Bedřich; Elman, Howard C.
2016
Use of linear algebra kernels to build an efficient finite element solver. Zbl 0875.68511
Elman, Howard C.; Lee, Dennis K.-Y.
1995
Performance enhancement and parallel algorithms for two multilevel preconditioners. Zbl 0786.65025
Elman, H. C.; Guo, Xian-Zhong
1993
The (new) Yale sparse matrix package. Zbl 0562.65014
Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H.; Sherman, Andrew H.
1984
Stochastic least-squares Petrov-Galerkin method for parameterized linear systems. Zbl 1388.35232
Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.
2018
Fourier analysis of multigrid for a model two-dimensional convection-diffusion equation. Zbl 1098.65105
Elman, Howard C.; Ramage, Alison
2006
Iterative methods for linear systems. Zbl 0832.65026
Elman, Howard C.
1994
Parallel sparse Cholesky factorization on a shared memory multiprocessor. Zbl 0757.65030
Zhang, G.; Elman, H. C.
1992
Low-rank solution methods for stochastic eigenvalue problems. Zbl 1420.65046
Elman, Howard C.; Su, Tengfei
2019
Introduction to the special issue on iterative methods for solving systems of algebraic equations. Zbl 0888.00015
1997
On the convergence of line iterative methods for cyclically reduced non- symmetrizable linear systems. Zbl 0795.65016
Elman, Howard C.; Golub, Gene H.; Starke, Gerhard
1994
Stochastic collocation with kernel density estimation. Zbl 1354.65258
Elman, Howard C.; Miller, Christopher W.
2012
Collocation methods for exploring perturbations in linear stability analysis. Zbl 1398.65176
Elman, Howard C.; Silvester, David J.
2018
Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media. Zbl 07504691
Bui, Quan M.; Elman, Howard C.
2020
A low-rank solver for the stochastic unsteady Navier-Stokes problem. Zbl 1442.76065
Elman, Howard C.; Su, Tengfei
2020
Semi-smooth Newton methods for nonlinear complementarity formulation of compositional two-phase flow in porous media. Zbl 07504691
Bui, Quan M.; Elman, Howard C.
2020
A low-rank solver for the Navier-Stokes equations with uncertain viscosity. Zbl 1442.35568
Lee, Kookjin; Elman, Howard C.; Sousedík, Bedřich
2019
Low-rank solution methods for stochastic eigenvalue problems. Zbl 1420.65046
Elman, Howard C.; Su, Tengfei
2019
A low-rank multigrid method for the stochastic steady-state diffusion problem. Zbl 1390.35437
Elman, Howard C.; Su, Tengfei
2018
Stochastic least-squares Petrov-Galerkin method for parameterized linear systems. Zbl 1388.35232
Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.
2018
Collocation methods for exploring perturbations in linear stability analysis. Zbl 1398.65176
Elman, Howard C.; Silvester, David J.
2018
Algebraic multigrid preconditioners for multiphase flow in porous media. Zbl 1392.65024
Bui, Quan M.; Elman, Howard C.; Moulton, David J.
2017
A preconditioned low-rank projection method with a rank-reduction scheme for stochastic partial differential equations. Zbl 1373.60126
Lee, Kookjin; Elman, Howard C.
2017
Block preconditioners for stable mixed nodal and edge finite element representations of incompressible resistive MHD. Zbl 1349.76903
Phillips, Edward G.; Shadid, John N.; Cyr, Eric C.; Elman, Howard C.; Pawlowski, Roger P.
2016
Stochastic Galerkin methods for the steady-state Navier-Stokes equations. Zbl 1349.76268
Sousedík, Bedřich; Elman, Howard C.
2016
Efficient iterative algorithms for linear stability analysis of incompressible flows. Zbl 1425.65052
Elman, Howard C.; Rostami, Minghao W.
2016
Inverse subspace iteration for spectral stochastic finite element methods. Zbl 1336.65060
Sousedík, Bedřich; Elman, Howard C.
