Sean Ingimarson Ph.D. 2023
July 2023 -, Staff Scientist, Applied Research Associates
Papers:
1) S. Ingimarson, An energy, momentum and angular momentum conserving scheme for a regularization model of incompressible flow,
Journal of Numerical Mathematics, 30(1), 1-22, 2022.
2) S. Ingimarson, L. Rebholz and T. Iliescu, Full and reduced order model consistency of the nonlinearity discretization in incompressible flows,
Computer Methods in Applied Mechanics and Engineering, 401B, 115620, 1-16, 2022.
3) S. Ingimarson, M. Neda, L. Rebholz, J. Reyes and A. Vu, Improved long time accuracy for projection methods for Navier-Stokes equations using EMAC formulation,
International Journal of Numerical Analysis and Modeling, 20(2), 176-198, 2023.
Duygu Vargun Ph.D. 2023
September 2023 -, Postdoc, Oak Ridge National Lab
Awards:
Michael Case Award for Outstanding Promise in Applied/Computational Mathematics, 2021
Papers:
1) M. Gardner, A. Larios, L. Rebholz, D. Vargun and C. Zerfas,
Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations,
American Institute of Mathematical Sciences Electronic Research Archive, 29(3): 2223-2247, 2021. Arxiv preprint
2) L. Rebholz, D. Vargun and M. Xiao, Enabling fast convergence of the iterated penalty Picard iteration with $O(1)$ penalty parameter for incompressible
Navier-Stokes via Anderson acceleration, Computer Methods in Applied Mechanics and Engineering, 387 (114178), 1-17, 2021.
Arxiv preprint
3) S. Pollock, L. Rebholz and D. Vargun, An efficient nonlinear solver and convergence analysis for a viscoplastic flow model,
Numerical Methods for Partial Differential Equations, 39:3874-3896, 2023.
4) P. Guven Geredeli, L. Rebholz, D. Vargun and A. Zytoon, Improved convergence of the Arrow-Hurwicz iteration for the Navier-Stokes equation via grad-div stabilization and Anderson acceleration,
Journal of Computational and Applied Mathematics, 422, 114920, 1-16, 2023.
Camille Zerfas Ph.D. 2019
2022-, Data Scientist, Mitre
2019-2022 , Data Scientist, NextEra Energy
Awards:
College of Science Outstanding Graduate in Teaching, 2019
Outstanding Graduate in Teaching, School of Mathematical and Statistical Sciences, 2019
Michael Case Award for Outstanding Promise in Applied/Computational Mathematics, 2017
Papers:
1) L. Rebholz, C. Zerfas and K. Zhao, Global in time analysis and sensitivity analysis for the reduced NS-$\alpha$ model of incompressible flow,
Journal of Mathematical Fluid Mechanics, 19(3), 445-467, 2017.
2) M. Akbas, L. Rebholz and C. Zerfas, Optimal vorticity accuracy in an efficient velocity-vorticity method for the 2D Navier-Stokes equations,
Calcolo, 55(1):3, 1-29, 2018.
3) L. Rebholz, D. Wang, Z. Wang, K. Zhao, and C. Zerfas, Initial boundary value problems for a system of parabolic conservation laws arising
from a Keller-Segel type chemotaxis model in multiple space dimensions, DCDS-A, 39(7), 3789-3838, 2019.
4) A. Larios, L. Rebholz and C. Zerfas,
Global in time stability and accuracy of IMEX-FEM data assimilation schemes
for Navier-Stokes equations,
Computer Methods in Applied Mechanics and Engineering,
345, 1077-1093, 2019.
5) L. Rebholz and C. Zerfas, Simple and efficient continuous data assimilation of evolution equations via algebraic nudging,
Numerical Methods for Partial Differential Equations, 37 (3), 2588-2612, 2021.
