Publications

Journal Articles

Nicole E. Buczkowski, Mikil D. Foss, Michael L. Parks, and Petronela Radu, Sensitivity analysis for solutions to heterogeneous nonlocal systems: Theoretical and numerical studies, Journal of Peridynamics and Nonlocal Modeling, 2022.

Matthias Bolten, Eric de Sturler, Camilla Hahn, and Michael L. Parks, Krylov Subspace Recycling for Evolving Structures, Computer Methods in Applied Mechanics and Engineering, 114222, 2022.

Guofei Pang, Marta D’Elia, Michael L. Parks, George E. Karniadakis, nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and ApplicationsJournal of Computational Physics, 422, 109760, 2020.

Nathaniel Trask, Huaiqian You, Yue Yu, and Michael Parks, An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamicsComputer Methods in Applied Mechanics and Engineering, 343, pp. 151-165, 2019.

Yue Yu, Fabiano F. Bargos, Huaiqian You, Michael L. Parks, Marco L. Bittencourt, and George E. Karniadakis, A partitioned coupling framework for peridynamics and classical theory: Analysis and simulationsComputer Methods in Applied Mechanics and Engineering, 340, pp. 905-931, 2018.

Stewart A. Silling, Michael L. Parks, James R. Kamm, Olaf Weckner, and Mostafa Rassaian, Modeling shockwaves and impact phenomena with Eulerian peridynamicsInternational Journal of Impact Engineering, 107, pp. 47-57, 2017.

Rohan Panchadhara, Peter A. Gordon, and Michael L. Parks, Modeling propellant-based stimulation of a borehole with peridynamicsInternational Journal of Rock Mechanics and Mining Sciences, 93, pp. 330-343, 2017.

Wenxiao Pan, Kyungjoo Kim, Mauro Perego, Alexandre M. Tartakovsky, and Michael L. Parks, Modeling Electrokinetic Flows by Consistent Implicit Incompressible Smoothed Particle HydrodynamicsJournal of Computational Physics, 334, pp. 125-144, 2017.

Pablo Seleson, Qiang Du, and Michael L. Parks, On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity modelsComputer Methods in Applied Mechanics and Engineering, 311, pp. 698-722, 2016.

Payton Lindsay, Michael L. Parks, and Arun Prakash, Enabling fast, stable and accurate peridynamic computations using multi-time-step integrationComputer Methods in Applied Mechanics and Engineering, 306, pp. 382-405, 2016.

Daniel Turner, Bart van Bloemen Waanders and Michael L. Parks, Inverse problems in heterogeneous and fractured media using peridynamicsJournal of Mechanics of Materials and Structures, 10(5), pp. 573-590, 2015.

Xiaofan Yang, Yashar Mehmani, William A. Perkins, Andrea Pasquali, Martin Schönherr, Kyungjoo Kim, Mauro Perego, Michael L. Parks, Nathaniel Trask, Matthew T. Balhoff, Marshall C. Richmond, Martin Geier, Manfred Krafczyk, Li-Shi Luo, Alexandre M. Tartakovsky, and Timothy D. Scheibe, Intercomparison of 3D Pore-scale Flow and Solute Transport Simulation MethodsAdvances in Water Resources, 95, pp. 176–189, 2016.

Nathaniel Trask, Martin Maxey, Kyungjoo Kim, Mauro Perego, Michael L. Parks, Kai Yang, and Jinchao Xu, A scalable consistent second-order SPH solver for unsteady low Reynolds number flowsComputer Methods in Applied Mechanics and Engineering, 289, pp. 155-178, 2015.

Amalie L. Frischknecht, Deaglan O. Halligan, and Michael L. Parks, Electrical double layers and differential capacitance in molten salts from density functional theoryThe Journal of Chemical Physics, 141(5), 054708, 2014.

Pablo Seleson, Michael L. Parks, and Max Gunzburger, Peridynamic state-based models and the embedded-atom model, Communications in Computational Physics, 15(1), pp. 179-205, 2014.

Pablo Seleson, Max Gunzburger, and Michael L. Parks, Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domainsComputer Methods in Applied Mechanics and Engineering, 266, pp. 185-204, 2013.

