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• Applied Mathematics and Computation Seminar
  
• Numerical Analysis Group at math.oregonstate
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• IJNAM
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• E-print Network and DOE Science Accelerator

My research interests are in mathematical modeling and numerical analysis and simulation of phenomena of flow and transport in porous media. Such phenomena are typically described by nonlinear coupled PDEs whose data have highly heterogeneous character, frequently at multiple scales. A typical example is the coupled multiphase multicomponent flow and transport in fractured porous media. I am interested in analysis of solutions to such models as well as in various ways to characterize and describe the heterogeneity and uncertainty of the data. The upscaled models which arise, for example, by way of homogenization, have typically a nonlocal character in time (memory terms) and/or in space. These present significant challenges when analyzed and solved numerically using finite element or finite difference methods.

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 issues including domain decomposition and parallel solution techniques. I became interested in Parallel Computing even before it became a reality (80's); back then temporal logic applied to concurrent processes stated that "Sometime" is sometimes "not never". (L. Lamport). (Temporal logic is one of the tools used in proving accuracy and non-blocking of parallel (concurrent) processes.) These days computing has reached "terascale" levels; I have been involved in various terascale reservoir simulation and characterization projects which involve data-intense parallel and grid computing, optimization and visualization techniques.

Continuing my early interest in domain decomposition (Schwartz) methods, I have worked on multiphysics and multinumerics couplings of models of multiphase multicomponent flow, transport, and coupled elastic deformation in porous media. Recently I have proposed adaptivity of such couplings based on a-posteriori error estimators for mortar mixed finite element methods.

Grants and projects:

• Project "Model adaptivity for porous media" supported by the National Science Foundation.
• Project "Modeling, analysis and simulation of preferential flow in porous media" supported by Department of Energy, Office of Science.
• 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:

• Workshop on Modeling, Analysis and Simulation of Multiscale Nonlinear Systems to be held at Oregon State University, June 25-29
• Rocky Mountain Mathematics Consortium Summer School
• Multiscale Mathematics and High-Performance Computing Summer School
• 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