Date & Time: Monday, August 2, 2010, 16:00-17:00.
Venue: Ramanujan Hall
Title:Multilevel Solution Algorithms on Adaptively Refined Grids: Analysis and Performance
Speaker: Bobby Philip
Computer Science and Mathematics Division, Oak Ridge National Laboratory
Abstract: Continuum partial differential equation (PDE) descriptions of complex physical phenomena often exhibit multiscale solution features that span extreme spatio- temporal scales. Examples include magnetohydrodynamics (MHD), multiphase multicomponent reactive groundwater flows, hurricane system models, and astrophysical jets, where the spatial and temporal scales often easily span more than six orders in magnitude. Accuracy considerations often dictate that fine scale solution features be resolved. However, uniform grid simulation at the finest resolution required are infeasible even on today’s largest supercomputers and will continue to be so for the foreseeable future. Adaptive mesh refinement (AMR) is a numerical technique to introduce local grid resolution only where required, significantly reducing the memory footprint and computational cost associated with such simulations. This talk will concentrate on two aspects for the accurate, efficient, and robust long term time integration of stiff multiscale, multiphysics systems on AMR grids. Firstly, the mathematical analysis and performance of an asynchronous multilevel iterative solution algorithm, AFACx, for elliptic PDE systems will be described. AMR level independent condition number estimates for the AFACx error propagation operator will be presented and the performance of the solver on First Order System Least Squares (FOSLS) formulations of scalar elliptic and Stokes systems on curvilinear AMR grids will be presented. Secondly, examples of accurate and efficient implicit time integration of nonlinear 2D reduced resistive MHD, equilibrium, and non-equilibrium radiation diffusion on AMR grids will be presented. Time permitting, ongoing research on massively parallel groundwater flow simulations on AMR grids and the design of scientific computing frameworks will be briefly presented.