P. Kuberry, P. Bochev, J. Koester, N. Trask, A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids, Engineering with Computers, 2024. doi: 10.1007/s00366-024-02036-5. Link

P. Bochev, J. Owen, P. Kuberry, J. Connors, Dynamic flux surrogate-based partitioned methods for interface problems, Computer Methods in Applied Mechanics and Engineering, 429, 117115, 2024. doi: 10.1016/j.cma.2024.117115. Link

J. Connors, J. Owen, P. Kuberry, P. Bochev, A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models, Computer Methods in Applied Mechanics and Engineering, 426, 116975, 2024. doi: 10.1016/j.cma.2024.116975. Link

A. de Castro, P. Bochev, P. Kuberry, I. Tezaur, Explicit synchronous partitioned scheme for coupled reduced order models based on composite reduced bases, Computer Methods in Applied Mechanics and Engineering, 116398, 2023. doi: 10.1016/j.cma.2023.116398. arXiv:2306.05531, Link

Andrew M. Jones, Peter A. Bosler, Paul A. Kuberry, Grady B. Wright Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives, Computers and Mathematics with Applications, 147, 1-13, 2023. doi: 10.1016/j.camwa.2023.07.015. Link

K.C. Sockwell, P. Bochev, K. Peterson, P. Kuberry, Interface Flux Recovery Framework for Constructing Partitioned Heterogeneous Time-Integration Methods, Numerical Methods for Partial Differential Equations, 39(5), 3572-3593, 2023. doi: 10.1002/num.23015. Link

Q. Ha, P. Kuberry, N. Trask, E. Ryan, Parallel implementation of a compatible high-order meshless method for the Stokes' equations, submitted. arXiv:2104.14447

V.S. Mahadevan, J.E. Guerra, X. Jiao, P. Kuberry, Y. Li, P. Ullrich, D. Marsico, R. Jacob, P. Bochev, P. Jones, Metrics for Intercomparison of Remapping Algorithms (MIRA) applied to Earth System Models, Geoscientific Model Development, 15(17), 6601-6635, 2022. doi: 10.5194/gmd-15-6601-2022. Link

B.J. Gross, P. Kuberry, P.J. Atzberger, First-Passage Time Statistics on Surfaces of General Shape: Surface PDE Solvers using Generalized Moving Least Squares (GMLS), Journal of Computational Physics, 453, 2022. doi: 10.1016/j.jcp.2021.110932. arXiv:2102.02421, Link

M. Anguiano, P. Kuberry, P. Bochev, A. Masud, Synchronous and Concurrent Multi-domain Computing Method for Cloud Computing Platforms, SIAM Journal on Scientific Computing, S565-S591, 2021.
doi: 10.1137/20M1349278. Link

K.C. Sockwell, K. Peterson, P. Kuberry, P. Bochev, N. Trask, Interface Flux Recovery coupling method for the ocean-atmosphere system, Results in Applied Mathematics, 8, 2020. doi: 10.1016/j.rinam.2020.100110. Link

B.J. Gross, N. Trask, P. Kuberry, and P. J. Atzberger, Meshfree methods on manifolds for hydrodynamic flows on curved surfaces: A Generalized Moving Least-Squares (GMLS) approach,
Journal of Computational Physics, 409, 2020. doi: 10.1016/j.jcp.2020.109340. arXiv:1905.10469, Link

P. Bochev, N. Trask, P. Kuberry, and M. Perego, Mesh-hardened finite element analysis through a Generalized Moving Least-Squares approximation of variational problems,
International Conference on Large-Scale Scientific Computing, pp. 67-75. Springer, Cham, 2020.
doi: 10.1007/978-3-030-41032-2_7. Preprint, Link.

B.S.M. Ebna Hai, M. Bause, and P. Kuberry, Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach,
Applied Mathematical Modelling, 75, 916-939, 2019. doi: 10.1016/j.apm.2019.07.007. Link

B.S.M. Ebna Hai, M. Bause, and P. Kuberry, Modeling and simulation of Ultrasonic Guided Waves propagation in the fluid-structure domain by a monolithic approach,
Journal of Fluids and Structures, 88, 100-121, 2019. doi: 10.1016/j.jfluidstructs.2019.04.014. Link

N. Trask, P. Kuberry, Compatible meshfree discretization of surface PDEs,
Computational Particle Mechanics, 2019. doi: https://doi.org/10.1007/s40571-019-00251-2. Preprint, Link

K. Peterson, P. Bochev, and P. Kuberry, Explicit synchronous partitioned algorithms for interface problems based on Lagrange multipliers, Computers & Mathematics with Applications,
78(2), 459-482, 2019. doi: 10.1016/j.camwa.2018.09.045. Link

P. Kuberry, P. Bochev, and K. Peterson, A virtual control, mesh-free coupling method for non-coincident interfaces, ECCM-ECFD Conferences 2018. Link

P. Bochev, P. Kuberry, and K. Peterson, A virtual control coupling approach for problems with non-coincident discrete interfaces, International Conference on Large-Scale Scientific Computing,
pp. 147-155. Springer, Cham, 2018. doi: 10.1007/978-3-319-73441-5_15. Link

P. Kuberry, P. Bochev, and K. Peterson, An optimization-based approach for elliptic problems with interfaces, SIAM Journal on Scientific Computing, 39(5), S757-S781, 2017.
doi: 10.1137/16M1084547. Link

P. Kuberry, H. Lee, Convergence of a fluid-structure interaction problem decoupled by a Neumann control over a single time-step, Journal of Mathematical Analysis and Applications, 437(1), 645-667, 2016.
doi: 10.1016/j.jmaa.2016.01.022. Link

