Papers and Reports

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 synopsis of citations to my publications.

Complex Fracture Nucleation and Evolution with Nonlocal Elastodynamics, (with R.P. Lipton, P.K. Jha,) Journal of Peridynamics and Nonlocal Modeling, Volume 1, pp 122-130, 2019, DOI: 10.1007/s42102-019-00010-0.
Parameter covariance and non-uniqueness in material model calibration using the Virtual Fields Method (with E.M.C. Jones, J.D. Carroll, K.N. Karlson, S.L.B. Kramer, R.B. Lehoucq, P.L. Reu, Dan Turner) Computational Materials Science, Volume 152, September 2018, Pages 268-290 DOI:10.1016/j.commatsci.2018.05.037
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.
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.
Nonlocal Convection-Diffusion Problems on Bounded Domains and Finite-Range Jump Processes, (with Marta D’Elia, Qiang Du, Max Gunzburger), Comput. Methods Appl. Math. 2017; DOI:10.1515/cmam-2017-0029.
A Radial Basis Function Galerkin Method for Inhomogeneous Nonlocal Diffusion (with S.T. Rowe), Computer Methods in Applied Mechanics and Engineering, Volume 299, pp 366-380, 2016, DOI:10.1016/j.cma.2015.10.021.
A Novel Class of Strain Measures for Digital Image Correlation, (with Phil Reu, Dan Turner), Strain, Volume 51, pp. 265–275, 2015, DOI:10.1111/str.12138. Published version is a revision of A Nonlocal Strain Measure for Digital Image Correlation Sandia National Laboratories, Technical report.
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.
Fractional diffusion on bounded domains (with Ozlem Defterli, Marta D’Elia), Qiang Du, Max Gunzburger, Mark M. Meerschaert), Fractional Calculus and Applied Analysis, Volume 18, pp. 342-360, 2015, DOI:10.1515/fca-2015-0023.

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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.
The exit-time problem for a Markov jump process (with Nathanial Burch and Marta D’Elia, Eur. Phys. J. Special Topics, Volume 223, pp. 3257–3271, 2014, DOI:10.1140/epjst/e2014-02331-7.
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.
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.
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 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.
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 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.
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.
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.
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.
Continuous Time Random Walks on Bounded Domains (with Nate Burch), Physical Review E, Volume 83, 012105, 2011, DOI:10.1103/PhysRevE.83.012105.
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.
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.
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.
Translation of Walter Noll’s “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.
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
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
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.
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.
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.
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.
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.
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.
On Atomistic-To-Continuum Coupling by Blending, (with Santiago Badia, Pavel Bochev, Jacob Fish, Max Gunzburger, Multiscale Modeling and Simulation, Volume 7, pp. 381-406, 2008, DOI:10.1137/07069969X
Connecting Atomistic-to-Continuum Coupling and Domain Decomposition, (with Pavel Bochev, Multiscale Modeling and Simulation, Volume 7, pp. 362-380, 2008, DOI:10.1137/070682848.
A Force-Based Blending Model for Atomistic-to-Continuum Coupling, (with Santiago Badia, Pavel Bochev, Jacob Fish, Max Gunzburger, M. Nuggehally, International Journal for Multiscale Computational Engineering, Volume 5, pp. 387-406, 2007, DOI:10.1615/IntJMultCompEng.v5.i5.30.
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.
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.
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.
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.
Regularization and stabilization of discrete saddle-point variational problems, (with Pavel Bochev), ETNA, Volume 22, pp. 97-113, 2006.
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.
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.
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.
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.
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.
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.
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.
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, DOI:10.1108/09615530410544328.
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.
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.
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.
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.
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.
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.
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.
The Computation of Elementary Unitary Matrices, ACM Transactions on Mathematical Software, Volume 22, pp. 393-400, 1996, DOI:10.1145/235815.235817.
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.

Articles in Proceedings

Solving a steady-state PDE using spiking networks and neuromorphic hardware (with J. D. Smith and W. Severa and A. J. Hill and L. Reeder and B. Franke and O. Parekh, and J. B. Aimone) ICONS 2020: International Conference on Neuromorphic Systems 2020 July 2020 Article No.: 27 Pages 1–8, DOI:10.1145/3407197.3407202
Spiking Neural Algorithms for Markov Process Random Walk (with W. Severa, O. Parekh, and J. B. Aimone) 2018 International Joint Conference on Neural Networks (IJCNN), Rio de Janeiro, 2018, pp. 1-8, DOI:10.1109/IJCNN.2018.8489628.
Combining Full-Field Measurements and Inverse Techniques for Smart Material Testing, (with E. M. C. Jones, J. D. Carroll, K. N. Karlson, S. L. B. Kramer, P. L. Reu, Dan Turner), International Digital Imaging Correlation Society. Conference Proceedings of the Society for Experimental Mechanics Series (2017) DOI:10.1007/978-3-319-51439-0_9.
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.
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.
Bridging Methods for Coupling Atomistic and Continuum Models, (with Santiago Badia, Pavel B. Bochev, Max Gunzburger) 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
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.
On Stabilized Finite Element Methods for Transient Problems with Varying Time Scales, (with Pavel Bochev and Max Gunzburger), Proceedings of the ECCOMAS 2004 Congress.
Regularized Formulations of FETI, (with Pavel Bochev), Proceedings of the 14th International Conference on Domain Decomposition Methods in Cocoyoc, Mexico.
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.

Edited Volumes

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

Supervised thesis

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

Technical Reports

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
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 SAND2014-16610.
Complex fracture nucleation and evolution with nonlocal elastodynamics (with Rob Lipton, Stewart Silling), Sandia National Laboratories, Technical report.
A Mixed Finite Element Method for Constraining and Regularizing the Optical Flow Constraint (with Dan Turner), Sandia National Laboratories, Technical report.
A Deterministic Hitting-Time Moment Approach to Seed-set Expansion over a Graph (with Alexander H. Foss, W. Zachary Stuart, J. Derek Tucker, Jonathan W. Berry), Sandia National Laboratories, Technical report.
Zero-Truncated Poisson Regression for Zero-Inflated Multiway Count Data (with Oscar López, Daniel M. Dunlavy) Sandia National Laboratories Technical report SAND2022-0803R
Sensitivity Analysis for Monte Carlo Sampling-Based Particle Simulations (with Stephen Bond, Brian Franke, Scott McKinley, J. Darby Smith), Sandia National Laboratories Technical report SAND2022-12721.
Entropy and its Relationship with Statistics (with Carolyn Mayer and Derek Tucker), Sandia National Laboratories Technical report SAND2022-15094.