Rich Lehoucq's papers and reports (updated 5/18/2018)
Papers
Click on the DOI (Digital Object Identifier) below to display the abstract, and optionally download the paper (if your institution holds a subscription).
See Google Scholar or Microsoft Academic Search for a synoposis of citations to my publications.
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration, (with D.C. Sorensen)
SIAM Journal on Matrix Analysis and Applications, Volume 17, Number 4, pp. 789-821, 1996,
DOI:10.1137/S0895479895281484.
The Computation of Elementary Unitary Matrices,
ACM Transactions on Mathematical Software, Volume 22, pp. 393-400, 1996,
DOI:10.1145/235815.235817.
Compiler Blockability of Dense Matrix Factorizations,
(with Steve Carr), ACM Transactions on Mathematical Software, Volume 23, pp. 336-361, 1997,
DOI:10.1145/275323.275325.
Vibrational Eigenstates of Four-Atom Molecules: A Parallel Strategy
Employing the Implicitly Restarted Lanczos Method,
(with S. K. Gray, D. H. Zhang and J. C. Light)
Computer Physics Communications, Volume 109, pp. 15-26, 1998,
DOI:10.1016/S0010-4655(98)00002-2.
Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method, (with Karl Meerbergen),
SIAM Journal on Matrix Analysis and Applications, Volume 20, Number 1, pp.131-148, 1998,
DOI:10.1137/S0895479896311220.
Large-Scale Eigenvalue Calculations for Stability Analysis of Steady
Flows on Massively Parallel Computers, (with Andy Salinger),
International Journal for Numerical Methods in Fluids, Volume 36, pp. 309-327, 2001,
DOI:10.1002/fld.135.
Implicitly Restarted Arnoldi Methods and Subspace Iteration,
SIAM Journal on Matrix Analysis and Applications, Volume 23, Number 2, pp.
551-562, 2001,
DOI:10.1137/S0895479899358595.
Computational Bifurcation and Stability Studies of the 8:1 Thermal Cavity
Problem (with Andy Salinger, Roger Pawlowski and John Shadid),
International Journal for Numerical Methods in Fluids, Volume 40, pp. 1059-1073,
2002, DOI:10.1002/fld.392.
An Automated Multilevel Substructuring Method for Eigenspace Computation
in Linear Elastodynamics (with J. K. Bennighof),
SIAM Journal on Scientific Computing, Volume 25, Number 6, pp. 2084-2106, 2004,
DOI:10.1137/S1064827502400650.
Krylov Subspace Iterations for Deterministic k-Eigenvalue Calculations,
(with J. S. Warsa, T. A. Warming, J. E. Morel and J. M. McGhee),
Nuclear Science and Engineering,
Volume 147, pp. 26-42, 2004,
DOI:10.13182/NSE04-1.
On finite element discretizations of the pure Neumann problem,
(with Pavel Bochev),
SIAM Review, Volume 47, Number 1, pp. 50-66, 2005,
DOI:10.1137/S0036144503426074.
A Comparison of Eigensolvers for Large-scale 3D Modal Analysis Using AMG-Preconditioned Iterative Methods,
(with Peter Arbenz,
Ulrich Hetmaniuk,
Ray Tuminaro),
International Journal for Numerical Methods in Engineering, Volume 64, pp. 204-236, 2005,
DOI:10.1002/nme.1365.
An Overview of the Trilinos Project, (with Michael A. Heroux and Roscoe A. Bartlett and
icki E. Howle and Robert J. Hoekstra and Jonathan J. Hu and Tamara G. Kolda and
Richard B. Lehoucq and Kevin R. Long and Roger P. Pawlowski and Eric T. Phipps and
Andrew G. Salinger and Heidi K. Thornquist and Ray S. Tuminaro and James M. Willenbring and
Alan Williams and Kendall S. Stanley), ACM Transactions on
Mathematical Software Volume 31, Number 3 pp. 397-423, 2005,
DOI:10.1145/1089014.1089021.
Large-scale Stabilized FE Computational Analysis of Nonlinear Steady
State Transport/Reaction Systems, (with J.N. Shadid, A.G. Salinger, R.P. Pawlowski, P.T. Lin,
G.L. Hennigan, R.S. Tuminaro, R.B. Lehoucq),
Computer Methods in Applied Mechanics and Engineering, Volume 195, pp. 1846-1871, 2006,
DOI:10.1016/j.cma.2005.05.047.
