Parallel 3D Adaptive Mesh Refinement in Titanium

We describe a 3-dimensional adaptive mesh refinement Poisson solver. The complete program consists of about 3,500 lines of Titanium code and runs on both shared-memory and distributed-memory architectures. This paper focuses on the algorithm and on our experiences in writing AMR and tuning its performance. 1 Introduction This paper is a case study in the use of an experimental programming language in implementing a useful numerical method---adaptive mesh refinement (AMR) for solving Poisson's equation, \Delta' = ae, over the cube\Omega = [0; 1] 3 . Poisson's equation and its close relatives arise in many applications such as fluid mechanics, gravitation, heat flow, and electromagnetics. Poisson solvers are also used as components of some other PDE solvers. The authors have been involved in the design and implementation of the Titanium language, a dialect of Java intended for use in parallel computation [9]. Here, we attempt to show that Titanium is well-suited to the implementation ..