Efficiently solving large sets of coupled scalar species is critical in several scientific and industrial domains, ranging from computational fluid dynamics to chemical reaction kinetics. Traditional algorithms face scalability and computational efficiency challenges, especially when dealing with complex configurations characterised by high Reynolds numbers and elevated pressures. To address these challenges, this Innovation Study presents a disruptive algorithm that aims to efficiently solve large sets of coupled scalar species using the spectral element method (SEM) in conjunction with mixed-precision evaluation on graphics processing units (GPUs). By combining SEM with state-of-the-art GPU capabilities, this study anticipates significant improvements in both time-to-solution and energy-to-solution compared to current algorithms. This approach not only promises significant improvements in computational performance, but also overcomes the memory limitations inherent in today’s GPU architectures, enabling the simulation of industrially relevant configurations that were previously unattainable with classical algorithms.

At the heart of Ex3S is the Spectral Element Method (SEM), a high-order numerical technique known for its accuracy and efficiency in handling complex geometries and boundary conditions. SEM is able to achieve superior solution accuracy while efficiently exploiting the computational capabilities of modern GPUs. For greater computational efficiency, mixed-precision evaluation techniques are employed, taking advantage of the computational power offered by GPUs with improved memory bandwidth and throughput. This integration introduces challenges such as Gibbs-type oscillations and scaling issues due to reduced local problem sizes. To address these challenges, this study employs a novel hybrid stabilisation approach for SEM coupled with asynchronous communication techniques. Furthermore, the use of SEM elements instead of classical grid points overcomes the memory limitations of today’s GPU architectures and allows for larger setups, which are crucial for industrial applications with increased pressure and high Reynolds numbers. This method ensures efficient data transfer and synchronisation between GPU cores. Experiments have shown promising results, with significant speed-ups and energy savings across a range of test cases.

In conclusion, Ex3S as a disruptive algorithm enables the efficient solution of large sets of coupled scalar species by integrating the spectral element method with mixed-precision evaluation on GPUs. This Innovative Study offers significant improvements in computational performance and memory utilisation, and enables the simulation of industrially relevant configurations. This study aims to demonstrate the effectiveness and scalability of Ex3S in various scientific and industrial domains.