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## Elman, Howard C.

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 Author ID: elman.howard-c Published as: Elman, H.; Elman, H. C.; Elman, Howard; Elman, Howard C.
 Documents Indexed: 101 Publications since 1983, including 5 Books
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 O’Leary, Dianne P. 5 Ramage, Alison 4 Babuška, Ivo 4 Ernst, Oliver G. 4 Howle, Victoria E. 4 Walker, Homer F. 3 Benzi, Michele 3 Duff, Iain S. 3 Freund, Roland W. 3 Kelley, Tim 3 Kilmer, Misha E. 3 Lee, Kookjin 3 Phillips, Edward G. 3 Saylor, Paul E. 3 Schultz, Martin H. 3 Shuttleworth, Robert R. 3 Sousedík, Bedřich 3 Su, Tengfei 3 Xue, Fei 2 Ashby, Steve 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 Powell, Catherine Elizabeth 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 Bui, Quan M. 1 Carlberg, Kevin T. 1 Chan, Tony Fan-Cheong 1 Freund, Ronal 1 Guo, Xianzhong 1 Higham, Nicholas J. 1 Keyes, David Elliot 1 Knoll, Dana A. 1 Lee, Dennis K.-Y. 1 Liao, Qifeng 1 Livshits, Ira 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 Rostami, Minghao W. 1 Saad, Yousef 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, Guangpeng 1 Zhang, Xuejun
all top 5

#### Serials

 20 SIAM Journal on Scientific Computing 6 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 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 BIT 3 Linear Algebra and its Applications 2 Journal of Computational and Applied Mathematics 2 Parallel Computing 2 SIAM Review 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 ETNA. Electronic Transactions on Numerical Analysis 1 Communications on Pure and Applied Analysis 1 International Journal for Uncertainty Quantification
all top 5

#### Fields

 91 Numerical analysis (65-XX) 44 Partial differential equations (35-XX) 33 Fluid mechanics (76-XX) 12 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 Statistics (62-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

