Future Directions for Adaptive Mesh Refinement in ASCI and Other LLNL Simulation Projects

We have surveyed various computational applications at Lawrence Livermore National Laboratory to determine future directions for adaptive mesh refinement (AMR) resemch and simulation technology. AMR techniques were originally developed for the numerical solution of hyperbolic equations in computational fluid dynamics. However, scientists are now beginning to extend this AIvfR methodology to new applications domains, including problems modeled by tightly coupled systems of hyperbolic and elliptic/parabolic equations, neutron trzmsport, hybrid approaches that combine different physical models (e.g., discrete and continuum), and Arbitrary Lagrangian Eulerian (ALE) methods. Extending the traditional AMR approach to these applications domains will require a better understanding of numerical methods, algorithms, fast linear and nonlinew solvers, parallelization techniques, and software frameworks. The future needs identified in this survey provide the basis for ongoing AMR research within the Center for Applied Scientific Computing (CASC) in support of ASCI and other Lab oratory efforts. To that end, we have begun the development of a parallel prototyping framework that will facilitate numerical and algorithmic exploration in AMR applications ad enable scientists to rapidly explore extensions of existing AMR technology.