Laura J. Douglas Frink, Amalie L. Frischknecht, Michael A. Heroux, Michael L. Parks, and Andrew G Salinger, Towards Quantitative Coarse-Grained Models of Lipids with Fluids Density Functional TheoryJournal of Chemical Theory and Computation, 8(4), pp. 1393-1408, 2012.

Qiang Du, James R. Kamm, Richard B. Lehoucq, and Michael L. Parks, A New Approach for a Nonlocal, Nonlinear Conservation Law, SIAM Journal on Applied Mathematics, 72(1), pp. 464-487, 2012.

Pablo Seleson and Michael L. Parks, On the Role of the Influence Function in the Peridynamic Theory, International Journal for Multiscale Computational Engineering, 9(6), pp. 689-706, 2011.

Burak Aksoylu and Michael L. Parks, Variational Theory and Domain Decomposition for Nonlocal Problems, Applied Mathematics and Computation, 217, pp. 6498-6515, 2011.

Pablo Seleson, Michael L. Parks, Max Gunzburger, and Richard B. Lehoucq, Peridynamics as an Upscaling of Molecular DynamicsMultiscale Modeling and Simulation, 8(1), pp. 204-227, 2009.

Michael L. Parks, Richard B. Lehoucq, Steven J. Plimpton, and Stewart A. Silling, Implementing Peridynamics within a Molecular Dynamics CodeComputer Physics Communications, 179(11), pp. 777-783, 2008.

Gregory J. Wagner, Reese E. Jones, Jeremy A. Templeton, and Michael L. Parks, An Atomistic-to-Continuum Coupling Method for Heat Transfer in SolidsComputer Methods in Applied Mechanics and Engineering, 197, pp. 3351-3365, 2008.

Michael L. Parks, Pavel B. Bochev, and Richard B. Lehoucq, Connecting Atomistic-to-Continuum Coupling and Domain DecompositionMultiscale Modeling and Simulation, 7, pp. 362-380, 2008.

Santiago Badia, Michael L. Parks, Pavel B. Bochev, Max Gunzburger, and Richard B. Lehoucq, On Atomistic-to-Continuum Coupling by BlendingMultiscale Modeling and Simulation, 7, pp. 381-406, 2008.

Santiago Badia, Pavel. B. Bochev, Jacob Fish, Max D. Gunzburger, Richard B. Lehoucq, Mohan. A. Nuggehally, Michael. L. Parks, A Force-Based Blending Model for Atomistic-to-Continuum CouplingInternational Journal for Multiscale Computational Engineering, 5, pp. 387-406, 2007.

Jacob Fish, Mohan A. Nuggehally, Mark S. Shephard, Catalin R. Picu, Santiago Badia, Michael L. Parks, and Max Gunzburger, Concurrent AtC coupling based on a blend of the continuum stress and the atomistic forceComputer Methods in Applied Mechanics and Engineering, 196, pp. 4548-4560, 2007.

Michael L. Parks, Louis A. Romero, and Pavel B. Bochev, A Novel Lagrange-Multiplier Based Method for Consistent Mesh TyingComputer Methods in Applied Mechanics and Engineering, 196, pp. 3335-3347, 2007.

Michael L. Parks, Louis A. Romero, Taylor-Aris Dispersion in High Aspect Ratio Columns of Nearly Rectangular Cross-SectionMathematical and Computer Modelling, 46, pp. 699-717, 2007.

Michael L. Parks, Eric de Sturler, Greg Mackey, Duane Johnson, and Spandan Maiti, Recycling Krylov Subspaces for Sequences of Linear SystemsSIAM Journal on Scientific Computing, 28(5), pp. 1651-1674, 2006. Also available as University of Illinois Department of Computer Science Technical Report UIUCDCS-R-2004-2421.

Conference Proceedings Articles

Santiago Badia, Pavel B. Bochev, Max Gunzburger, Richard B. Lehoucq, Michael L. Parks, Bridging Methods for Coupling Atomistic and Continuum Models, in Large-Scale Scientific Computing 6th International Conference, Sozopol, Bulgaria, June 5-9, 2007, I. Lirkov, S. Margenov, and J. Wasniewski, eds., vol. 4818 of Lecture Notes in Computer Science, pp. 16-27, 2009.