87 Publications have been cited 2,514 times in 1,644 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
Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041
Elman, Howard C.; Golub, Gene H.
1994
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
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
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-diagonal preconditioning for spectral stochastic finite-element systems. Zbl 1169.65007
Powell, Catherine E.; Elman, Howard C.
2009
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
Modified streamline diffusion schemes for convection-diffusion problems. Zbl 0957.76035
Shih, Yin-Tzer; Elman, Howard C.
1999
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
Reduced basis collocation methods for partial differential equations with random coefficients. Zbl 1282.35424
Elman, Howard C.; Liao, Qifeng
2013
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 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
Iterative methods for problems in computational fluid dynamics. Zbl 0957.76071
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
1997
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
Boundary conditions in approximate commutator preconditioners for the Navier-Stokes equations. Zbl 1391.76539
Elman, Howard C.; Tuminaro, Ray S.
2009
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
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
Complete stagnation of GMRES. Zbl 1025.65022
Zavorin, Ilya; O’Leary, Dianne P.; Elman, Howard
2003
Efficient iterative solution of the three-dimensional Helmholtz equation. Zbl 0929.65089
Elman, Howard C.; O’Leary, Dianne P.
1998
Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems. Zbl 0694.65011
Elman, Howard C.
1989
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
Fast iterative solvers for buoyancy driven flow problems. Zbl 1369.76040
Elman, Howard; Mihajlović, Milan; Silvester, David
2011
Line iterative methods for cyclically reduced discrete convection- diffusion problems. Zbl 0752.65067
Elman, Howard C.; Golub, Gene H.
1992
Iterative methods for cyclically reduced non-self-adjoint linear systems. II. Zbl 0716.65096
Elman, Howard C.; Golub, Gene H.
1991
Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration. Zbl 1201.65060
Xue, Fei; Elman, Howard C.
2010
Solving the stochastic steady-state diffusion problem using multigrid. Zbl 1141.65004
Elman, Howard; Furnival, Darran
2007
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
Fast inexact subspace iteration for generalized eigenvalue problems with spectral transformation. Zbl 1253.65059
Xue, Fei; Elman, Howard C.
2011
Preconditioning techniques for Newton’s method for the incompressible Navier-Stokes equations. Zbl 1244.76023
Elman, H. C.; Loghin, D.; Wathen, A. J.
2003
Polynomial iteration for nonsymmetric indefinite linear systems. Zbl 0605.65020
Elman, Howard C.; Streit, Roy L.
1986
An analysis of smoothing effects of upwinding strategies for the convection-diffusion equation. Zbl 1017.65090
Elman, Howard C.; Ramage, Alison
2002
Iterative methods for stabilized discrete convection-diffusion problems. Zbl 0980.65127
Shih, Yin-Tzer; Elman, Howard C.
2000
Eigenanalysis of some preconditioned Helmholtz problems. Zbl 0934.65119
Elman, Howard C.; O’Leary, Dianne P.
1999
Some aspects of parallel implementation of the finite-element method on message passing architectures. Zbl 0693.65077
Babuška, I.; Elman, H. C.
1989
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
Analysis and comparison of geometric and algebraic multigrid for convection-diffusion equations. Zbl 1133.65102
Wu, Chin-Tien; Elman, Howard C.
2006
A characterisation of oscillations in the discrete two-dimensional convection-diffusion equation. Zbl 1008.65083
Elman, Howard C.; Ramage, Alison
2003
A note on conjugate gradient convergence. Zbl 0905.65047
Naiman, Aaron E.; Babuška, Ivo M.; Elman, Howard C.
1997
Performance of the $$h-p$$ version of the finite element method with various elements. Zbl 0780.73071
Babuška, I.; Elman, H. C.
1993
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
Ordering techniques for the preconditioned conjugate gradient method on parallel computers. Zbl 0798.65038
Elman, Howard C.; Agrón, Elvira
1989
Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations. Zbl 1457.65174
Elman, Howard C.; Forstall, Virginia
2015
Block preconditioners for the discrete incompressible Navier-Stokes equations. Zbl 1019.76023
Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.
2002
Ordering effects on relaxation methods applied to the discrete convection-diffusion equation. Zbl 0803.65033
Elman, Howard C.; Chernesky, Michael P.
1994
Ordering effects on relaxation methods applied to the discrete one- dimensional convection-diffusion equation. Zbl 0790.65027
Elman, Howard C.; Chernesky, Michael P.
1993
Algebraic multigrid preconditioners for multiphase flow in porous media. Zbl 1392.65024
Bui, Quan M.; Elman, Howard C.; Moulton, David J.
2017
Stochastic Galerkin methods for the steady-state Navier-Stokes equations. Zbl 1349.76268
Sousedík, Bedřich; Elman, Howard C.
2016
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 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 new preconditioner for the Oseen equations. Zbl 1268.76036
Wathen, A.; Loghin, D.; Kay, D.; Elman, H.; Silvester, D.
2003
Approximate Schur complement preconditioners on serial and parallel computers. Zbl 0678.65018
Elman, Howard C.
1989
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
Inverse subspace iteration for spectral stochastic finite element methods. Zbl 1336.65060
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
A stochastic approach to uncertainty in the equations of MHD kinematics. Zbl 1351.76310
Phillips, Edward G.; Elman, Howard C.
2015
Fast iterative solver for convection-diffusion systems with spectral elements. Zbl 1209.65130
Lott, P. Aaron; Elman, Howard
2011
Use of linear algebra kernels to build an efficient finite element solver. Zbl 0875.68511
Elman, Howard C.; Lee, Dennis K.-Y.
1995
Iterative methods for linear systems. Zbl 0832.65026
Elman, Howard C.
1994
The (new) Yale sparse matrix package. Zbl 0562.65014
Eisenstat, Stanley C.; Elman, Howard C.; Schultz, Martin H.; Sherman, Andrew H.
1984
A low-rank multigrid method for the stochastic steady-state diffusion problem. Zbl 1390.35437
Elman, Howard C.; Su, Tengfei
2018
Fourier analysis of multigrid for a model two-dimensional convection-diffusion equation. Zbl 1098.65105
Elman, Howard C.; Ramage, Alison
2006
Multigrid and Krylov subspace methods for the discrete Stokes equations. Zbl 0814.65119
Elman, Howard C.
1994
Performance enhancement and parallel algorithms for two multilevel preconditioners. Zbl 0786.65025
Elman, H. C.; Guo, Xian-Zhong
1993
A low-rank solver for the stochastic unsteady Navier-Stokes problem. Zbl 1442.76065
Elman, Howard C.; Su, Tengfei
2020
Low-rank solution methods for stochastic eigenvalue problems. Zbl 1420.65046
Elman, Howard C.; Su, Tengfei
2019
Stochastic least-squares Petrov-Galerkin method for parameterized linear systems. Zbl 1388.35232
Lee, Kookjin; Carlberg, Kevin; Elman, Howard C.
2018
Stochastic collocation with kernel density estimation. Zbl 1354.65258
Elman, Howard C.; Miller, Christopher W.
2012
Introduction to the special issue on iterative methods for solving systems of algebraic equations. Zbl 0888.00015
Elman, Howard (ed.)
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
Parallel sparse Cholesky factorization on a shared memory multiprocessor. Zbl 0757.65030
Zhang, G.; Elman, H. C.
1992
A low-rank solver for the stochastic unsteady Navier-Stokes problem. Zbl 1442.76065
Elman, Howard C.; Su, Tengfei
2020
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
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
Inverse subspace iteration for spectral stochastic finite element methods. Zbl 1336.65060
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
Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations. Zbl 1457.65174
Elman, Howard C.; Forstall, Virginia
2015
A stochastic approach to uncertainty in the equations of MHD kinematics. Zbl 1351.76310
Phillips, Edward G.; Elman, Howard C.
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’Leary, Dianne P.; Stewart, Michael
2005
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
Complete stagnation of GMRES. Zbl 1025.65022
Zavorin, Ilya; O’Leary, Dianne P.; Elman, Howard
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’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’Leary, Dianne P.
1999
Efficient iterative solution of the three-dimensional Helmholtz equation. Zbl 0929.65089
Elman, Howard C.; O’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
Elman, Howard (ed.)
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
Iterative methods for linear systems. Zbl 0832.65026
Elman, Howard C.
1994
Multigrid and Krylov subspace methods for the discrete Stokes equations. Zbl 0814.65119
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
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#### Cited by 2,210 Authors

