An execution time and energy model for an energy-aware execution of a conjugate gradient method with CPU/GPU collaboration

• Execution time and energy model for a conjugate gradient method.
• Energy-aware workload distribution to the CPU and the GPU based on prediction by the model.
• Model-based dynamic redistribution of workload between the CPU and the GPU during execution.
• Model derived from the experiments covering energy, time, DVFS, and data transfer.

The parallel preconditioned conjugate gradient method (CGM) is used in many applications of scientific computing and often has a critical impact on their performance and energy consumption. This article investigates the energy-aware execution of the CGM on multi-core CPUs and GPUs used in an adaptive FEM. Based on experiments, an application-specific execution time and energy model is developed. The model considers the execution speed of the CPU and the GPU, their electrical power, voltage and frequency scaling, the energy consumption of the memory as well as the time and energy needed for transferring the data between main memory and GPU memory. The model makes it possible to predict how to distribute the data to the processing units for achieving the most energy efficient execution: the execution might deploy the CPU only, the GPU only or both simultaneously using a dynamic and adaptive collaboration scheme. The dynamic collaboration enables an execution minimising the execution time. By measuring execution times for every FEM iteration, the data distribution is adapted automatically to changing properties, e.g. the data sizes.