As high-performance computing moves to the petascale and beyond, a number of algorithmic and software challenges need to be addressed. This paper reviews the main performance-limiting factors in today's highperformance computing software and outlines a possible new programming paradigm to address them. The proposed paradigm is based on abstract parallel data structures and operations that encapsulate much of the complexity of an application, but still make communication overhead explicit. The authors argue that all numerical simulations can be formulated in terms of the presented abstractions, which thus define an abstract semantic specification language for parallel numerical simulations. Simulations defined in this language can automatically be translated to source code containing the appropriate calls to a middleware that implements the underlying abstractions. Finally, the structure and functionality of such a middleware are outlined while demonstrating its feasibility on the example of the parallel particle-mesh library (PPM).