Michael L. Parks

Computational Mathematics

Author profile picture

Computational Mathematics

mlparks@sandia.gov

(505) 845-0512

Sandia National Laboratories, New Mexico
P.O. Box 5800
Albuquerque, NM 87185-1320

Biography

My current research interests include computational mathematics, numerical linear algebra, linear solvers, multiscale modeling, and peridynamics.

Please see my professional webpage for more information.

Professional Experience

2014-PresentManager, Computational Mathematics Dept.
2013-2014Acting Manager, Computational Mathematics Dept.
2013-2014Principal Member of the Technical Staff
2007-2013Senior Member of the Technical Staff
2004-2007Postdoctoral Employee

Education

2005Ph.D., Computer Science, University of Illinois at Urbana-Champaign
2000M.S., Computer Science, Virginia Polytechnic Institute and State University (Virginia Tech)
1998B.S., Computer Science, Virginia Polytechnic Institute and State University (Virginia Tech)
1998B.S., Physics, Virginia Polytechnic Institute and State University (Virginia Tech)

Publications

Michael L. Parks, Petronela Radu, (2022). On Neumann-type Boundary Conditions for Nonlocal Models 9th U.S. National Congress on Theoretical and Applied Mechanics Document ID: 1551632

Michael L. Parks, (2022). Research and Opportunities in the Mathematical Sciences at Sandia National Laboratories Joint Mathematics Meetings (JMM 2022) Document ID: 1504704

Matthias Bolten, Eric de Sturler, Camilla Hahn, Michael L. Parks, (2021). Krylov Subspace Recycling for Evolving Structures Computer Methods in Applied Mechanics and Engineering Document ID: 1381013

Michael L. Parks, (2021). On Neumann-type Boundary Conditions for Nonlocal Models Mechanistic Machine Learning and Digital Twins for Computational Science, Engineering & Technology Document ID: 1368368

Guofei Pang, Marta D’Elia, Michael L. Parks, George E. Karniadakis, (2021). nPINNS: Nonlocal Physics-Informed Neural Networks 16th U.S. National Congress on Computational Mechanics Document ID: 1342921

Michael L. Parks, (2021). Computational Aspects of Nonlocal Models Center for Nonlinear Analysis, Department of Mathematical Sciences, Carnegie Mellon University Document ID: 1294036

Goufei Pang, Michael L. Parks, Marta D’Elia, George Karniadakis, (2021). nPINNS: Nonlocal Physics-Informed Neural Networks SIAM Conference on Computational Science and Engineering (CSE21) https://www.osti.gov/search/identifier:1847466 Document ID: 1279756

Goufei Pang, Marta D’Elia, Michael L. Parks, George Karniadakis, (2021). nPINNs: nonlocal Physics-Informed Neural Networks One Nonlocal World https://www.osti.gov/search/identifier:1841537 Document ID: 1256224

Michael L. Parks, Michael Powell, (2020). Summer Proceedings 2019 https://www.osti.gov/search/identifier:1665933 Document ID: 1196372

Marta D’Elia, Michael L. Parks, Guofei Pang, George Karniadakis, (2020). nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications https://www.osti.gov/search/identifier:1614899 Document ID: 1115647

Marta D’Elia, Michael L. Parks, Guofei Pang, George Karniadakis, (2020). Nonlocal Physics-Informed Neural Networks: A unified theoretical and computational framework for nonlocal models AAAI-MLPS 2020 (held virtually) https://www.osti.gov/search/identifier:1772713 Document ID: 1114875

Michael L. Parks, (2020). Nonlocal Models and Peridynamics Computational Math Seminar https://www.osti.gov/search/identifier:1770834 Document ID: 1104219

Bart G van Bloemen Waanders, David John Littlewood, Daniel Z. Turner, Michael L. Parks, (2020). Peridynamics to Predict Fracturing in the Subsurface American Geophysical Union Fall Meeting https://www.osti.gov/search/identifier:1767099 Document ID: 1067271

Marta D’Elia, Michael L. Parks, Guofei Pang, George Karniadakis, (2020). nPINNs: nonlocal Physics-Informed Neural Networks Coda2020 https://www.osti.gov/search/identifier:1767113 Document ID: 1092743

