Abstract
We present new GPU implementations of the tensor contractions arising from basis-related computations for high-order finite element methods. We consider both tensor and non-tensor bases. In the case of tensor bases, we introduce new kernels based on a series of fused device-level matrix multiplications (GEMMs), specifically designed to utilize the fast memory of the GPU. For non-tensor bases, we develop a tuned framework for choosing standard batch-BLAS GEMMs that will maximize performance across groups of elements. The implementations are included in a backend of the libCEED library. We present benchmark results for the diffusion and mass operators using libCEED integration through the MFEM finite element library and compare to those of the previously best-performing GPU backends for stand-alone basis computations. In tensor cases, we see improvements of approximately 10-30% for some cases, particularly for higher basis orders. For the non-tensor tests, the new batch-GEMMs implementation is twice as fast as what was previously available for basis function order greater than five and greater than approximately 105 degrees of freedom in the mesh; up to ten times speedup is seen for eighth-order basis functions.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of ScalA 2020 |
| Subtitle of host publication | 11th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, Held in conjunction with SC 2020: The International Conference for High Performance Computing, Networking, Storage and Analysis |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 53-60 |
| Number of pages | 8 |
| ISBN (Electronic) | 9781665422703 |
| DOIs | |
| State | Published - Nov 2020 |
| Externally published | Yes |
| Event | 11th IEEE/ACM Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2020 - Virtual, Atlanta, United States Duration: Nov 13 2020 → Nov 13 2020 |
Publication series
| Name | Proceedings of ScalA 2020: 11th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, Held in conjunction with SC 2020: The International Conference for High Performance Computing, Networking, Storage and Analysis |
|---|
Conference
| Conference | 11th IEEE/ACM Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems, ScalA 2020 |
|---|---|
| Country/Territory | United States |
| City | Virtual, Atlanta |
| Period | 11/13/20 → 11/13/20 |
Funding
This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, LLNL-CONF-815596. This research was supported by NVIDIA and the Exascale Computing Project (ECP), Project Number: 17-SC-20-SC, a collaborative effort of two DOE organizations (the Office of Science and the National Nuclear Security Administration) responsible for the planning and preparation of a capable exascale ecosystem, including software, applications, hardware, advanced system engineering, and early testbed platforms, in support of the nation's exascale computing imperative.
Keywords
- GPU
- Tensor contractions
- batched linear algebra
- finite elements
- high-order methods
- matrix-free FEM