Rich Lehoucq's papers and reports (updated 08/26/2014)

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.
  1. 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.
  2. The Computation of Elementary Unitary Matrices, ACM Transactions on Mathematical Software, Volume 22, pp. 393-400, 1996, DOI:10.1145/235815.235817.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Linear stability of flow in a differentially heated cavity via large-scale eigenvalue calculations, (with E.A. Burroughs, L.A. Romero, and A.J. Salinger), International Journal of Numerical Methods For Heat & Fluid Flow, Volume 14, Issue 6, pp. 803-822, 2004.
  11. 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.
  12. 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.
  13. 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.
  14. An Overview of the Trilinos Project, (with Michael A. Heroux and Roscoe A. Bartlett and Vicki 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.
  15. 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.
  16. 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.
  17. 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.
  18. Regularization and stabilization of discrete saddle-point variational problems, (with Pavel Bochev), ETNA, Volume 22, pp. 97-113, 2006.
  19. Basis selection in LOBPCG, (with Ulrich Hetmaniuk), Journal of Computational Physics, Volume 218, pp. 324-332, 2006, DOI:10.1016/j.jcp.2006.02.007.
  20. 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.
  21. 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.
  22. 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.
  23. A Force-Based Blending Model for Atomistic-to-Continuum Coupling, (with Santiago Badia, Pavel Bochev, Jacob Fish, Max Gunzburger, M. Nuggehally, Mike Parks), International Journal for Multiscale Computational Engineering, Volume 5, pp. 387-406, 2007, DOI:10.1615/IntJMultCompEng.v5.i5.30.
  24. 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.
  25. On Atomistic-To-Continuum Coupling by Blending, (with Santiago Badia, Pavel Bochev, Jacob Fish, Max Gunzburger, Mike Parks) Multiscale Modeling and Simulation, Volume 7, pp. 381-406, 2008, DOI:10.1137/07069969X
  26. 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.
  27. Implementing peridynamics within a molecular dynamics code (with Mike Parks, Steve Plimpton, Stewart Silling), Computer Physics Communication, Volume 179, pp. 777-783, 2008, DOI:10.1016/j.cpc.2008.06.011.
  28. Anasazi software for the numerical solution of large-scale eigenvalue problems, (with Chris Baker, Ulrich Hetmaniuk, Heidi Thornquist), ACM Transactions on Mathematical Software, Volume 36, Article No. 13, 2009, DOI:10.1145/1527286.1527287.
  29. 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.
  30. 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.
  31. 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.
  32. Peridynamics as an Upscaling of Molecular Dynamics (with Pablo Seleson, Max Gunzburger, Mike Parks), Multiscale Modeling and Simulation, Volume 8, pp. 204-227, 2009, DOI:10.1137/09074807X
  33. 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
  34. Translation of Walter Nollís ``Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics'' (with Anatole Von Lilienfeld-Toal), Journal of Elasticity, Volume 100, pp. 5-24, 2010, DOI:10.1007/s10659-010-9246-9. Walter Noll's (original) paper is available at Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der Statistischen Mechanik.
  35. Peridynamic Theory of Solid Mechanics (with Stewart Silling), Advances in Applied Mechanics, Volume 44, pp, 73-168, 2010, DOI:10.1016/S0065-2156(10)44002-8. Also available as Sandia National Labs Technical report SAND 2010-1233J.
  36. 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.
  37. 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.
  38. Continuous Time Random Walks on Bounded Domains (with Nate Burch), Physical Review E, Volume 83, 012105, 2011, DOI:10.1103/PhysRevE.83.012105.
  39. 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.
  40. 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.
  41. 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.
  42. 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.
  43. 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.
  44. 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.
  45. 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.

Articles in Proceedings

  1. 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.
  2. Regularized Formulations of FETI, (with Pavel Bochev), Proceedings of the 14th International Conference on Domain Decomposition Methods in Cocoyoc, Mexico.
  3. On Stabilized Finite Element Methods for Transient Problems with Varying Time Scales, (with Pavel Bochev and Max Gunzburger), Proceedings of the ECCOMAS 2004 Congress.
  4. 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.
  5. Bridging Methods for Coupling Atomistic and Continuum Models, (with Santiago Badia, Pavel B. Bochev, Max Gunzburger, Richard B. Lehoucq, Michael L. Parks) in Large-Scale Scientific Computing 6th International Conference, Sozopol, Bulgaria, June 5-9, 2007, I. Lirkov, S. Margenov, and J. Wasniewski, eds., vol. 4818, pp. 16-27 of Lecture Notes in Computer Science
  6. Peridynamics for multiscale materials modeling, (with Abe Askari, Florian Bobaru, Mike Parks, Stewart Silling, Olaf Weckner), J. Phys.: Conf. Ser. 125 012078, DOI:10.1088/1742-6596/125/1/012078.
  7. Peridynamics: a nonlocal continuum theory (with Etienne Emmrich and Dimitri Puhst), Meshfree Methods for Partial Differential Equations VI, Lecture Notes in Computational Science and Engineering Volume 89, 2013, pp 45-65. DOI:10.1007/978-3-642-32979-1_3.

Edited Volumes

  1. Volume 7 (1998) special issue of ETNA on large-scale eigenvalue problems.
  2. Volume 22 (2006) special issue of ETNA on Saddle Point Problems: Numerical Solution and Applications.
  3. 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.)

Supervised thesis

  1. Exponential Integrators for the Incompressible Navier-Stokes Equations, by Chris Newman. Also available as Sandia National Laboratories, Technical report SAND 2004-3742.

Technical Reports

  1. Integral approximations to classical diffusion and smoothed particle hydrodynamics (with Qiang Du, Alex Tartakovsky ), Sandia National Laboratories, Technical report SAND 2014-17136J.
  2. Fractional diffusion on bounded domains (with Ozlem Defterli, Marta D'Elia, Qiang Du, Max Gunzburger, Mark M. Meerschaert ), Sandia National Laboratories, Technical report SAND 2014-17064J.
  3. Installing the Anasazi Eigensolver Package with Application to Some Graph Eigenvalue Problems (with Erik G. Boman, Karen D. Devine, Nicole L. Slattengren, Heidi Thornquist ), Sandia National Laboratories, Technical report SAND 2014-16610.
  4. The exit-time problem for a Markov jump process (with Nathanial Burch and Marta D'Elia), Sandia National Laboratories, Technical report SAND 2014-16434J.
  5. Finite range jump processes and volume-constrained diffusion problems (with Marta D'Elia, Qiang Du, Max Gunzburger), Sandia National Laboratories, Technical report SAND 2014-2584J.
  6. Computing the exit-time for a symmetric finite-range jump process (with Nate Burch), Sandia National Laboratories, Technical report SAND 2013-2354J.
  7. An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices, (with J. A. Scott) Preprint MCS-P547-1195, Argonne National Laboratory. Get the Postscript Version

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