A primal based penalty preconditioner for elliptic saddle point systems,
(with Clark Dohrmann),
SIAM Journal on Numerical Analysis, Volume 44, pp. 270-282, 2006,
DOI:10.1137/040619016.
Uniform accuracy of eigenpairs from a shift-invert Lanczos method, (with
Ulrich Hetmaniuk),
SIAM Journal on Matrix Analysis and Applications,
Volume 28, pp. 927-948, 2006,
DOI:10.1137/050629288.
Regularization and stabilization of discrete saddle-point variational problems,
(with Pavel Bochev),
ETNA, Volume 22, pp. 97-113, 2006.
On stabilized finite element methods for the Stokes problem in the small time-step limit,
(with Pavel Bochev
and Max Gunzburger),
International Journal for Numerical Methods in Fluids, Volume 53, pp. 573-597, 2007,
DOI:10.1002/fld.1295.
Estimating the critical time-step in explicit dynamics using the Lanczos method,
(with Richard Koteras),
International Journal for Numerical Methods in Engineering, Volume 69, pp. 2780-2788, 2007,
DOI:10.1002/nme.1865.
Force Flux and the Peridynamic Stress Tensor,
(with Stewart Silling),
Journal of Mechanics and Physics of Solids, Volume 56, pp. 1566-1577, 2007
DOI:10.1016/j.jmps.2007.08.004.
Connecting Atomistic-to-Continuum Coupling and Domain Decomposition,
(with Pavel Bochev,
Mike Parks),
Multiscale Modeling and Simulation, Volume 7, pp. 362-380, 2008,
DOI:10.1137/070682848.
Convergence of Peridynamics to Classical Elasticity Theory,
(with Stewart Silling), Journal of Elasticity,
Volume 93, pp. 13-37, 2008,
DOI:10.1007/s10659-008-9163-3.
Dynamical Systems and Non-hermitian Iterative Eigensolvers
(with Mark Embree),
SIAM Journal on Numerical Analysis, Volume 47, pp. 1445-1473, 2009,
DOI:10.1137/07070187X.
Pseudo-transient continuation for nonlinear transient elasticity
(with Michael Gee and
Tim Kelley),
International Journal for Numerical Methods in Engineering,
Volume 78, pp. 1209-1219, 2009,
DOI:10.1002/nme.2527.
Preconditioning Constrained Eigenvalue Problems
(with Chris Baker), Linear Algebra Applications, Volume 431, pp. 396-408, 2009,
special Issue in honor of Henk van der Vorst,
DOI:10.1016/j.laa.2009.02.018.
Special finite element methods based on component mode synthesis techniques
(with Ulrich Hetmaniuk),
ESAIM: Mathematical Modelling and Numerical Analysis, Volume 44, pp. 401-420, 2010,
DOI:10.1051/m2an/2010007
A nonlocal vector calculus with application to nonlocal boundary value problems
(with Max Gunzburger),
Multiscale Modeling & Simulation, Volume 8, pp. 1581-1598, 2010,
DOI:10.1137/090766607.
Classical, Nonlocal, and Fractional Diffusion Equations on bounded domains
(with Nate Burch),
International Journal for Multiscale Computational Engineering, Volume 9, pp. 661-674, 2011,
DOI:10.1615/IntJMultCompEng.2011002402.
Continuous Time Random Walks on Bounded Domains
(with Nate Burch), Physical Review E, Volume 83, 012105, 2011,
DOI:10.1103/PhysRevE.83.012105.
Energy Principles and Finite Element Methods for Pure Traction Linear Elasticity
(with Pavel Bochev),
Computational Methods in Applied Mathematics, Volume 11, pp. 173-191, 2011,
DOI: 10.2478/cmam-2011-0009.
The statistical mechanical foundation of the peridynamic nonlocal
continuum theory: energy and momentum conservation laws(with Mark Sears),
Physical Review E, Volume 84, 031112, 2011,
DOI:10.1103/PhysRevE.84.031112.
Analysis and approximation of nonlocal diffusion problems with volume constraints
(with Qiang Du,
Max Gunzburger, Kun Zhou),
SIAM review, Volume 54, pp. 667-696, 2012,
DOI:10.1137/110833294.
A new approach for a nonlocal, nonlinear conservation law
(with Qiang Du, James R. Kamm,
Mike Parks),
SIAM J. Appl. Math., Volume 72, pp. 464-487, 2012,
DOI:10.1137/110833233.
