Los Alamos National Laboratory Parallel Object - Oriented Adaptive Mesh Refinement

In this paper we study adaptive mesh refinement (AMR) for elliptic and hyperbolic systems. We use the Asynchronous Fast Adaptive Composite Grid Method (AFACx) [4], a parallel algorithm based upon the of Fast Adaptive Composite Grid Method (FAC) [5] as a test case of an adaptive elliptic solver. For our hyperbolic system example we use TVD and EN0 schemes for solving the Euler and MHD equations 125, 26, 271. We use the structured grid load balancer MLB [lo] as a tool for obtaining a load balanced distribution in a parallel environment. Parallel adaptive mesh refinement poses difficulties in expressing both the basic single grid solver, whether elliptic or hyperbolic, in a fashion that parallelizes seamlessly. It also requires that these basic solvers work together within the adaptive mesh refinement algorithm which uses the single grid solvers as one part of its adaptive solution process. We show that use of AMR++ [3], an object-oriented library within the OVERTURE Framework [ll], simplifies the development of AMR applications. Parallel support is provided and abstracted through the use of the P++ parallel array class [6, 7, 81.