Arxiv preprint
6) C. Zerfas, L. Rebholz, M. Schneier and T. Iliescu,
Continuous data assimilation reduced order models of fluid flow, Computer Methods in Applied Mechanics and Engineering, 357, 112596, 1-21, 2019.
arxiv
Mengying Xiao Ph.D. 2018 (co-advisor Timo Heister)
2020-, (tenure track) Assistant Professor, University of West Florida
2019-2020, Postdoc, University of Florida
2018-2019, Visiting Assitant Professor, William & Mary
Awards (while a student):
College of Science Outstanding Graduate in Discovery, 2018
Most Outstanding Graduate Student Researcher award, Department of Mathematical Sciences, 2018
Outstanding Graduate Student Researcher award, Department of Mathematical Sciences, 2017
Outstanding TA award, Department of Mathematical Sciences, 2016
Michael Case award for Outstanding Promise in Applied/Computational Mathematics, 2014
Papers:(while a student)
1) L. Rebholz and M. Xiao, On reducing the splitting error in Yosida methods for the Navier-Stokes equations, Computer
Methods in Applied Mechanics and Engineering, 294, 259-277, 2015.
2) T. Heister, L. Rebholz and M. Xiao, Flux-preserving enforcement of
inhomogeneous Dirichlet boundary conditions for strongly divergence-free
mixed finite element methods for flow problems,
Journal of Mathematical Analysis and Applications, 438(1), 507-513, 2016.
3) L. Rebholz and M. Xiao, Improved accuracy in algebraic splitting methods for \
Navier-Stokes equations, SIAM Journal of Scientific Computing, 39(4), A1489-A1513, 2017.
4) M. Akbas, M. Mohebujjaman, L. Rebholz, and M. Xiao,
High order algebraic splitting for magnetohydrodynamics simulation, Journal of Computational and
Applied Mathematics, 321, 128-142, 2017.
5) L. Rebholz, S.M. Wise, and M. Xiao, Penalty-Projection Schemes for the Cahn-Hilliard
Navier-Stokes Diffuse Interface Model of Two Phase Flow, and their Connection to Divergence-Free Coupled Schemes,
International Journal of Numerical Analysis and Modeling, 15(4), 649-676, 2018.
6) L. Rebholz, A. Viguerie and M. Xiao, Efficient nonlinear iteration schemes based on algebraic splitting for the
incompressible Navier-Stokes equations, Mathematics of Computation, 88, 1533-1557, 2019.
Sergey Charnyi Ph.D. 2018 (co-advisor Timo Heister)
2021-, Staff Scientist, Siemens
2019-2021, Postdoc, Naval Postgraduate School
Papers:(while a student)
1) S. Charnyi, T. Heister, M. Olshanskii, and L. Rebholz, On conservation laws of Navier-Stokes
Galerkin discretizations, Journal of Computational Physics, 337, 289-308, 2017.
2) S. Charnyi, T. Heister, M. Olshanskii and L. Rebholz, Efficient discretizations for the EMAC
formulation of the incompressible Navier-Stokes equations, Applied Numerical Mathematics,
141, 220-233, 2019.
Muhammad Mohebujjaman Ph.D. 2017 (co-advisor Timo Heister)
2023-, (tenure track) Assistant Professor, University of Alabama Birmingham
2020-2023, (tenure track) Assistant Professor, Texas A&M International University
2019-2020, Postdoc, MIT
2017-January 2019 , Postdoc, Virginia Tech
Papers (while a student):
1) M. Akbas, S. Kaya, M. Mohebujjaman and L. Rebholz, Numerical analysis and testing of
a fully discrete, decoupled penalty-projection algorithm for MHD in Elsasser variable,
International Journal of Numerical Analysis and Modeling, 13(1), 90-113, 2016.
2) N. Jiang, M. Mohebujjaman, L. Rebholz and C. Trenchea, Analysis of a family of optima$
Computer Methods in Applied Mechanics and Engineering, 310, 388-405, 2016.
3) T. Heister, M. Mohebujjaman and L. Rebholz, Decoupled, unconditionally stable, higher$
for MHD flow simulation, Journal of Scientific Computing, 71(1), 21-43, 2017.
