On the performance of maximum-principle enforcing methods applied to large-scale subsurface problems

Thursday, 18 December 2014
Satish Karra1, Justin Chang2 and Kalyana Nakshatrala2, (1)Los Alamos National Laboratory, Los Alamos, NM, United States, (2)University of Houston, Houston, TX, United States
It is well known that numerical formulations (either finite element, finite volume or finite difference) do not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. But these mathematical properties and physical constraints are important for predictive simulations in subsurface modeling. Recently, optimization-based methodologies have been proposed for diffusion-type equations that respect maximum principles and meet the non-negative constraint on general computational grids. Till date these methodologies have been tested only on small-scale academic problems with few thousands of degrees-of-freedom. But for practical problems in subsurface modeling, the degrees-of-freedom easily run into millions and sometimes into billions. The purpose of this research is to systematically study the performance of the non-negative methodologies for large-scale problems and in a parallel setting. We shall use PETSc for parallel environment, and TAO for parallel optimization solvers. Numerical simulations on real sites using our methodologies will be presented.