A Semantics-based Approach to Optimizing Unstructured Mesh Abstractions

ions obfuscate; they should instead illuminate. The use of high-level abstractions, such as matrices and differential operators, is a key to achieving high-productivity scientific computing [44]. Abstractions are frequently implemented in domain-specific libraries as user-defined types and the procedures acting on them. Such abstractions are a closer match to the concepts and notations employed in scientific domains than low-level implementations that expose raw details, such as matrix element storage and mesh spacing. Ignoring such details allows domain experts to more concisely setup and solve problems. For example, Dinesh et al. [21] found a 30% reduction in code size and, with it, a significant and quantifiable improvement in programmer productivity and code maintainability when side-effect free algebraic notion was used to solve partial differential equations rather than an object-oriented style inconsistent with mathematical notion. Choosing from a library of well-constructed abstractions improves code reuse, and with it software maintainability, and allows domain experts to focus their efforts on science rather than on computer science. The attendant improved productivity can have a significant impact on funding since scientific applications at government laboratories, such as Lawrence Livermore National Laboratory, are evaluated primarily on the richness of their feature sets.