Computers are becoming more and more powerful, and the structure of modern parallel computers is simultaneously becoming more and more complicated. Therefore, it is not a very easy task to tune an already existing computer program to efficiently solve very big computational problems, for example, when one parallel architecture is replaced by another. This is why it is worthwhile to develop some autotuning tools for existing parallel code that will be run on different parallel architectures.

Scherg et al. discuss the possibility of achieving, in a relatively easy way, good performance via automatic tuning, particularly in cases where explicit methods for solving large systems of ordinary differential equations (ODEs) are handled. The goal to ensure good performance when implementing hybrid MPI/OpenMP code for solving ODE systems via parallel iterated Runge-Kutta (PIRK) methods.

Scherg et al. describe their approach very carefully. They provide many pieces of short code to help readers understand the main ideas and the decisions made. Numerical results are presented in several tables and figures. At the end of the paper, they sketch plans to more efficiently apply these ideas in the future, including to more complicated numerical problems.

The results described in this paper are very important; partial differential equations (PDEs) describe many scientific and engineering models, which are transformed into huge systems of ODEs after the discretization of the spatial derivatives. As mathematician Arthur Jaffe explained, in 1984:

Although the fastest computers can execute millions of operations in one second, they are always too slow. This may seem like a paradox, but the heart of the matter is that the bigger and better computers become, the larger are the problems scientists and engineers want to solve. [1]

This is why scientists and engineers cannot solely rely on the theoretical power of new computers. They must also design parallel algorithms that nearly automatically resolve any problems that arise when one parallel computer architecture is replaced by another.