Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

A Library for Pattern-based Sparse Matrix Vector Multiply

Pattern-based Representation (PBR) is a novel approach to improving the performance of Sparse Matrix-Vector Multiply (SMVM) numerical kernels. Motivated by our observation that many matrices can be divided into blocks that share a small number of distinct patterns, we generate custom multiplication kernels for frequently recurring block patterns. The resulting reduction in index overhead significantly reduces memory bandwidth requirements and improves performance. Unlike existing methods, PBR requires neither detection of dense blocks nor zero filling, making it particularly advantageous for matrices that lack dense nonzero concentrations. SMVM kernels for PBR can benefit from explicit prefetching and vectorization, and are amenable to parallelization. The analysis and format conversion to PBR is implemented as a library, making it suitable for applications that generate matrices dynamically at runtime. We present sequential and parallel performance results for PBR on two current multicore architectures, which show that PBR outperforms available alternatives for the matrices to which it is applicable, and that the analysis and conversion overhead is amortized in realistic application scenarios