E. Askari, Florin Bobaru, Richard B. Lehoucq, Michael L. Parks, Stewart A. Silling, and Olaf Weckner, Peridynamics for multiscale materials modeling, in SciDAC 2008, Seattle, Washington, July 13-17, 2008, vol. 125 of Journal of Physics: Conference Series, (012078) 2008.

Book Chapters

Pablo Seleson and Michael Parks, Links to Atomistic Modeling, in Handbook of Peridynamic Modeling, ed. by F. Bobaru, J.T. Foster, P. Geubelle, and S.A. Silling, CRC Press, 2016.

Pavel Bochev, Richard Lehoucq, Michael Parks, Santiago Badia, and Max Gunzburger, Blending methods for coupling atomistic and continuum models, in Multiscale Methods: Bridging the Scales in Science and Engineering, ed. by Jacob Fish, Oxford University Press, pp. 165-191, 2009.

Technical Reports

N.E. Buczkowski, M.D. Foss, M.L. Parks, J. Trageser, and P. Radu, Two Nonlocal Biharmonic Operators, in Computer Science Research Institute Summer Proceedings 2021, J.D. Smith and E.Galvan, eds., Technical Report SAND2022-0653R, Sandia National Laboratories, 2021, pp. 3-15.

N.E. Buczkowski, M. D’Elia and M.L. Parks, Nonlocal Physics-Informed Neural Networks, in Computer Science Research Institute Summer Proceedings 2019, M. Powell and M.L. Parks, eds., Technical Report SAND2020-9969R, Sandia National Laboratories, 2020, pp. 29-40.

David J. Littlewood, Stewart A. Silling, John A. Mitchell, Pablo D. Seleson, Stephen D. Bond, Michael L. Parks, Daniel Z. Turner, Damon J. Burnett, Jakob Ostien, and Max Gunzburger, Strong Local-Nonlocal Coupling for Integrated Fracture Modeling, Technical Report SAND2015-7998, Sandia National Laboratories, September 2015.

P.E Lindsay and M.L. Parks, A Multi-Timestepping Extension to the Peridynamic Theory, in CSRI
Summer Proceedings 2014
, D.P. Kouri and M.L. Parks, eds., Sandia National Laboratories, 2014, pp.
15-25. Available as Sandia National Laboratories Technical Report SAND2015-3829O.

Michael L. Parks, David J. Littlewood, John A. Mitchell, and Stewart A. Silling, Peridigm Users’ Guide v1. 0.0, Technical Report SAND2012-7800, Sandia National Laboratories, Sept. 2012.

K. Ahuja, M. L. Parks, E. T. Phipps, A. G. Salinger, and E. de Sturler, Krylov Recycling for Climate Modeling and Uncertainty Quantification, in CSRI Summer Proceedings 2010, E. C. Cyr and S. S. Collis, eds., Sandia National Laboratories, 2010, pp. 103-111. Available as Sandia National Laboratories Technical Report SAND2010-8783P.

Michael L. Parks, Pablo Seleson, Steven J. Plimpton, Richard B. Lehoucq, and Stewart A. Silling, Peridynamics with LAMMPS: A User Guide, Technical Report SAND2010-5549, Sandia National Laboratories, August 2010.

Pablo Seleson, Michael L. Parks, and Max Gunzburger, Peridynamics as an upscaling of Molecular Dynamics, in CSRI Summer Proceedings [PDF], D. Ridzal and S. S. Collis, eds., Sandia National Laboratories, 2008, pp. 177-184. Available as Sandia National Laboratories Technical Report SAND2008-8257P.

Pavel B. Bochev, S. Scott Collis, Reese E. Jones, Richard B. Lehoucq, Michael L. Parks, Guglielmo Scovazzi, Stewart A. Silling, Jeremy A. Templeton, and Gregory J. Wagner, A Mathematical Framework for Multiscale Science and Engineering: the Variational Multiscale Method and Interscale Transfer Operators, Technical Report SAND2007-0905, Sandia National Laboratories, October 2007.

