An Interface from M++ to Ginkgo for Accelerated Linear Algebra on HPCs

The M++ [1] finite element library is designed for large-scale, MPI-parallelized simulations on CPU-based HPC systems, with applications in scientific computing like wave propagation, cardiovascular simulations, dislocation dynamics, and uncertainty quantification. However, it traditionally lacked the ability to leverage the massive parallelism of modern multi-GPU architectures.We address this by introducing a new linear algebra backend based on the high-performance Ginkgo library [2], enabling M++ to flexibly and efficiently utilize heterogeneous HPC systems. Our interface is designed to efficiently convert M++’s data structures into the Ginkgo formats so that Ginkgo can handle the linear solve. This “Ginkgo solver” can be configured to use any of Ginkgo’s preconditioners or solvers. The new features are added to M++’s advanced CI pipeline that not only tests but also benchmarks and guarantees compatibility with projects that rely on M++ [3].We showcase the multi-GPU performance on the HoreKa HPC, highlighting a successful strategy for porting large, MPI-based applications to heterogeneous architectures. [1] N. Baumgarten and C. Wieners. The parallel finite element system M++ with in-tegrated multilevel preconditioning and multilevel Monte Carlo methods. Comput. Math. Appl., 81:391–406, 2021. ISSN 0898-1221. doi: 10.1016/j.camwa.2020.03.004.[2] H. Anzt, T. Cojean, G. Flegar, F. Göbel, T. Grützmacher, P. Nayak, T. Ribizel, Y. M. Tsai, and E. S. Quintana-Ortí. Ginkgo: a modern linear operator algebra frameworkfor high performance computing. ACM Trans. Math. Software, 48(1):Art. 2, 33, 2022.ISSN 0098-3500. doi: 10.1145/3480935.[3] N. Baumgarten and D. Corallo. Continuous Benchmarking of Numerical Algorithms Implemented in M++ via Gitlab CI/CD and Google Benchmark. Proceedings of the 9th bwHPC Symposium 2023