Energy and Performance Improvement of Parallel ODE Solvers by Application-Specific Program Transformations

Solution methods for ordinary differential equations (ODEs) are important for science and engineering, for example when solving time-dependent partial differential equations (PDEs) with the method of lines. In this article, we investigate multithreaded solution methods for ODEs with a focus on their performance and energy behavior. In particular, we investigate application-specific program transformations that can be used to modify the memory access behavior of the ODE solvers without affecting their computational scheme and the resulting numerical behavior. We provide new multithreaded versions for ODE solvers and present a detailed investigation of the resulting performance and energy consumption considering different aspects, such as the ODE problem to be solved, the number of threads used, or the usage of frequency scaling. As ODE solvers, we use the popular embedded Runge-Kutta methods with error correction and apply them to ODEs resulting from discretized PDEs.