Parallel matrix-free computation of the gyrokinetic Poisson equation from fusion plasma applications using extrapolated geometric multigrid

Kurzfassung

This thesis has successfully achieved its primary objectives: transforming the legacy GMGPolar solver into a robust, maintainable, and scalable system, while further developing a GPU-accelerated implementation to significantly enhance its computational performance. Through a systematic refactoring process, the solver's architecture was restructured to improve modularity, readability, and adaptability. These enhancements not only ensure the solver's longevity but also facilitate its seamless integration into future gyrokinetic codes, such as GyselaX. By combining modern software engineering practices with high-performance computing techniques, this work provides a strong foundation for advancing large-scale gyrokinetic simulations and paves the way for further innovation in the field. In large-scale simulations, efficient memory usage is critical. The sheer volume of data processed - across thousands of cross-sections and millions of time steps - can quickly overwhelm computational resources. To address this challenge, the refactoring of GMGPolar prioritized minimizing the memory footprint. By restructuring the computational grid, we not only enhanced cache efficiency but also enabled additional structural and algorithmic improvements to the smoother. These changes resulted in a 60\% reduction in memory consumption and a significant decrease in computational complexity. Additionally, replacing the task-based approach with standard for-loop parallelization proved to be a pivotal step, ultimately resulting in a highly scalable solver. To further enhance performance, we introduced support for the `Take' method, exploring its potential to significantly accelerate execution times at the expense of increased memory usage. We also incorporated full multigrid cycle support to provide a robust initial approximation, which drastically reduced the number of iterations needed for convergence. The inclusion of W-cycle and F-cycle support further contributed to improved solver efficiency. Moreover, refactoring the code into a more object-oriented design not only streamlined the overall structure but also greatly facilitated the process of porting the solver to the GPU. Despite these advancements, certain challenges persist. The current grid configuration remains a limitation in terms of flexibility, which could hinder the seamless integration of GMGPolar into the GyselaX framework. Addressing this issue will require further research and innovation. Potential solutions may lie in domain decomposition and multipatch methods, which could divide the computational domain into smaller, more manageable regions. Such approaches would enable more flexible handling of complex geometries and pave the way for broader applicability in advanced simulation frameworks. In summary, the work presented in this thesis establishes a solid foundation for the evolution of the GMGPolar solver. The improvements in memory efficiency, computational speed, and code organization not only enhance current performance but also open up new possibilities for its application in complex, large-scale simulation environments.