Marta D’Elia, Michael L. Parks, Guofei Pang, George Karniadakis, (2019). Nonlocal Physics-Informed Neural Networks ? A unified theoretical and computational framework for nonlocal models Aaai-mlps 2020 Document ID: 1056057

Marta D’Elia, Michael L. Parks, Nicole Buczkowski, (2019). Nonlocal Physics Informed Neural Networks SIAM Central States Section Meeting https://www.osti.gov/search/identifier:1642837 Document ID: 1033470

Michael L. Parks, Petronela Radu, (2019). On Neumann-type Boundary Conditions for Nonlocal Models International Congress on Industrial and Applied Mathematics https://www.osti.gov/search/identifier:1640998 Document ID: 984543

Attila Cangi, Michael L. Parks, (2019). Summer Proceedings 2018, The Center for Computing Research at Sandia National Laboratories https://www.osti.gov/search/identifier:1762384 Document ID: 960229

Michael L. Parks, Petronela Radu, (2019). On Neumann-type Boundary Conditions for Nonlocal Models 9th International Congress on Industrial and Applied Mathematics (ICIAM) Document ID: 960465

Michael L. Parks, Dan Turner, Bart van Bloeman Waanders, Rohan Panchadhara, Peter Gordon, (2019). Subsurface Applications for Peridynamics SIAM Conference on Computational Science and Engineering (CSE19) https://www.osti.gov/search/identifier:1601931 Document ID: 925327

Michael L. Parks, (2018). Domain Decomposition Methods: Origins and Applications to Multiscale Modeling University of Nebraska Continuum Mechanics Seminar https://www.osti.gov/search/identifier:1806997 Document ID: 889936

Michael L. Parks, (2018). Solving Real-World Problems with Mathematics and Computing University of Nebraska Math Department Colloquium https://www.osti.gov/search/identifier:1806983 Document ID: 889937

Michael L. Parks, Daniel Z. Turner, Bart G van Bloemen Waanders, Rohan Panchadhara, Peter Gordon, (2018). Subsurface Applications for Peridynamics Workshop on Dynamics, Control and Numerics for Fractional PDEs https://www.osti.gov/search/identifier:1575975 Document ID: 889938

Nathaniel Albert Trask, Huaiqian You, Yue Yu, Michael L. Parks, (2018). An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics Computer Methods in Applied Mechanics and Engineering https://www.osti.gov/search/identifier:1474082 Document ID: 853596

Michael L. Parks, Daniel Z. Turner, Bart G van Bloemen Waanders, Rohan Panchadhara, Peter Gordon, (2018). Subsurface Applications for Peridynamics 6th European Congress on Computational Mechanics https://www.osti.gov/search/identifier:1505286 Document ID: 783712

Kara J. Peterson, Michael L. Parks, Eric Ackerman, Ray Bambha, Diana L Bull, Jennifer M Frederick, Jasper O. E. Hardesty, Anastasia Gennadyevna Ilgen, John Davis Jakeman, Amy Jo Powell, Matthew Gregor Peterson, Erika Louise Roesler, Cosmin Safta, David John Stracuzzi, Irina Kalashnikova Tezaur, (2018). Arctic Tipping Points Triggering Global Change Geoscience External Advisory Board Meeting https://www.osti.gov/search/identifier:1513640 Document ID: 749594

Nathaniel Albert Trask, Huaiqian You, Yue Yu, Michael L. Parks, (2018). A meshfree quadrature rule for nonlocal mechanics Computer Methods in Applied Mechanics and Engineering Document ID: 738213

Nathaniel Albert Trask, Nathaniel Albert Trask, Huaiqian You, Yue Yu, Michael L. Parks, (2017). Asymptotically compatible meshfree discretization MANNAModeling, Analysis and Numerics for Nonlocal Applications https://www.osti.gov/search/identifier:1512052 Document ID: 737879