2016
A stochastic approach to uncertainty in the equations of MHD kinematics. Zbl 1351.76310
Phillips, Edward G.; Elman, Howard C.
2015
Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations. Zbl 1457.65174
Elman, Howard C.; Forstall, Virginia
2015
Finite elements and fast iterative solvers. With applications in incompressible fluid dynamics. 2nd ed. Zbl 1304.76002
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2014
IFISS: A computational laboratory for investigating incompressible flow problems. Zbl 1426.76645
Elman, Howard C.; Ramage, Alison; Silvester, David J.
2014
A block preconditioner for an exact penalty formulation for stationary MHD. Zbl 1308.76333
Phillips, Edward G.; Elman, Howard C.; Cyr, Eric C.; Shadid, John N.; Pawlowski, Roger P.
2014
Reduced basis collocation methods for partial differential equations with random coefficients. Zbl 1282.35424
Elman, Howard C.; Liao, Qifeng
2013
Lyapunov inverse iteration for computing a few rightmost eigenvalues of large generalized eigenvalue problems. Zbl 1425.65053
Elman, Howard C.; Wu, Minghao
2013
Efficient iterative solvers for stochastic Galerkin discretizations of log-transformed random diffusion problems. Zbl 1251.35200
Ullmann, Elisabeth; Elman, Howard C.; Ernst, Oliver G.
2012
Lyapunov inverse iteration for identifying Hopf bifurcations in models of incompressible flow. Zbl 1247.65047
Elman, Howard C.; Meerbergen, Karl; Spence, Alastair; Wu, Minghao
2012
Fast inexact implicitly restarted Arnoldi method for generalized eigenvalue problems with spectral transformation. Zbl 1263.65041
Xue, Fei; Elman, Howard C.
2012
Stochastic collocation with kernel density estimation. Zbl 1354.65258
Elman, Howard C.; Miller, Christopher W.
2012
Assessment of collocation and Galerkin approaches to linear diffusion equations with random data. Zbl 1229.65026
Elman, Howard C.; Miller, Christopher W.; Phipps, Eric T.; Tuminaro, Raymond S.
2011
Fast iterative solvers for buoyancy driven flow problems. Zbl 1369.76040
Elman, Howard; Mihajlović, Milan; Silvester, David
2011
Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation. Zbl 1253.65059
Xue, Fei; Elman, Howard C.
2011
Fast iterative solver for convection-diffusion systems with spectral elements. Zbl 1209.65130
Lott, P. Aaron; Elman, Howard
2011
Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration. Zbl 1201.65060
Xue, Fei; Elman, Howard C.
2010
$$H(\text{div})$$ preconditioning for a mixed finite element formulation of the diffusion problem with random data. Zbl 1216.65155
Elman, Howard C.; Furnival, Darran G.; Powell, Catherine E.
2010
Block-diagonal preconditioning for spectral stochastic finite-element systems. Zbl 1169.65007
Powell, Catherine E.; Elman, Howard C.
2009
Boundary conditions in approximate commutator preconditioners for the Navier-Stokes equations. Zbl 1391.76539
Elman, Howard C.; Tuminaro, Ray S.
2009
A non-self-adjoint quadratic eigenvalue problemdescribing a fluid-solid interaction. II: Analysis of convergence. Zbl 1153.74015
Bourne, David; Elman, Howard; Osborn, John E.
2009
A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations. Zbl 1290.76023
Elman, Howard; Howle, V. E.; Shadid, John; Shuttleworth, Robert; Tuminaro, Ray
2008
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow. Zbl 1365.65326
Elman, Howard C.; Ramage, Alison; Silvester, David J.
2007
Least squares preconditioners for stabilized discretizations of the Navier-Stokes equations. Zbl 1166.65326
Elman, Howard; Howle, Victoria E.; Shadid, John; Silvester, David; Tuminaro, Ray
2007
Solving the stochastic steady-state diffusion problem using multigrid. Zbl 1141.65004
Elman, Howard; Furnival, Darran
2007
Block preconditioners based on approximate commutators. Zbl 1100.65042
Elman, Howard; Howle, Victoria E.; Shadid, John; Shuttleworth, Robert; Tuminaro, Ray
2006
Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations. Zbl 1133.65102
Wu, Chin-Tien; Elman, Howard C.
