arXiv subjects

Dali Chang

Publications and source records attributed to Dali Chang.

2 recordsLinked to original sources

arXiv2026

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

MFEM is a widely used finite-element library, but its native linear-elasticity Partial Assembly (PA) path still applies an $O((p+1)^6)$ contraction in the element operator, leaving the CPU operator-throughput sweet spot near $p\approx 2$ 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 $7\text{--}83\times$ kernel speedup and $3.6\text{--}16.8\times$ end-to-end speedup across $p\in\{1,2,4,8\}$. 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 $p\ge 6$. 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 will be released on GitHub.

cs.DC↗

arXiv2025

Relative-Absolute Fusion: Rethinking Feature Extraction in Image-Based Iterative Method Selection for Solving Sparse Linear Systems

Iterative method selection is crucial for solving sparse linear systems because these methods inherently lack robustness. Though image-based selection approaches have shown promise, their feature extraction techniques might encode distinct matrices into identical image representations, leading to the same selection and suboptimal method. In this paper, we introduce RAF (Relative-Absolute Fusion), an efficient feature extraction technique to enhance image-based selection approaches. By simultaneously extracting and fusing image representations as relative features with corresponding numerical values as absolute features, RAF achieves comprehensive matrix representations that prevent feature ambiguity across distinct matrices, thus improving selection accuracy and unlocking the potential of image-based selection approaches. We conducted comprehensive evaluations of RAF on SuiteSparse and our developed BMCMat (Balanced Multi-Classification Matrix dataset), demonstrating solution time reductions of 0.08s-0.29s for sparse linear systems, which is 5.86%-11.50% faster than conventional image-based selection approaches and achieves state-of-the-art (SOTA) performance. BMCMat is available at https://github.com/zkqq/BMCMat.

cs.CV↗