Computational scientists are frequently confronted with a choice: implement algorithms using high-level abstractions, such as matrices and mesh entities, for greater programming productivity or code them using low-level language constructs for greater execution efficiency. We have observed that the cost of implementing a representative unstructured mesh code with high-level abstractions is poor computational intensity---the ratio of floating point operations to memory accesses. Related scientific applications frequently produce little ``science per cycle'' because their abstractions both introduce additional overhead and hinder compiler analysis and subsequent optimization. Our work exploits the semantics of abstractions, as employed in unstructured mesh codes, to overcome these limitations and to guide a series of manual, domain-specific optimizations that significantly improve computational intensity.

We propose a framework for the automation of such high-level optimizations within the ROSE
source-to-source compiler infrastructure.
The specification of optimizations is left to
domain experts and library writers who best understand the semantics of their applications and libraries and who are thus best poised to describe their optimization.
Our source-to-source approach translates different constructs (e.g., C code written in a procedural style or C++ code written in an object-oriented style) to a procedural form in order to simplify the specification of optimizations. This is accomplished through raising operators, which are specified by a domain expert and are used to
project a concrete application from an implementation space to an abstraction space, where optimizations are applied. The transformed code in the abstraction space is then reified as a concrete implementation via lowering operators, which are automatically inferred by inverting the raising operators. Applying optimizations within the abstraction space, rather than the implementation space, leads to greater optimization portability.

We use this framework to automate two high-level optimizations. The first uses an inspector/executor approach to avoid costly and redundant traversals of a static mesh by memoizing the relatively few references required to perform the mathematical computations. During the executor phase, the stored entities are accessed directly without resort to the indirection inherent in the original traversal. The second optimization lowers an object-oriented mesh framework, which uses C++ objects to access the mesh and iterate over mesh entities, to a low-level implementation, which uses integer-based access and iteration.