Michael L. Parks, (2017). PDLAMMPS: Peridynamics in LAMMPS MANNAModeling, Analysis and Numerics for Nonlocal Applications https://www.osti.gov/search/identifier:1484933 Document ID: 727079

Kara J. Peterson, Michael L. Parks, Eric Ackerman, Ray Bambha, Diana L Bull, Jennifer M Frederick, Jasper O. E. Hardesty, Anastasia Gennadyevna Ilgen, John Davis Jakeman, Matthew Gregor Peterson, Amy Jo Powell, Erika Louise Roesler, Cosmin Safta, David John Stracuzzi, Irina Kalashnikova Tezaur, (2017). Arctic Tipping Points Triggering Global Change Geoscience External Review Board Document ID: 726774

Wenxiao (PNNL) Pan, Kyungjoo Kim, Mauro Perego, Alexandre M. (PNNL) Tartakovsky, Michael L. Parks, (2017). Modeling Electrokinetic Flows by Implicit Incompressible Smoothed Particle Hydrodynamics Journal of Computational Physics Document ID: 692773

Michael L. Parks, Payton Lindsay, Michael L. Parks, Arun (Purdue) Prakash, (2017). A Multi-Time-Step Method forPartitioned Time Integration of Peridynamics 14th US National Congress on Computational Mechanics https://www.osti.gov/search/identifier:1506223 Document ID: 637733

Stewart A. Silling, Michael L. Parks, James R. Kamm, Olaf Weckner, Mostafa Rassaian, (2017). Modeling shockwaves and impact phenomena with Eulerian peridynamics International Journal of Impact Engineering https://www.osti.gov/search/identifier:1360921 Document ID: 623998

Michael L. Parks, (2017). Computational and Mathematical Aspects of Nonlocal Models Center for Computational & Applied Mathematics Seminar, Purdue University https://www.osti.gov/search/identifier:1456682 Document ID: 612226

Michael L. Parks, Payton Lindsay, Michael L. Parks, Arun (Purdue) Prakash, (2017). A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics SIAM Conference on Computational Science and Engineering https://www.osti.gov/search/identifier:1425302 Document ID: 589211

James Brian Carleton, Michael L. Parks, (2017). Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories https://www.osti.gov/search/identifier:1343384 Document ID: 565954

Payton Lindsay, Michael L. Parks, Arun (Purdue) Prakash, (2016). A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics USACM Conference on Isogeometric Analysis and Meshfree Methods https://www.osti.gov/search/identifier:1398860 Document ID: 531322

Nathaniel Trask, Martin Maxey, Kyungjoo Kim, Mauro Perego, Michael L. Parks, Kai Yang, Jinchao Xu, Wenxiao Pan, Alex Tartakovsky, (2016). A Massively Parallel Scalable Implicit SPH Solver SIAM Conference on Nonlinear Waves and Coherent Structures https://www.osti.gov/search/identifier:1422175 Document ID: 507507

Pablo Seleson, Qiang Du, Michael L. Parks, (2016). On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models Computer Methods in Applied Mechanics and Engineering https://www.osti.gov/search/identifier:1297917 Document ID: 506999

Pavel B. Bochev, James Cheung, Marta D’Elia, Amalie Frischknecht, Michael L. Parks, Mauro Perego, (2016). Coupling of Multi-fidelity Models: Applications to PNP-cDFT and local-nonlocal Poisson equations CM4 Summer school https://www.osti.gov/search/identifier:1428032 Document ID: 475286

Michael L. Parks, Kirk M. Soodhalter, Daniel M. Szyld, (2016). A Block Recycled GMRES Method with Investigations Into Aspects of Solver Performance SIAM Journal on Scientific Computing Document ID: 431197

Michael L. Parks, (2016). Computational and Mathematical Aspects of Nonlocal Models Dept. of Mathematics Colloquium https://www.osti.gov/search/identifier:1346509 Document ID: 408659

Andrew Michael Bradley, Michael L. Parks, (2016). Center for Computing Research Summer Research Proceedings 2015 https://www.osti.gov/search/identifier:1237005 Document ID: 376196