Peridynamics: a nonlocal continuum theory
(with Etienne Emmrich and Dimitri Puhst),
Meshfree Methods for Partial Differential Equations VI, Chapter 3,
Lecture Notes in Computational Science and Engineering Volume 89, 2013, pp 45-65.
DOI:10.1007/978-3-642-32979-1_3.
A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws
(with Qiang Du,
Max Gunzburger, Kun Zhou),
Mathematical Models and Methods in Applied Sciences (M3AS), Volume 23, pp. 493-540, 2013,
DOI:10.1142/S0218202512500546.
Analysis of the volume-constrained peridynamic Navier equation of linear elasticity
(with Qiang Du,
Max Gunzburger, Kun Zhou),
Journal of Elasticity, Volume 113, pp. 193-217, 2013,
DOI:10.1007/s10659-012-9418-x.
A Galerkin Radial Basis Function Method for Nonlocal Diffusion
(with S.D. Bond, S.T. Rowe), Chapter 1,
Meshfree Methods for Partial Differential Equations VII, Lecture Notes in Computational Science and Engineering,
Volume 100, 2015, pp. 1-21,
DOI:10.1007/978-3-319-06898-5_1.
Nonlocal convection-diffusion volume-constrained problems and jump processes
(with Qiang Du, Zhan Huang),
Discrete and continuous dynamical systems series B, Volume 19, pp. 373-389, 2014,
DOI:10.3934/dcdsb.2014.19.373.
Integral approximations to classical diffusion and smoothed particle hydrodynamics
(with Qiang Du, Alex Tartakovsky),
Computer Methods in Applied Mechanics and Engineering, Volume 286, pp. 216–229, 2015,
DOI:10.1016/j.cma.2014.12.019.
Computing the exit-time for a symmetric finite-range jump process
(with Nate Burch),
Monte Carlo Methods and Applications, Volume 21, pp 139–152, 2015,
DOI:10.1515/mcma-2014-0015.
The Effect of the Ill-posed Problem on Quantitative Error Assessment in Digital Image Correlation,
(with Phil Reu,
Dan Turner),
Experimental Mechanics, pp 1-13,
DOI:10.1007/s11340-017-0360-5.
A Meshless Galerkin Method for Non-local Diffusion using Localized Kernel Bases,
(with
F.J. Narcowich,
S.T. Rowe,
J.D. Ward,)
Mathematics of Computation, Volume 87, pp 2233-2258, 2018,
DOI:10.1090/mcom/3294.
Articles in Proceedings
Massively parallel linear stability analysis with P_ARPACK for 3D fluid
flow modeled with MPSalsa, (with Andy Salinger), Applied Parallel Computing,
4th International Workshop, PARA'98, B. Kågström,
J. Dongarra, E. Elmroth and J. Wasniewski (editors),
Lecture Notes in Computer Science, No. 1541, pp. 286-295, 1998, Springer-Verlag, Berlin.
Multilevel Methods for Eigenspace Computations in Structural Dynamics,
(with Ulrich Hetmaniuk),
in Domain Decomposition Methods in Science and Engineering XVI, Lecture Notes in
Computational Science and Engineering, Olof B. Widlund, David Keyes (editors),
No. 55, pp. 103-114, 2007, Springer-Verlag, Berlin.
A Nonlocal Strain Measure for DIC,
(with Phil Reu,
Dan Turner),
Chapter 10, pp 79-83, in
Advancement of Optical Methods in Experimental Mechanics, Volume 3,
Proceedings of the 2015 Annual Conference on Experimental and Applied Mechanics, Jin, H., Yoshida, S., Lamberti, L., Lin, M.-T. (Eds.)
DOI:10.1007/978-3-319-22446-6.
Edited Volumes
Volume 7 (1998) special issue of ETNA
on large-scale eigenvalue problems.
Volume 22 (2006) special issue of ETNA
on Saddle Point Problems: Numerical Solution and Applications.
Compatible Spatial Discretizations, Series: The IMA Volumes in Mathematics and its Applications,
Vol. 142 Arnold, D.N.; Bochev, P.B.; Lehoucq, R.B.; Nicolaides, R.A.; Shashkov, M. (Eds.)
An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices,
(with J.
A. Scott) Preprint MCS-P547-1195, Argonne National Laboratory.
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