Santiago Badia, Pavel Bochev, Max Gunzburger, Richard Lehoucq, Michael L. Parks, Blended Atomistic-to-Continuum coupling analyses and methods, Technical Report SAND2007-0905, Sandia National Laboratories, February 2007.

E. B. Vanderzee, M. L. Parks, and P. Knupp, Numerical experiments for local quasicontinuum analysis, in NECIS Summer Proceedings, S. S. Collis, J. Lee, and J. Zimmerman, eds., Sandia National Laboratories, 2006, pp. 194-202. Available as Sandia National Laboratories Technical Report SAND2006-6564.

Michael L. Parks, Louis A. Romero, and Joshua Whiting, A Reduced Order Model for the Study of Asymmetries in Linear Gas Chromatography for Homogeneous Tubular Columns, Technical Report SAND2005-4868, Sandia National Laboratories, August 2005.

Michael L. Parks, The Iterative Solution of a Sequence of Linear Systems Arising from Nonlinear Finite Element Analysis, Ph.D. Dissertation, University of Illinois at Urbana-Champaign, 2005. Available as University of Illinois Technical Report UIUCDCS-R-2005-2497.

Michael L. Parks, Efficient Numeric Computation of a Phase Diagram in Biased Diffusion of Two Species, Master’s Thesis, Virginia Polytechnic Institute and State University (Virginia Tech), 2000. Available as Virginia Tech Electronic Thesis etd-05172000-14430029.

Proceedings Edited

Ahmad A. Rushdi and Michael L. Parks, editors, Computer Science Research Institute Summer Proceedings 2020, The Computer Science Research Institute at Sandia National Laboratories, Albuquerque, NM, 2020. Available as Sandia National Laboratories Technical Report SAND2020-12580R.

Michael Powell and Michael L. Parks, editors, Center for Computing Research Summer Proceedings 2019, The Computer Science Research Institute at Sandia National Laboratories, Albuquerque, NM, 2019. Available as Sandia National Laboratories Technical Report SAND2020-9969R.

Attila Cangi and Michael L. Parks, editors, Center for Computing Research Summer Proceedings 2018, The Center for Computing Research at Sandia National Laboratories, Albuquerque, NM, 2018. Available as Sandia National Laboratories Technical Report SAND2019-5093R.

Andrew D. Baczewski and Michael L. Parks, editors, Center for Computing Research Summer Proceedings 2017, The Center for Computing Research at Sandia National Laboratories, Albuquerque, NM, 2017. Available as Sandia National Laboratories Technical Report SAND2018-2780O.

James B. Carleton and Michael L. Parks, editors, Center for Computing Research Summer Proceedings 2016, The Center for Computing Research at Sandia National Laboratories, Albuquerque, NM, 2016. Available as Sandia National Laboratories Technical Report SAND2017-1294R.

Andrew M. Bradley and Michael L. Parks, editors, Center for Computing Research Summer Proceedings 2015, The Center for Computing Research at Sandia National Laboratories, Albuquerque, NM, 2015. Available as Sandia National Laboratories Technical Report SAND2016-0830R.

Drew P. Kouri and Michael L. Parks, editors, Center for Computing Research Summer Proceedings 2014, The Center for Computing Research at Sandia National Laboratories, Albuquerque, NM, 2014. Available as Sandia National Laboratories Technical Report SAND2015-3829O.

Sivasankaran Rajamanickam, Michael L. Parks, and S. Scott Collis, editors, CSRI Summer Proceedings 2013, The Computer Science Research Institute at Sandia National Laboratories, Albuquerque, NM, 2007 Available as Sandia National Laboratories Technical Report SAND2014-20409R.

Michael L. Parks and S. Scott Collis, editors, CSRI Summer Proceedings 2007, The Computer Science Research Institute at Sandia National Laboratories, Albuquerque, NM, 2007 Available as Sandia National Laboratories Technical Report SAND2007-7977.

Other

Michael L. Parks, Richard B. Lehoucq, Researchers Discuss Atomistic-to-Continuum (AtC) Coupling, SIAM News, Vol. 39, No. 7 (September 2006).