Michael L. Parks, (2016). Nonlocal Models and Peridynamics Applied Mathematics and Statistics Dept. Colloquium https://www.osti.gov/search/identifier:1342458 Document ID: 397362

Nathaniel Trask, Martin Maxey, Kyungjoo Kim, Mauro Perego, Michael L. Parks, Kai Yang, Wenxiao Pan, Alex Tartakovsky, (2015). A Massively Parallel Scalable Implicit SPH Solver 2016 Joint Mathematics Meetings https://www.osti.gov/search/identifier:1337919 Document ID: 376308

Rohan Panchadhara, Peter Gordon, Michael L. Parks, (2015). Modeling propellant-based stimulation of a borehole with peridynamics International Journal of Rock Mechanics & Mining Sciences https://www.osti.gov/search/identifier:1356219 Document ID: 376121

Payton Lindsay, Michael L. Parks, Arun Parkash, (2015). A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics Workshop on Nonlocal Models in Mathematics, Computation, Science, and Engineering https://www.osti.gov/search/identifier:1334929 Document ID: 342898

Payton Lindsay, Michael L. Parks, Arun Prakash, (2015). Enabling fast, stable and accurate peridynamic computations using multi-time-step integration Computer Methods in Applied Mechanics and Engineering https://www.osti.gov/search/identifier:1263548 Document ID: 320826

David John Littlewood, Stewart A. Silling, John A. Mitchell, Pablo D. (ORNL) Seleson, Stephen D Bond, Michael L. Parks, Daniel Z. Turner, Damon J. Burnett, Jakob Ostien, Max (FSU) Gunzburger, (2015). Strong Local-Nonlocal Coupling for Integrated Fracture Modeling https://www.osti.gov/search/identifier:1221526 Document ID: 321749

Kyungjoo Kim, Nathaniel Trask, Martin Maxey, Mauro Perego, Michael L. Parks, Kai Yang, Jinchao Xu, (2015). Development of Scalable Parallel Implicit SPH using LAMMPS and Trilinos LAMMPS Users’ Workshop and Symposium https://www.osti.gov/search/identifier:1530974 Document ID: 319519

Nathaniel (Brown) Trask, Kyungjoo Kim, Alexadre (PNNL) Tartakovsky, Mauro Perego, Michael L. Parks, (2015). A Highly-Scalable Implicit SPH Code for Simulating Single- and Multi-phase Flows in Geometrically Complex Bounded Domains Supercomputing 2015 https://www.osti.gov/search/identifier:1261589 Document ID: 264514

Michael L. Parks, Payton Lindsay, Arun Prakash, (2015). A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics Pan-American Conference on Computational Mechanics https://www.osti.gov/search/identifier:1249290 Document ID: 264655

Michael L. Parks, Payton Lindsay, Arun (Purdue) Prakash, (2015). A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics Conference on Recent Developments in Continuum Mechanics and PDEs https://www.osti.gov/search/identifier:1248594 Document ID: 254152

Yashar Mehmani, Martin Schoenherr, Andrea Pasquali, Colin Clark, William A Perkins, Kyungjoo Kim, Mauro Perego, Michael L. Parks, Matthew T Balhoff, Marshall C Richmond, Martin Geier, Manfred Krafczyk, Li-Shi Luo, Alexandre M Tartakovsky, C. L Winter, (2015). Intercomparison of 3D Pore-scale Flow and Solute Transport Simulation Methods Advances in Water Resources https://www.osti.gov/search/identifier:1237471 Document ID: 243975

Kyungjoo Kim, Mauro Perego, Michael L. Parks, (2015). Efficient Parallel Implementation of Implicit SPH/MLS using LAMMPS and Trilinos Siam Cse 2015 Document ID: 232671

Mauro Perego, Kyungjoo Kim, M. Maxey, Wei Pan, Michael L. Parks, N. Trask, Christopher Siefert, (2014). A Parallel Implicit Implementation of Smoothed Paricle Hydrodynamics for Electrokinetic Applications MRS, 2014 Fall Meeting & Exhibit https://www.osti.gov/search/identifier:1315417 Document ID: 218757

