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STUDENTS
Current Ph.D. students
Aycil Cesmelioglu. Multiphysics problem.
Prince Chidyagwai. Multiphysics problem. Research partially funded by NSF grant.
Mark Tronzo. Modeling of migration of enterocytes via TLR4 signaling.
Past Ph.D. students
Qi Mi. PhD "Modeling The Wound Healing In Necrotizing Enterocolitis And Diabetic Foot Ulcer". Graduation 2007.
Joint supervision with Prof. D. Swigon. Research partially funded by NIH grant.
Currently assistant professor in the School of Health and Medicine at University of Pittsburgh.
Yekaterina Epshteyn.
PhD "Hp Primal Discontinuous Galerkin Finite Element Methods For Two-Phase Flow In Porous Media".
Graduation 2007. Research partially funded by NSF and NIH grants. Currently postdoctoral fellow at Carnegie Mellon University
(three year position funded by NSF). Yekaterina was the most highly recruited graduate student in our department.
Songul Kaya.
PhD "Numerical Analysis of a Variational Multiscale Method". Graduation 2004. Joint supervision with Prof. W. Layton .
Winner of the 2004 Hales Distinguished Research Award for the best doctoral dissertation.
Currently, assistant professor at Middle East Technical University, Turkey.
Past M.S. students
Michael Chiacchiero. Master thesis "Efficient PETSc Solvers for Discontinuous Galerkin Methods Applied to Elliptic Problems". Graduation 2007.
Ahmet Izmirlioglu. Master thesis on Numerical and theoretical studies of high order methods. Graduation 2008.
Past undergraduate students
William Klieber. Bachelor of Philosophy thesis
"Numerical Simulations of Two-Phase Flow", 2006.
Research funded by CDRF (Spring 2004) and a Brackenridge Fellowship (Summer 2004). Currently, graduate student
in Computer Science department at Carnegie Mellon University.
RESEARCH INTERESTS
Numerical Analysis of Discontinuous Galerkin (DG) Finite Element Methods:
I am mostly interested in the primal DG methods such as NIPG, SIPG or IIPG.
Elliptic equations
Parabolic equations: with or without convection term
Slope limiters on unstructured nonconforming meshes
Linear elasticity equations
Quasi-static and dynamic viscoelasticity equations
Acoustic and elastic wave equations
Nonlinear equations: Navier-Stokes equations, nonlinear non-Fickian diffusion in viscoelastic polymers
Multiphase Flow: Simulations and Analysis
Sequential approach v. fully coupled approach, mesh and time adaptivity, DG methods, 2D/3D simulations, gravity, well models.
Incompressible Flow: Simulations and Analysis
Stokes equations, Navier-Stokes equations, subgrid eddy viscosity turbulence model, CG and DG methods.
Multi-numerics and/or Multi-physics Approach
Coupling of DG and Mixed Finite Elements (MFE) for single phase flow
Coupling of Stokes and Darcy using DG
Coupling of Navier-Stokes and Darcy using DG
Coupling of Stokes and Darcy using DG coupled with MFE
Modeling of Inflammatory Response and Necrotizing Enterocolitis
Inflammation: Center for Inflammation and Regenerative Modeling
Mixed Finite Element (MFE) Methods: Theoretical Error Analysis
Acoustic wave equations
Other Applications: Simulations
Single phase flow: highly discontinuous permeability, fractures
Miscible displacement: stable and unstable flow
Acoustic wave propagation
Optical tomography inverse problem
CURRENT COLLABORATORS
Peter Bastian, IWR, Heidelberg University
Vivette Girault, Laboratoire Jacques-Louis Lions, Universite Paris VI
David Hackam, Surgery, University of Pittsburgh School of Medicine
William Layton, Mathematics, University of Pittsburgh
Jennifer Proft, Mathematics, University of Texas at Austin
Simon Shaw, BICOM, Brunel University
Taufiquar Khan, Clemson University
Mary F. Wheeler, ICES, The University of Texas at Austin
John Whiteman, BICOM, Brunel University
Ivan Yotov, Mathematics, University of Pittsburgh
Useful Links
IMA
MathSciNet
NA Digest
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