The main focus of this project is to investigate dynamic, h-p adaptive strategies, based on mathematically-sound error estimates, for the numerical solution of shallow water models.
A major outcome of the proposed research is a computing portal which will enable reservoir simulation and geophysical calculations to interact dynamically with the data and with each other and that will provide a variety of visual and quantitative tools.
The main objective of this project is to develop new approaches for solving linear and nonlinear problems in saturated-unsaturated groundwater flow application that ranges from higher-order Newton-Krylov methods and preconditioning by means of constraint/decoupling operators for two-phase flow.
During 2002-2003, under EQM006, a posteriori error bounds and estimators/indicators have been derived for several time dependent EQM applications and prototype software has been developed.
The ultimate goal is to develop a geomechanics/reservoir model with millions of degrees of freedom implemented on NPACI resources.
A mathematical approach coupled with quantitative experiments will permit one to elucidate the inter-cellular growth patterns of the vessels within a tissue subjected to other biological and physical indicators.
Our team has focused on developing angiogenesis strategies for the fields of autologous tissue transfer and tissue engineering, specifically to repair tissue deficits resulting from tumor resection, trauma, and congenital abnormalities.
Our objective is to develop a comprehensive uncertainty quantification framework to describe the fate and transport of energetic materials in the vadose and saturated zones underlying DoD's firing ranges.