Linear and Nonlinear Solvers for Environmental Modeling

Dr. Klíe's research focuses on optimizing algorithms for data-driven applications that couple geophysical modeling and flow simulation. In this project, he and his group tackle some particularly complex problems of groundwater flow in unsaturated systems, when the system is being recharged from the ground surface (e.g., by rain or, in the case of oil drilling practices, injection of water into wells). In such cases, the boundary conditions imposed by the physiographic framework and the distribution of recharge can be extremely variable. In environmental quality modeling, complexity arises from coupling specific state variables and constitutive relations with the equations that describe such phenomena as transport of a substance (e.g., water) through variable media (e.g., rocks of varying porosity). The bottleneck in solution of model groundwater and similar systems is the time spent in solving the linear and nonlinear systems of equations that govern the flows. Dr. Klíe and his group are using the Lonestar machine at TACC to develop scalable, parallel, and efficient solvers for unsaturated flow problems, addressing in particular the problems imposed by variable boundary conditions.