Sivasankaran Rajamanickam, Michael L. Parks, Samuel Scott Collis, (2014). Csri Summer Proceedings 2013 https://www.osti.gov/search/identifier:1459606 Document ID: 166357

Payton Lindsay, Michael L. Parks, Arun Prakash, (2014). A Multi-Time-Step Method for Partitioned Time Integration of Peridynamics 1st PanAmerican Conference on Computational Mechanics Document ID: 165852

Daniel Z. Turner, Bart G van Bloemen Waanders, Michael L. Parks, (2014). Inverse Problems in Heterogenous and Fractured Media Using Peridynamics Computational Methods In Applied Mechanics and Engineering https://www.osti.gov/search/identifier:1248618 Document ID: 155223

Nathaniel Trask, Martin Maxey, Kyungjoo Kim, Mauro Perego, Michael L. Parks, Kai Yang, Jinchao Xu, (2014). A consistent second order projection scheme for simulating transient viscous flow with Smoothed Particle Hydrodynamics Cmame https://www.osti.gov/search/identifier:1183073 Document ID: 143873

David John Littlewood, Stewart A. Silling, John A. Mitchell, Michael L. Parks, Jakob Ostien, Daniel Z. Turner, P.D. Seleson, M. Gunzburger, (2014). Coupling Peridynamics and Classical Finite Element Analysis for Integrated Fracture Modeling Cis Erb Document ID: 5336016

Amalie Frischknecht, Michael L. Parks, Deaglan O. Halligan, (2014). Electrical Double Layers and Differential Capacitance in Molten Salts from Density Functional Theory Journal of Chemical Physics https://www.osti.gov/search/identifier:1143029 Document ID: 5335507

David John Littlewood, Stewart A. Silling, Richard B. Lehoucq, Michael L. Parks, John A. Mitchell, Daniel Z. Turner, Stephen D Bond, (2014). Peridynamic Modeling of Material Failure and Fracture Cis Eab https://www.osti.gov/search/identifier:1706390 Document ID: 5335185

William G. Rhodes, Brian M. Adams, Aidan P. Thompson, Steven J. Plimpton, Suzanne M. Kelly, Michael L. Parks, David John Littlewood, Dena Vigil, (2013). Computing Research Center Enabling computational simulations of complex physical systems 2nd Annual Sandia Research & Technology Showcase Document ID: 5326676

David John Littlewood, Michael L. Parks, John A. Mitchell, Stewart A. Silling, (2013). The Peridigm Framework for Peridynamic Simulations U.S. National Congress on Computational Mechanics https://www.osti.gov/search/identifier:1106141 Document ID: 5325229

David John Littlewood, Michael L. Parks, John A. Mitchell, Stewart A. Silling, (2013). The Peridigm Framework for Peridynamic Simulations U.S. National Congress on Computational Mechanics https://www.osti.gov/search/identifier:1062955 Document ID: 5318561

Stewart A. Silling, David John Littlewood, Michael L. Parks, (2012). Composite and Nanoscale Material Failure Industry-National Laboratory Workshop on Modeling and Simulation https://www.osti.gov/search/identifier:1657422 Document ID: 5305182

Pablo Seleson, Michael L. Parks, Steven J. Plimpton, Stewart A. Silling, Richard B. Lehoucq, (2011). Peridynamics with LAMMPS: A User Guide v0.3 Beta https://www.osti.gov/search/identifier:1031301 Document ID: 5301483

Heidi K. Thornquist, Mark Frederick Hoemmen, Michael A. Heroux, Richard B. Lehoucq, Michael L. Parks, David M. Day, Christopher Grover Baker, (2011). A Tutorial on Anasazi and Belos Trilinos User’s Group Meeting 2011 https://www.osti.gov/search/identifier:1661524 Document ID: 5301312

James R Kamm, Richard B. Lehoucq, Qiang Du, Michael L. Parks, (2011). An Approach to Nonlocal, Nonlinear Advection SIAM Journal on Applied Mathematics https://www.osti.gov/search/identifier:1108206 Document ID: 5294390

