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• Applied Mathematics and Computation Seminar
  
• Numerical Analysis Group at math.oregonstate
• MATLAB resources for research and teaching at math.oregonstate
• Numerical Analysis links
• IJNAM
• JAM
• E-print Network and DOE Science Accelerator

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.

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:

• 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)

• SIAM Annual San Diego July 7-11. Minisymposium on Multiscale Solution Algorithms with Applications to Earth Science (organizer: Sue Minkoff).
• Multiscale Mathematics and High-Performance Computing Summer School 2008, Richland, WA, 2008.

• 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.

• Mathematical and Numerical Treatment of Fluid Flow and Transport in Porous Media May 22-26, 2006 at University of Nevada, Las Vegas.
• Northwest Consortium in Multiscale Mathematics Workshop on Multiscale Modeling of Materials, May 25 - 30, 2006 Tacoma, WA.
• Workshop in Utrecht Modeling Coupled Processes in Porous Media