4) M. Mohebujjaman and L. Rebholz, An efficient algorithm for computation of MHD flow en$
Computational Methods in Applied Mathematics, 17(1), 121-137, 2017.
5) M. Akbas, M. Mohebujjaman, L. Rebholz, and M. Xiao,
High order algebraic splitting for magnetohydrodynamics simulation,
Journal of Computational and Applied Mathematics, 321, 128-142, 2017.
Mine Akbas, Ph.D. 2016 (co-advisor Songul Kaya at Middle East Technical University)
2022-, Associate Professor, Duzce University
2018-, Assistant Professor, Duzce University
2016-2018 , Postdoc, Duzce University
Papers (while a student):
1) M. Akbas Belenli, S. Kaya, L. Rebholz, and N. Wilson, A subgrid stabilization finite element method for incompressible magnetohydrodynamics, International Journal of Computer Mathematics, 90(7) 1506-1523, 2013.
2) M. Akbas Belenli, S. Kaya, and L. Rebholz, An explicitly decoupled variational multiscale method for incompressible, non-isothermal flows,
Computational Methods in Applied Mathematics, 15(1), 1-20, 2015.
3) M. Akbas Belenli, L. Rebholz, and F. Tone, A note on the importance of mass conservation in long-time stability of Navier-Stokes equations
Applied Mathematics Letters, 45, 98-102, 2015.
4) M. Akbas Belenli, S. Kaya, M. Mohebujjaman and L. Rebholz, Numerical analysis and testing of a fully discrete, decoupled penalty-projection
algorithm for MHD in Elsasser variable, International Journal of Numerical Analysis and Modeling, 13(1), 90-113, 2016.
5) M. Akbas Belenli, S. Kaya and L. Rebholz, On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressib$
flow problems, Numerical Methods for Partial Differential Equations, 33(4), 995-1017, 2017.
Abigail Bowers, Ph.D. 2014
2022-, Risk Analyst, Disney
2016-2022 , Assistant Professor, Florida Polytechnic University
2014-2016 , Visiting Assistant Professor, Clemson
Papers (while a student):
7) A. Bowers, S. Le Borne, and L. Rebholz, Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization,
Computer Methods in Applied Mechanics and Engineering, 275, 1-19, 2014.
6) A. Bowers and L. Rebholz, Numerical study of a regularization model for incompressible flow with deconvolution-based adaptive nonlinear filtering, Computer Methods in Applied Mechanics and Engineering, 258, 1-12, 2013.
5) A. Bowers, Numerical approximation of a multiscale Leray model for incompressible, viscous flow,
In: Recent Advances in Scientific Computing and Applications: Proceedings of the 8th International Conference on Scientific Computing and Applications, edited by: Jichun Li, Eric Macharro, and Hongtao Yang, AMS Contemporary Mathematics, volume 586, 2013.
4) A. Bowers, T.-Y. Kim, M. Neda, L. Rebholz, and E. Fried,
The Leray-$\alpha\beta$-deconvolution model: energy analysis and numerical
algorithms, Applied Mathematical Modelling, 37(3), 1225-1241, 2013.
3) A. Bowers, L. Rebholz, A. Takhirov, and C. Trenchea,
Improved accuracy in regularization models of
incompressible flow via adaptive nonlinear filtering,
International Journal for Numerical Methods in Fluids, 70, 805-828, 2012.
2) A. Bowers and L. Rebholz, Increasing accuracy and efficiency in FE computations of the Leray-deconvolution model,
Numerical Methods for Partial Differential Equations, 28(2), 720-736, 2012.
1) A. Bowers, B. Cousins, A. Linke and L. Rebholz, New connections between finite element
formulations of the Navier-Stokes equations, Journal of
Computational Physics, 229(24), 2090-2095, 2010.