Steven J. Plimpton, James R Kamm, Richard B. Lehoucq, Michael L. Parks, Mark P. Sears, Stewart A. Silling, (2011). Peridynamics as a Rigorous Coarse-Graining of Atomistics for Multiscale Materials Design https://www.osti.gov/search/identifier:1007313 Document ID: 5286984

Jeremy Lieber Sprung, Michael L. Parks, (2011). A Model for Nonlocal Advection MFO Mini-workshop on the Mathematics of Peridynamics https://www.osti.gov/search/identifier:1110616 Document ID: 5290471

Louis Romero, Michael L. Parks, (2009). On the Two-Domain Equations for Gas Chromatography https://www.osti.gov/search/identifier:978912 Document ID: 5268800

Heidi K. Thornquist, Michael A. Heroux, Michael L. Parks, Richard B. Lehoucq, (2008). Belos: A Framework for Next-generation Iterative Linear Solvers Copper Mountain Conference on Iterative Methods https://www.osti.gov/search/identifier:1712856 Document ID: 5260964

Pavel B. Bochev, Samuel Scott Collis, Reese E. Jones, Richard B. Lehoucq, Michael L. Parks, Guglielmo Scovazzi, Stewart A. Silling, Jeremy Alan Templeton, Gregory J. Wagner, (2007). A Mathematical Framework for Multiscale Science and Engineering: the Variational Multiscale Method and Interscale Transfer Operators https://www.osti.gov/search/identifier:922756 Document ID: 5256010

Pavel B. Bochev, Michael L. Parks, Santiago Badia, Max Gunzburger, (2007). Bridging methods for coupling atomistic and continuum models 6th International Conference on Large-Scale Scientific Computations https://www.osti.gov/search/identifier:1147195 Document ID: 5254910

Pavel B. Bochev, Michael L. Parks, SANTIAGO BADIA, MAX GUNZBURGER, (2007). On Atomistic-to-continuum (atc) Coupling By Blending Multiscale Modeling and Simulation https://www.osti.gov/search/identifier:1147443 Document ID: 5254797

Jeremy Lieber Sprung, Michael L. Parks, (2007). Analysis of Atomistic-to-Continuum (AtC) Coupling Methods 2007 Applied Mathematics Research Program Annual PI Meeting https://www.osti.gov/search/identifier:1147835 Document ID: 5252665

Devon Dalton, Jeremy Alan Templeton, Michael L. Parks, Richard B. Lehoucq, David Olmsted, Gregory J. Wagner, (2007). An Atomistic-to-Continuum Coupling Method for Non-Equilibrium Heat Transfer in Solids Second Workshop on Atomistic-to-Continuum Coupling Methods https://www.osti.gov/search/identifier:1157540 Document ID: 5250877

Jeffrey W. Martin, Michael L. Parks, Louis Romero, Edward B. Overton, Gordon R. Lambertus, Abhinav Bhushan, Ernest Hasselbrink, Richard Sacks, (2007). A Model Describing the Impact of Geometric Dispersion on GC System Performance Pittcon 2007 https://www.osti.gov/search/identifier:1267233 Document ID: 5250100

Pavel B. Bochev, Louis Romero, Michael L. Parks, (2006). A Novel Lagrange-Multiplier Based Method for Consistent Mesh Tying Computer methods in applied mechanics and engineering Document ID: 5247050

Gregory J. Wagner, Reese E. Jones, Michael L. Parks, Alexander Slepoy, Richard B. Lehoucq, (2006). Atomistic-to-continuum coupling for heat transfer in solids World Congress on Computational Mechanics https://www.osti.gov/search/identifier:893560 Document ID: 5244124

Louis Romero, Michael L. Parks, (2005). Taylor Dispersion in High Aspect Ratio Tubes of Nearly Rectangular Cross Section Journal of Fluid Mechanics https://www.osti.gov/search/identifier:886620 Document ID: 5237442

Louis Romero, Joshua J. Whiting, Michael L. Parks, (2005). A Reduced Order Model for the Study of Asymmetries in Linear Gas Chromatography for Homogeneous Tubular Columns https://www.osti.gov/search/identifier:923173 Document ID: 5234932

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Software

Peridigm