Route to exascale: Novel mathematical methods, scalable algorithms and Computational Science skills

This editorial outlines the research context, the needs and challenges on the route to exascale. In particular the focus is on novel mathematical methods and mathematical modeling approaches together with scalable scientific algorithms that are needed to enable key science applications at extreme-scale. This is especially true as HPC systems continue to scale up in compute node and processor core count. These extreme-scale systems require novel mathematical methods to be developed that lead to scalable scientific algorithms to hide network and memory latency, have very high computation/communication overlap, have minimal communication, have fewer synchronization points. It stresses the need of scalability at all levels, starting from mathematical methods level through algorithmic level, and down to systems level in order to achieve overall scalability. It also points out that with the advances of Data Science in the past few years the need of such scalable mathematical methods and algorithms able to handle data and compute intensive applications at scale becomes even more important. The papers in the special issue are selected to address one or several key challenges on the route to exascale.