M-Tree: A Parallel Abstract Data Type for Block-Irregular Adaptive Applictions

This paper describes an abstract data type called M-Tree — a generalization of a quadtree which captures both the data structure and computational structure common to many adaptive problems in science and engineering. It is equipped with a rich set of access functions including higher-order operators describing commonly used computational patterns in parallel adaptive computations. This provides a uniform high level abstraction of a wide range of applications including adaptive mesh refinement and adaptive particle simulation and thus enables such applications to be constructed systematically and efficiently. We present examples in which an M-tree is used to solve both an adaptive heat-flow problem and N-body particle simulation. The structured abstraction of commonly-occurring computation patterns in the application provides us with the opportunity to investigate various approaches to load balancing and communication minimization using caching and other techniques. These optimizations are applicable to other problems with a similar structure.