2006
Fourier analysis of multigrid for a model two-dimensional convection-diffusion equation. Zbl 1098.65105
Elman, Howard C.; Ramage, Alison
2006
Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Zbl 1083.76001
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2005
Preconditioning strategies for models of incompressible flow. Zbl 1203.76098
Elman, H. C.
2005
Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering. Zbl 1091.76032
Elman, Howard C.; Ernst, Oliver G.; O&rsquo;Leary, Dianne P.; Stewart, Michael
2005
Complete stagnation of GMRES. Zbl 1025.65022
Zavorin, Ilya; O&rsquo;Leary, Dianne P.; Elman, Howard
2003
A parallel block multi-level preconditioner for the 3D incompressible Navier-Stokes equations. Zbl 1061.76058
Elman, Howard C.; Howle, Victoria E.; Shadid, John N.; Tuminaro, Ray S.
2003
Preconditioning techniques for Newton’s method for the incompressible Navier-Stokes equations. Zbl 1244.76023
Elman, H. C.; Loghin, D.; Wathen, A. J.
2003
A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation. Zbl 1008.65083
Elman, Howard C.; Ramage, Alison
2003
A new preconditioner for the Oseen equations. Zbl 1268.76036
Wathen, A.; Loghin, D.; Kay, D.; Elman, H.; Silvester, D.
2003
Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations. Zbl 1143.76531
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2002
Preconditioners for saddle point problems arising in computational fluid dynamics. Zbl 1168.76348
Elman, Howard C.
2002
An analysis of smoothing effects of upwinding strategies for the convection-diffusion equation. Zbl 1017.65090
Elman, Howard C.; Ramage, Alison
2002
Block preconditioners for the discrete incompressible Navier-Stokes equations. Zbl 1019.76023
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2002
A multigrid method enhanced by Krylov subspace iteration for discrete Helmholtz equations. Zbl 1004.65134
Elman, Howard C.; Ernst, Oliver G.; O&rsquo;Leary, Dianne P.
2001
Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow. Zbl 0983.76051
Silvester, David; Elman, Howard; Kay, David; Wathen, Andrew
2001
Iterative methods for stabilized discrete convection-diffusion problems. Zbl 0980.65127
Shih, Yin-Tzer; Elman, Howard C.
2000
Preconditioning for the steady-state Navier–Stokes equations with low viscosity. Zbl 0935.76057
Elman, Howard C.
1999
Modified streamline diffusion schemes for convection-diffusion problems. Zbl 0957.76035
Shih, Yin-Tzer; Elman, Howard C.
1999
Eigenanalysis of some preconditioned Helmholtz problems. Zbl 0934.65119
Elman, Howard C.; O&rsquo;Leary, Dianne P.
1999
Efficient iterative solution of the three-dimensional Helmholtz equation. Zbl 0929.65089
Elman, Howard C.; O&rsquo;Leary, Dianne P.
1998
Iterative methods for problems in computational fluid dynamics. Zbl 0957.76071
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
1997
A note on conjugate gradient convergence. Zbl 0905.65047
Naiman, Aaron E.; Babuška, Ivo M.; Elman, Howard C.
1997
Introduction to the special issue on iterative methods for solving systems of algebraic equations. Zbl 0888.00015
1997
Fast nonsymmetric iterations and preconditioning for Navier-Stokes equations. Zbl 0843.65080
Elman, Howard; Silvester, David
1996
Multigrid and Krylov subspace methods for the discrete Stokes equations. Zbl 0865.76078
Elman, Howard C.