 34 Zhang, Guofeng 31 Ma, Changfeng 28 Elman, Howard C. 26 Liang, Zhao-Zheng 26 Wathen, Andrew John 25 Bai, Zhongzhi 20 Cao, Yang 19 Huang, Ting-Zhu 18 Stoll, Martin 18 Wu, Yujiang 18 Yang, Aili 17 Axelsson, Axel Owe Holger 17 Olshanskii, Maxim A. 17 Vuik, Cornelis 16 Benzi, Michele 15 Shang, Yueqiang 15 Silvester, David J. 14 Quarteroni, Alfio M. 13 Zhang, Jun 12 Badia, Santiago 12 Fan, Hongtao 12 Greif, Chen 12 Pestana, Jennifer 12 Rebholz, Leo G. 12 Simoncini, Valeria 11 Benner, Peter 11 Cao, Zhihao 11 Huang, Na 11 Saad, Yousef 11 Wei, Yimin 11 Zhang, Naimin 10 Cui, Jingjing 10 Ferronato, Massimiliano 10 Huang, Zhengge 10 Wang, Ligong 10 Wu, Shiliang 10 Xu, Zhong 10 Zheng, Bing 9 Khojasteh Salkuyeh, Davod 9 Niu, Qiang 9 Pearson, John W. 9 Spence, Euan A. 9 Szyld, Daniel B. 9 Vanroose, Wim 9 Xu, Jinchao 9 Zheng, Qingqing 8 Bergamaschi, Luca 8 Deparis, Simone 8 Graham, Ivan G. 8 Li, Cuixia 8 Li, Wen 8 MacLachlan, Scott P. 8 Neytcheva, Maya G. 8 Powell, Catherine Elizabeth 8 Sousedík, Bedřich 8 Zhu, Xinyun 8 Zikatanov, Ludmil T. 7 Auricchio, Ferdinando 7 Cai, Xiao-Chuan 7 Chao, Zhen 7 Gambolati, Giuseppe 7 Han, Danfu 7 He, Yinnian 7 Hu, Xiaozhe 7 Karátson, János 7 Li, Changjun 7 Manzoni, Andrea 7 Peng, Xiaofei 7 Ramage, Alison 7 Reichel, Lothar 7 Sadok, Hassane 7 Schwab, Christoph 7 Shadid, John N. 7 Shao, Xinhui 7 Shao, Xinping 7 Tuminaro, Raymond S. 6 Bacuta, Constantin 6 Castelletto, Nicola 6 Chen, Guoliang 6 Dou, Yan 6 Golub, Gene Howard 6 Heil, Matthias 6 Il’in, Valeriĭ Pavlovich 6 Jia, Zhongxiao 6 Lin, Yiqin 6 Lu, Junfeng 6 Notay, Yvan 6 Šístek, Jakub 6 Van Gijzen, Martin Bastiaan 6 Veneziani, Alessandro 6 Wang, Zengqi 6 Yang, Xi 5 Adler, James H. 5 Aulisa, Eugenio 5 Bespalov, Alexei 5 Brenner, Susanne Cecelia 5 Burda, Pavel 5 Chen, Peng 5 Cools, Siegfried 5 Cyr, Eric C. ...and 2,110 more Authors
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#### Cited in 149 Serials

