Shifting the Sweet Spot: High-Performance Matrix-Free Method for High-Order Elasticity

MFEM is a widely used finite-element library, but the CPU operator-throughput sweet spot of its native linear-elasticity Partial Assembly (PA) path remains near polynomial degree p = 2 in our baseline measurements. This work closes this implementation gap for MFEM linear elasticity on affine tensor-product hexahedral meshes by integrating four well-established tensor-product PA optimizations (sum factorization, Voigt notation, macro-kernel fusion, and slice-wise loop reorganization) into MFEM’s native linear-elasticity PA path. The resulting operator is evaluated in high-order GMG-PCG solves using MFEM’s geometric multigrid (GMG) components. On AMD EPYC 7713, the optimized operator achieves 7–83× kernel speedup and 3.6–16.8× end-to-end speedup across p ∈ {1,2,4,8}. At fixed problem size, the kernel-time operator throughput peaks around p = 6 and remains high at p = 8, shifting the operator-throughput sweet spot to p ≥ 6. The same trend is reproduced on Huawei Kunpeng 920 (ARMv8.2). These results are accompanied by per-stage ablation and hardware-counter characterization; the implementation is publicly available at https://github.com/momoquq/mfem-elasticity-pa.