A multilevel approach to algorithm and software design for exaflops supercomputers

A strategy is proposed for the development of algorithms and software for exaflops supercomputers. This strategy consists of three stages. The first stage is the co-design understood as considering the architecture of the supercomputer at all steps of the development of the code. The second stage is the forward-looking development of algorithms and software for the most promising exaflops supercomputers. The forward-looking development is based on the simulation of the algorithm behavior within a given supercomputer architecture. The third stage is the estimation of energy efficiency of the algorithm with various implementations for a particular architecture or for different supercomputer architectures. The proposed approach is illustrated by the examples of solving two problems from astrophysics and plasma physics.