Keith Galvin, Ph.D. 2013 (co-advised by Hyesuk Lee)
August 2013-May 2014, Postdoc, University of Michigan
May 2014 - present, Mathematician, Applied Physical Sciences
Papers while a student:
1) K. Galvin, New subgrid artificial viscosity methods for the
Navier-Stokes equations, Computer Methods in Applied Mechanics and
Engineering, 200(1-4), 242-250, 2011.
Download
2) K. Galvin, H.K. Lee and L. Rebholz, A Numerical Study for a Velocity-Vorticity-Helicity formulation of
the 3D Time-Dependent NSE, International Journal of Numerical Analysis
and Modeling, Series B, 2(4), 355-368, 2011.
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3) K. Galvin, H.K. Lee, and L. Rebholz, Approximation of
viscoelastic
flows with defective boundary conditions, Journal of Non-Newtonian Fluid Mechanics, 169-170, 104-113, 2012.
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4) K. Galvin, A. Linke, L. Rebholz, and N. Wilson, Stabilizing poor mass conservation in incompressible
flow problems with large irrotational forcing and application to thermal convection,
Computer Methods in Applied Mechanics and Engineering, 237, 166-176, 2012.
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5) K. Galvin and H.K. Lee, Analysis and approximation of the Cross model for quasi-Newtonian flows with defective boundary conditions, Appl. Math. and Compt., 222, 244-254, 2013.
6) K. Galvin, L. Rebholz, and C. Trenchea, Efficient, unconditionally stable, and optimally accurate FE algorithms for approximate deconvolution models, SIAM Journal on Numerical Analysis, to appear.
Awards during time at Clemson:
(Most) Outstanding PhD Student award, Clemson University Dept of Mathematical Sciences, 2012
Voted worst golfer in computational math golf group, 2011-2013.
Nicholas Wilson, Ph.D. 2012
August 2012-May 2013: Visiting Assistant Professor, Michigan Tech
May 2013-present: Risk Analyst, Disney
Publications during time at Clemson:
1) M. Case, A. Labovsky, L. Rebholz, and N. Wilson,
A high physical accuracy method for incompressible magnetohydrodynamics, International
Journal of Numerical Analysis and Modeling, Series B, 1(2), 219-238, 2010.
2) B. Cousins, L. Rebholz, and N. Wilson, Enforcing energy, helicity and strong mass
conservation in FE computations for incompressible
Navier-Stokes simulations, Applied Mathematics and Computation, 218, 1208-1221, 2011.
3) M. Case, V. Ervin, A. Linke, L. Rebholz, and N. Wilson, Stable
computing with an enhanced
physics based scheme for the 3D Navier-Stokes equations, International Journal
of Numerical Analysis and Modeling, 8(1), 118-136, 2011.
4) C. Manica, M. Neda, M. Olshanskii, L. Rebholz, and N. Wilson,
On an efficient finite element method for Navier-Stokes-omega with strong
mass conservation, Computational Methods in Applied Mathematics,
11(1), 3-22, 2011.
5) A. Linke, L. Rebholz, and N. Wilson,
On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius
solutions for incompressible flow problems,
Journal of Mathematical Analysis and Applications, 381,
612-626, 2011.
6) N. Wilson, On the Leray-deconvolution model for the
incompressible Magnetohydrodynamics equations, Applied Mathematics and Computation, 218(21), 10557-10571, 2012.
7) K. Galvin, A. Linke, L. Rebholz, and N. Wilson, Stabilizing poor mass conservation in incompressible
flow problems with large irrotational forcing and application to thermal convection,
Computer Methods in Applied Mechanics and Engineering, 237, 166-176, 2012.
8) P. Kuberry, A. Larios, L. Rebholz, and N. Wilson, Numerical approximation of the Voigt
regularization of incompressible NSE and MHD flows, Computers and Mathematics with Applications,
64(8), 2647-2662, 2012.
9) M. Belenli, S. Kaya, L. Rebholz, and N. Wilson, A subgrid stabilization finite element method for incompresible
magnetohydrodynamics, International Journal of Computer Mathematics, 90(7), 1506-1523, 2013..
