K. Sockwell, K. Peterson, P. Kuberry, P. Bochev, N. Trask, Interface flux recovery coupling method for the ocean-atmosphere system, submitted.

K. Aadithya, P. Kuberry, B. Paskaleva, P. Bochev, K. Leeson, A. Mar, T. Mei, and E. Keiter, Development, Demonstration, and Validation of Data-driven Compact Diode Models for Circuit Simulation and Analysis, submitted. arXiv:2001.01699

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, 2020. doi: 10.1016/ 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: 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


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. Bosler, and N. Trask, Compadre Toolkit, Github. doi: 10.5281/zenodo.2560287. Link


Derivative Free Optimization by a Hybridization of Methods:: March 2011 - April 2012
A version of the BLX-Alpha genetic algorithm is hybridized with the Nelder-mead local search method. The hybrid is created by a relay implementation between the genetic algorithm and Nelder-Mead when stalling is detected. BLX-Alpha, Nelder-Mead, and the hybrid of the two are then tested on two classical engineering problems as well as on an experimental extrusion filter design. Numerical results are compared with known optimal solutions for the engineering problems and with previously published results for the multilayer extrusion filter design.

Immersed Interface Boundary Method:: May 2010 - August 2010
This project focused on understanding the IIM method as well as creating a program to implement it in 2 and 3D. IIM is a second order accurate method of solving a Poisson Elliptic differential equation with possible discontinuities in both the first and second derivatives. It is superior to Peskin's Immersed Boundary method which is only first order accurate in most cases due to smoothing or smearing discontinuous sections.

Shortest Distance Algorithm Applied to Tile Maps:: January, 2010 - May, 2010
Tiled maps create a problem for a shortest distance algorithm such as Djikstra's due to creation of a tree with an overabundance of edges. By weighting each vertex on the map by considering adjacent obstructions, a method is developed that eliminates edges in an efficient manner. The result is that Djikstra's Algorithm can now be applied to a tile set.

Design of a Traffic Roundabout[COMAP]:: March 15th, 2009 - March 19th, 2009
A traffic circle or roundabout is a traffic control mechanism used to control traffic in an efficient and safe manner. These designs minimize the potential conflicts between vehicles by having traffic continually flow in a clockwise direction. Traffic is consistently flowing around the roundabout which should ideally reduce congestion in and around the roundabout. At most roundabouts, the incoming traffic must yield to the traffic in the circle, but others may use traffic lights or place the yield sign within the traffic circle giving priority to the incoming traffic. Our model is used to find the best traffic control mechanism for each of the incoming lanes with respect to the effect that it will have on the other incoming traffic lanes and other intersections in the city.