1996
Algebraic analysis of the hierarchical basis preconditioner. Zbl 0828.65032
Elman, Howard C.; Zhang, Xuejun
1995
Use of linear algebra kernels to build an efficient finite element solver. Zbl 0875.68511
Elman, Howard C.; Lee, Dennis K.-Y.
1995
Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041
Elman, Howard C.; Golub, Gene H.
1994
Ordering effects on relaxation methods applied to the discrete convection-diffusion equation. Zbl 0803.65033
Elman, Howard C.; Chernesky, Michael P.
1994
Multigrid and Krylov subspace methods for the discrete Stokes equations. Zbl 0814.65119
Elman, Howard C.
1994
Iterative methods for linear systems. Zbl 0832.65026
Elman, Howard C.
1994
On the convergence of line iterative methods for cyclically reduced non- symmetrizable linear systems. Zbl 0795.65016
Elman, Howard C.; Golub, Gene H.; Starke, Gerhard
1994
Performance of the $$h-p$$ version of the finite element method with various elements. Zbl 0780.73071
Babuška, I.; Elman, H. C.
1993
Ordering effects on relaxation methods applied to the discrete one- dimensional convection-diffusion equation. Zbl 0790.65027
Elman, Howard C.; Chernesky, Michael P.
1993
Performance enhancement and parallel algorithms for two multilevel preconditioners. Zbl 0786.65025
Elman, H. C.; Guo, Xian-Zhong
1993
Line iterative methods for cyclically reduced discrete convection- diffusion problems. Zbl 0752.65067
Elman, Howard C.; Golub, Gene H.
1992
Parallel implementation of the $$hp$$-version of the finite element method on a shared-memory architecture. Zbl 0765.65101
Babuška, I.; Elman, H. C.; Markley, K.
1992
Parallel sparse Cholesky factorization on a shared memory multiprocessor. Zbl 0757.65030
Zhang, G.; Elman, H. C.
1992
Iterative methods for cyclically reduced non-self-adjoint linear systems. II. Zbl 0716.65096
Elman, Howard C.; Golub, Gene H.
1991
Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021
Elman, Howard C.; Golub, Gene H.
1990
Fourier analysis of iterative methods for elliptic problems. Zbl 0684.65092
Chan, Tony F.; Elman, Howard C.
1989
Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems. Zbl 0694.65011
Elman, Howard C.
1989
Some aspects of parallel implementation of the finite-element method on message passing architectures. Zbl 0693.65077
Babuška, I.; Elman, H. C.
1989
Ordering techniques for the preconditioned conjugate gradient method on parallel computers. Zbl 0798.65038
Elman, Howard C.; Agrón, Elvira
1989
Approximate Schur complement preconditioners on serial and parallel computers. Zbl 0678.65018
Elman, Howard C.
1989
A stability analysis of incomplete LU factorizations. Zbl 0621.65024
Elman, Howard C.
1986
Preconditioning by fast direct methods for nonself-adjoint nonseparable elliptic equations. Zbl 0619.65093
Elman, Howard C.; Schultz, Martin H.
1986
A hybrid Chebyshev Krylov subspace algorithm for solving nonsymmetric systems of linear equations. Zbl 0613.65031
Elman, Howard C.; Saad, Youcef; Saylor, Paul E.
1986
Polynomial iteration for nonsymmetric indefinite linear systems. Zbl 0605.65020
Elman, Howard C.; Streit, Roy L.
1986
The (new) Yale sparse matrix package. Zbl 0562.65014
Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H.; Sherman, Andrew H.
1984
Variational iterative methods for nonsymmetric systems of linear equations. Zbl 0524.65019
Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H.