 147 Journal of Computational and Applied Mathematics 130 Journal of Computational Physics 124 Computer Methods in Applied Mechanics and Engineering 102 Applied Mathematics and Computation 93 SIAM Journal on Scientific Computing 89 Computers & Mathematics with Applications 73 Applied Numerical Mathematics 70 Numerical Linear Algebra with Applications 60 Numerical Algorithms 47 Linear Algebra and its Applications 45 Numerische Mathematik 40 International Journal of Computer Mathematics 36 BIT 34 Journal of Scientific Computing 28 Mathematics of Computation 22 SIAM Journal on Matrix Analysis and Applications 22 Computational and Applied Mathematics 21 International Journal for Numerical Methods in Engineering 19 Computers and Fluids 19 International Journal for Numerical Methods in Fluids 19 SIAM/ASA Journal on Uncertainty Quantification 17 Applied Mathematics Letters 13 Advances in Computational Mathematics 13 East Asian Journal on Applied Mathematics 12 Mathematics and Computers in Simulation 12 SIAM Journal on Numerical Analysis 12 Numerical Methods for Partial Differential Equations 10 Computational Mechanics 8 Computational Optimization and Applications 8 Engineering Analysis with Boundary Elements 8 Computing and Visualization in Science 8 Computational Geosciences 8 Journal of Applied Mathematics and Computing 7 Japan Journal of Industrial and Applied Mathematics 7 Archives of Computational Methods in Engineering 7 Journal of Numerical Mathematics 6 Journal of Fluid Mechanics 6 Calcolo 6 Computing 6 Numerical Functional Analysis and Optimization 6 Applied Mathematical Modelling 6 International Journal of Numerical Methods for Heat & Fluid Flow 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Computational Methods in Applied Mathematics 4 Applications of Mathematics 4 Applied Mathematics. Series B (English Edition) 4 ETNA. Electronic Transactions on Numerical Analysis 4 Engineering Computations 4 Journal of Applied Mathematics 4 Acta Numerica 3 Mathematical Methods in the Applied Sciences 3 Mathematical and Computer Modelling 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Review 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 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Multiscale Modeling & Simulation 3 International Journal of Computational Methods 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 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 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 Vietnam Journal of Mathematics 2 Optimization Methods & Software 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial 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 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 Linear and Multilinear Algebra 1 Transport Theory and Statistical Physics 1 Wave Motion 1 ACM Transactions on Mathematical Software 1 Annals of the Institute of Statistical Mathematics 1 Journal of the Korean Mathematical Society 1 Journal of Optimization Theory and Applications 1 Journal of Soviet Mathematics 1 Kybernetika 1 SIAM Journal on Control and Optimization 1 Theoretical Computer Science 1 Tokyo Journal of Mathematics ...and 49 more Serials
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#### Cited in 38 Fields

 1,437 Numerical analysis (65-XX) 448 Fluid mechanics (76-XX) 406 Partial differential equations (35-XX) 123 Mechanics of deformable solids (74-XX) 119 Linear and multilinear algebra; matrix theory (15-XX) 67 Probability theory and stochastic processes (60-XX) 64 Calculus of variations and optimal control; optimization (49-XX) 44 Optics, electromagnetic theory (78-XX) 32 Operations research, mathematical programming (90-XX) 29 Geophysics (86-XX) 28 Biology and other natural sciences (92-XX) 22 Computer science (68-XX) 19 Operator theory (47-XX) 19 Systems theory; control (93-XX) 17 Classical thermodynamics, heat transfer (80-XX) 15 Ordinary differential equations (34-XX) 13 Statistics (62-XX) 11 Approximations and expansions (41-XX) 11 Integral equations (45-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Information and communication theory, circuits (94-XX) 6 Combinatorics (05-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Potential theory (31-XX) 3 Difference and functional equations (39-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Functional analysis (46-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Integral transforms, operational calculus (44-XX) 2 Quantum theory (81-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Mechanics of particles and systems (70-XX)