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My research interests are mainly in mathematical and computational
modeling of flow, transport, and other coupled processes in porous
media such as aquifers or oil and gas reservoirs. Such phenomena are
typically described by nonlinear coupled PDEs whose data have highly
heterogeneous character, frequently at multiple scales, and present
challenges to analysis and computation. I am interested in i) analysis
of solutions to such models, ii) construction of stable, accurate, and
efficient numerical algorithms, and iii) characterization of
heterogeneity and uncertainty of the data. Our recent results include
a model for coupled flow and transport which does not assume
separation of scales, an upscaled model for quasilinear elliptic
equations describing non-Darcy flow in porous media at mesoscale and
at porescale, and multiscale analysis and simulation of a
pseudo-parabolic system involving dynamic capillary
pressure. Numerical algorithms include a-posteriori error
estimators for mortar mixed finite element methods and for multilevel
elliptic-parabolic systems.
I have always been interested in computing. This includes both
rigorous numerical analysis and in paticular derivation of a-priori
and a-posteriori error estimates, as well as high-performance
computing techniques including domain decomposition (multiphysics) and
parallel algorithms. Recently computing has reached terascale
levels; we have some new projects
using CUDA
technology, and some new ones on coupling continuum and
discrete scale models.
My mathematical genealogy
and the tree
Grants and projects:
- "Coupling of discrete and continuum models of metastable
configurations" (Fulbright
Research Scholar Fellowship, 2009-2010), in collaboration with
Interdisciplinary Centre for Modeling (ICM),
University of Warsaw, Warsaw, Poland.
- Project
"Model adaptivity for porous media"
supported by the National Science Foundation.
Students involved/partially supported: Kyle Augustson, Shannon
Biederman, Scott Clark, Cristiano Garibotti, Ken Kennedy, Viviane Klein.
-
Project
"Modeling, analysis and simulation of preferential flow in porous media"
supported by Department of Energy, Office of Science (PI: R.E. Showalter).
Students involved/partially supported: Kyle Augustson, Ken
Kennedy, Viviane Klein, Cheryl Woodall.
- NSF-sponsored
Modeling, Analysis and Simulation of Multiscale Nonlinear Systems: Workshop at Oregon State University: May 2007-October 2008.
-
RERF OSU Research Fund, Spring 2006 Award
``High Performance Computing Cluster Nodes for Computational Science
Research in College of Science''
-
(Faculty Advisor of)
Scott Clark, "Finite Element Modeling of Uncertain Interfaces",
Winter-Spring 2008.
Recent/upcoming events and conferences:
2009:
- MathFest , Invited
Paper Session "Applications of Fluid Dynamics", August 6-8, 2009.
- SIAM
Geosciences in Leipzig, June 15-19, 2009.
- ICCS 2009 Conference
Baton Rouge, May 25-27, Louisiana.
Minsiymposium on Multiscale, Multiphysics Applications
- IMA Workshop
"Molecular Simulations: Algorithms, Analysis, and Applications"
May 18-22, 2009
Minisymposium on
Upscaling and Multiscale Techniques for Subsurface Flow and Transport
(organizers: Y. Efendiev, Y. Chen, S. Lee).
Minisymposium on Modeling of Inertia and Non-Equilibrium Processes
(organizer: M. Peszynska)
2008:
2007:
-
Workshop on Modeling, Analysis and Simulation of Multiscale Nonlinear
Systems held at Oregon State University, June 25-29, 2007.
-
Rocky Mountain Mathematics Consortium Summer School
- Multiscale Mathematics
and High-Performance Computing Summer School 2007, Corvallis, 2007.
- Subsurface Transport
Over Multiple Phases (STOMP) simulator short course on OSU
campus, May 24-25, 2007, in Memorial Union and Math Learning Center
-
Finite Element Circus, April 20-21 Univ. Maryland
- DOE Computational Sciences Subsurface Workshop January 9-12, 2007, Bethesda, Maryland.
2006:
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