Awards during time at Clemson:
(Most) Outstanding PhD Student award, Clemson University Dept of Mathematical Sciences, 2011.
Clayton & Claire Aucoin Enhancement Award (Travel money award for PhD students with outstanding potential to
be leaders in research), 2011.
Michael Case, Ph.D. 2010 (co-advised by Lea Jenkins)
Publications during time at Clemson:
1) M. Case, A. Labovsky, L. Rebholz, and N. Wilson,
A high physical accuracy method for incompressible magnetohydrodynamics, International Journal
of Numerical Analysis and Modeling, Series B, 1(2), 219-238, 2010.
Download
2) M. Case, V. Ervin, A. Linke and L. Rebholz, A connection between
Scott-Vogelius elements and grad-div stabilization, SIAM Journal on
Numerical Analysis, 49(4), 1461-1481, 2011.
Download
3) M. Case, V. Ervin, A. Linke, L. Rebholz, and N. Wilson, Stable computing with an enhanced
physics based scheme for the 3D Navier-Stokes equations, International Journal of
Numerical Analysis and Modeling, 8(1), 118-136, 2011.
Download
4) M. Case and H. MacMillan, On simulating the generation of mosaicism furing mammalian
cerebral cortical development, Journal of Biological Systems, 17(1), 27-62, 2009.
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Awards during time at Clemson:
SIAM Southeast Student Paper Prize, April 2010
Ph.D. Students completed
M.S. Students completed
Ryan Hill, 2010 (NAVSEA).
Abigail Bowers, 2010 (stayed for phd)
Keith Galvin, 2010 (stayed for phd)
Kara Kohler, 2012 (Salem Academy)
Erica D'Agnillo, 2012 (Epic Systems)
Michael Dowling, 2012 (stayed for phd)
Stacey Watro, 2013 (Thoughtworks)
Victoria Cuff, 2013 (Hanscom Air Force Base)
Muhammad 'Jaman' Mohebujjaman, 2015 (stayed for phd)
Monica Morales Hernandez, 2015 (Adelphi University)
Rebecca Knoll, 2016 (Rockbridge Academy)
Camille Zerfas, 2016 (stayed for phd)
Dominique Forbes, 2020 (Axos Bank)
Abigail Bowers, 2010 (stayed for phd)
Keith Galvin, 2010 (stayed for phd)
Kara Kohler, 2012 (Salem Academy)
Erica D'Agnillo, 2012 (Epic Systems)
Michael Dowling, 2012 (stayed for phd)
Stacey Watro, 2013 (Thoughtworks)
Victoria Cuff, 2013 (Hanscom Air Force Base)
Muhammad 'Jaman' Mohebujjaman, 2015 (stayed for phd)
Monica Morales Hernandez, 2015 (Adelphi University)
Rebecca Knoll, 2016 (Rockbridge Academy)
Camille Zerfas, 2016 (stayed for phd)
Dominique Forbes, 2020 (Axos Bank)
Undergraduates I advised research projects for
Ben Cousins, 2009-2012
Victoria Cuff, 2011-2012
Nathan Heavner, 2011-2014
Barbara Woo, 2014-2015
Sarah Malick, 2015-2016
Jacob Honeycutt, 2017-2018
'The' Sarah Kelly, 2017-2018
Claire Evans, 2018
Hannah Johnson, 2017-2019
Allison Miller, 2018-2019
Laura Setzer, 2019
Elizabeth Hite, 2020
Tori Luongo, 2023
Jessica Franklin, 2024
Victoria Cuff, 2011-2012
Nathan Heavner, 2011-2014
Barbara Woo, 2014-2015
Sarah Malick, 2015-2016
Jacob Honeycutt, 2017-2018
'The' Sarah Kelly, 2017-2018
Claire Evans, 2018
Hannah Johnson, 2017-2019
Allison Miller, 2018-2019
Laura Setzer, 2019
Elizabeth Hite, 2020
Tori Luongo, 2023
Jessica Franklin, 2024