1983
all top 5

### Cited by 2,370 Authors

 37 Zhang, Guofeng 33 Ma, Changfeng 32 Wathen, Andrew John 31 Liang, Zhaozheng 30 Elman, Howard C. 25 Bai, Zhongzhi 22 Stoll, Martin 20 Axelsson, Axel Owe Holger 19 Huang, Ting-Zhu 18 Benzi, Michele 18 Olshanskii, Maxim A. 18 Vuik, Cornelis 18 Wu, Yujiang 18 Yang, Aili 16 Shang, Yueqiang 15 Silvester, David J. 15 Simoncini, Valeria 14 Ferronato, Massimiliano 13 Khojasteh Salkuyeh, Davod 13 Quarteroni, Alfio M. 13 Saad, Yousef 13 Zhang, Jun 12 Fan, Hongtao 12 Spence, Euan A. 12 Zhang, Naimin 11 Badia, Santiago 11 Benner, Peter 11 Cao, Zhihao 11 Cui, Jingjing 11 Greif, Chen 11 Huang, Na 11 Huang, Zhengge 11 Pestana, Jennifer 11 Rebholz, Leo G. 11 Sousedík, Bedřich 11 Wang, Ligong 11 Wei, Yimin 11 Xu, Zhong 11 Zheng, Bing 10 Castelletto, Nicola 10 He, Yinnian 10 Niu, Qiang 10 Pearson, John W. 10 Powell, Catherine Elizabeth 10 Szyld, Daniel B. 10 White, Joshua A. 10 Xu, Jinchao 10 Zikatanov, Ludmil T. 9 Graham, Ivan G. 9 Hu, Xiaozhe 9 MacLachlan, Scott P. 9 Neytcheva, Maya G. 9 Shadid, John N. 9 Shao, Xinhui 9 Vanroose, Wim 9 Wu, Shiliang 9 Zheng, Qingqing 8 Bergamaschi, Luca 8 Deparis, Simone 8 Dou, Yan 8 Feng, Xinlong 8 Karátson, János 8 Li, Wen 8 Miao, Shu-Xin 8 Ramage, Alison 8 Zhu, Xinyun 7 Adler, James H. 7 Auricchio, Ferdinando 7 Bespalov, Alexei 7 Chao, Zhen 7 Cyr, Eric C. 7 Gambolati, Giuseppe 7 Golub, Gene Howard 7 Han, Danfu 7 Il’in, Valeriĭ Pavlovich 7 Li, Changjun 7 Liu, Jun 7 Notay, Yvan 7 Pavarino, Luca Franco 7 Peng, Xiaofei 7 Schwab, Christoph 7 Shao, Xinping 7 Tuminaro, Raymond S. 7 Wang, Zengqi 7 Zhang, Guodong 6 Aulisa, Eugenio 6 Bacuta, Constantin 6 Brenner, Susanne Cecelia 6 Cai, Xiao-Chuan 6 Chen, Guoliang 6 Heil, Matthias 6 Howle, Victoria E. 6 Janna, Carlo 6 Jia, Zhongxiao 6 Ke, Guoyi 6 Ke, Yifen 6 Lee, Kookjin 6 Li, Cuixia 6 Liao, Lidan 6 Liao, Qifeng ...and 2,270 more Authors
all top 5

### Cited in 169 Serials

 149 Journal of Computational and Applied Mathematics 148 Journal of Computational Physics 136 Computer Methods in Applied Mechanics and Engineering 122 SIAM Journal on Scientific Computing 108 Applied Mathematics and Computation 103 Computers & Mathematics with Applications 76 Applied Numerical Mathematics 70 Numerical Linear Algebra with Applications 63 Numerical Algorithms 49 Numerische Mathematik 48 International Journal of Computer Mathematics 47 Linear Algebra and its Applications 42 Journal of Scientific Computing 41 BIT 30 Mathematics of Computation 28 SIAM Journal on Matrix Analysis and Applications 27 Computational and Applied Mathematics 21 International Journal for Numerical Methods in Engineering 21 SIAM/ASA Journal on Uncertainty Quantification 19 Computers and Fluids 19 International Journal for Numerical Methods in Fluids 19 Advances in Computational Mathematics 16 Applied Mathematics Letters 15 Mathematics and Computers in Simulation 15 East Asian Journal on Applied Mathematics 14 SIAM Journal on Numerical Analysis 12 Numerical Methods for Partial Differential Equations 11 Computational Geosciences 10 Computational Mechanics 10 Computational Optimization and Applications 10 Engineering Analysis with Boundary Elements 9 ETNA. Electronic Transactions on Numerical Analysis 9 Journal of Applied Mathematics and Computing 9 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 8 Journal of Fluid Mechanics 8 Calcolo 8 Japan Journal of Industrial and Applied Mathematics 8 Applied Mathematical Modelling 8 Computing and Visualization in Science 8 Journal of Numerical Mathematics 8 Communications in Computational Physics 7 Archives of Computational Methods in Engineering 7 Computational Methods in Applied Mathematics 6 Computing 