P. Kuberry, H. Lee, Analysis of a fluid-structure interaction problem recast in an optimal control setting, SIAM Journal on Numerical Analysis, 53(3), 1464-1487, 2015.
doi: 10.1137/140958220. Link

P. Kuberry, H. Lee, A decoupling algorithm for fluid-structure interaction problems based on optimization, Computer Methods in Applied Mechanics and Engineering, 267, 594-605, 2013.
doi: 10.1016/j.cma.2013.10.006. Link, Preprint

L. Zhilin, W. Li, E. Aspinwall, R. Cooper, P. Kuberry, A. Sanders, and K. Zeng, Some new analysis results for a class of interface problems, Mathematical Methods in the Applied Sciences, 2013.
doi: 10.1002/mma.2865. Link

P. Kuberry, A. Larios, L. Rebholz, N. Wilson, Numerical approximation of the Voigt regularization for incompressible Navier–Stokes and magnetohydrodynamic flows, Computers & Mathematics with Applications, 64(8), 2647-2662, 2012.
doi: 10.1016/j.camwa.2012.07.010. Link

E. Hawkins, P. Bochev, P. Kuberry, An Optimization-Based Approach for Coupling Projection-Based Reduced Order Models, Computer Science Research Institute Summer Proceedings 2023, S.K. Seritan and J.D. Smith, eds., Technical Report SAND2023-13916R, Sandia National Laboratories, 54–69, 2023. Link

E. Huynh, T. Meissner, P. Bochev, P. Kuberry, A Preliminary Study for Obtaining Inverse Sobolev-Type Inequalities for tanh Neural Networks, Computer Science Research Institute Summer Proceedings 2023, S.K. Seritan and J.D. Smith, eds., Technical Report SAND2023-13916R, Sandia National Laboratories, 303–322, 2023. Link

T. Meissner, E. Huynh, P. Bochev, P. Kuberry, A Deep Least-Squares Method for the Stokes Equations, Computer Science Research Institute Summer Proceedings 2023, S.K. Seritan and J.D. Smith, eds., Technical Report SAND2023-13916R, Sandia National Laboratories, 365–375, 2023. Link

A. de Castro, P. Kuberry, I. Tezaur, P. Bochev, A Novel Partitioned Approach for Reduced Order Model -- Finite Element Model (ROM-FEM) and ROM-ROM Coupling, Earth and Space 2022, 475-489, 2023. doi: 10.1061/9780784484470.044. arXiv:2206.04736, Link

A. de Castro, P. Kuberry, I. Tezaur, P. Bochev, A Synchronous Partitioned Scheme for Coupled Reduced Order Models Based on Separate Reduced Order Bases for the Interior and Interface Variables, Computer Science Research Institute Summer Proceedings 2022, S.K. Seritan and J.D. Smith, eds., Technical Report SAND2022-10280R, Sandia National Laboratories, 78–92, 2022. Link

A. de Castro, P. Kuberry, P. Bochev, Partitioned Solution of a Coupled Reduced Order Model – Finite Element Model (ROM-FEM model) for a Transmission Problem, Computer Science Research Institute Summer Proceedings 2021, J.D. Smith and E. Galvan, eds., Technical Report SAND2022-0653R, Sandia National Laboratories, 24-37, 2021. Link

K. Aadithya, P. Kuberry, B. Paskaleva, P. Bochev, K. Leeson, A. Mar, T. Mei, and E. Keiter, Data-driven compact models for circuit design and analysis, Proceedings of Machine Learning Research, 107, 555-572, 2020. arXiv:2001.01699, Link

B.S.M. Ebna Hai, M. Bause, P. Kuberry, Finite element approximation of the eXtended Fluid-Structure Interaction (eXFSI) Problem, ASME 2016 HT/FE/ICNMM Conferences - FEDSM2016-7506, Washington, D.C., July 10-14, 2016. Link

P. Bochev, P. Kuberry, A variational flux recovery approach for elastodynamics problems with interfaces, 1st Pan-American Congress on Computational Mechanics, Argentina, 2015. Link

P. Kuberry, P. Bochev, A new partitioned algorithm for explicit elastodynamics based on Variational Flux Recovery, Computer Science Research Institute Summer Proceedings 2014, 38-53, 2014. Link

D.C. Crowder, M.L. Trappett, P. Kuberry, S. Cardwell, J.D. Smith, S. Kumar, F. Chance, S. Yi, M. Swaminathan, A. Sengupta, R. Kumar, B. Manna, Artificial Intelligence-Enhanced, Multi-Level, Modular System Design, Sandia Report SAND2023-10948, 2023.

P. Kuberry, E. Keiter, An embedded Python model interpreter for Xyce (Xyce-PyMi), Sandia Report SAND2021-9504, 2021. doi:10.2172/1813650. Link

P. Kuberry, P. Bochev, J. Koester, N. Trask, Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids: LDRD Final Report, Sandia Report SAND2020-9980, 2020. doi:10.2172/1669732. Link

P. Bochev, P. Bosler, P. Kuberry, M. Perego, K. Peterson, N. Trask, Compatible Particle Discretizations. Final LDRD Report, Sandia Report SAND2019-10991, 2019. doi:10.2172/1569143. Link

P. Kuberry, P. Bosler, and N. Trask, Compadre Toolkit, https://www.github.com/sandialabs/compadre.
doi: 10.11578/dc.20190411.1.

P. Kuberry, Xyce Python Model Interpreter (Xyce-PyMi), Github. Link