Mesh algorithms for PDE with Sieve I: Mesh distribution. Scientific Programming 17

We have developed a new programming framework, called Sieve, to support parallel numerical PDE1 algorithms operating over dis-tributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on dis-tributed containers conforming to the Sieve interface. Sieve makes in-stances of the incidence relation, or arrows, the conceptual first-class objects represented in the containers. Further, generic algorithms act-ing on this arrow container are systematically used to provide natural geometric operations on the topology and also, through duality, on the data. Finally, coverings and duality are used to encode not only individual meshes, but all types of hierarchies underlying PDE data structures, including multigrid and mesh partitions. In order to demonstrate the usefulness of the framework, we show how the mesh partition data can be represented and manipulated us-ing the same fundamental mechanisms used to represent meshes. We 1Partial differential equation(s). 1 present the complete description of an algorithm to encode a mesh par-tition and then distribute a mesh, which is independent of the mesh dimension, element shape, or embedding. Moreover, data associated with the mesh can be similarly distributed with exactly the same al-gorithm. The use of a high level of abstraction within the Sieve leads to several benefits in terms of code reuse, simplicity, and extensibility. We discuss these benefits and compare our approach to other existing mesh libraries.