6 Numerical Functional Analysis and Optimization 6 Applications of Mathematics 6 International Journal of Numerical Methods for Heat & Fluid Flow 6 International Journal of Computational Methods 5 SIAM Review 5 Advances in Applied Mathematics and Mechanics 4 Applied Mathematics. Series B (English Edition) 4 Engineering Computations 4 Journal of Applied Mathematics 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Acta Numerica 4 Communications on Applied Mathematics and Computation 3 Mathematical Methods in the Applied Sciences 3 Journal of Computational Mathematics 3 Mathematical and Computer Modelling 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Journal of Mathematical Imaging and Vision 3 Advances in Engineering Software 3 Communications in Numerical Methods in Engineering 3 Journal of Mathematical Sciences (New York) 3 Mathematical Problems in Engineering 3 International Journal of Computational Fluid Dynamics 3 Mathematical Modelling and Analysis 3 Multiscale Modeling & Simulation 3 Frontiers of Mathematics in China 3 Science China. Mathematics 3 International Journal for Numerical Methods in Biomedical Engineering 3 S$$\vec{\text{e}}$$MA Journal 3 ISRN Applied Mathematics 2 Computer Physics Communications 2 Communications on Pure and Applied Mathematics 2 Journal of Engineering Mathematics 2 Linear and Multilinear Algebra 2 Journal of the Korean Mathematical Society 2 Applied Mathematics and Mechanics. (English Edition) 2 Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik 2 Parallel Computing 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 SIAM Journal on Mathematical Analysis 2 Vietnam Journal of Mathematics 2 Optimization Methods & Software 2 Journal of Inequalities and Applications 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Mediterranean Journal of Mathematics 2 Journal of Computational Acoustics 2 Inverse Problems in Science and Engineering 2 Advances in Numerical Analysis 2 Journal of Applied Mathematics & Informatics 2 ISRN Computational Mathematics 2 AIMS Mathematics 1 Applicable Analysis 1 International Journal of Engineering Science 1 International Journal for Numerical and Analytical Methods in Geomechanics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Transport Theory and Statistical Physics ...and 69 more Serials
all top 5

### Cited in 38 Fields

 1,643 Numerical analysis (65-XX) 543 Fluid mechanics (76-XX) 461 Partial differential equations (35-XX) 148 Linear and multilinear algebra; matrix theory (15-XX) 139 Mechanics of deformable solids (74-XX) 78 Calculus of variations and optimal control; optimization (49-XX) 77 Probability theory and stochastic processes (60-XX) 50 Optics, electromagnetic theory (78-XX) 44 Operations research, mathematical programming (90-XX) 32 Biology and other natural sciences (92-XX) 31 Computer science (68-XX) 31 Geophysics (86-XX) 20 Systems theory; control (93-XX) 18 Operator theory (47-XX) 17 Classical thermodynamics, heat transfer (80-XX) 14 Ordinary differential equations (34-XX) 14 Statistics (62-XX) 12 Integral equations (45-XX) 11 Approximations and expansions (41-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Information and communication theory, circuits (94-XX) 9 Combinatorics (05-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Potential theory (31-XX) 3 Functions of a complex variable (30-XX) 3 Difference and functional equations (39-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Quantum theory (81-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Integral transforms, operational calculus (44-XX) 1 Mathematical logic and foundations (03-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX)