The Sparse General Matrix-Matrix Multiplication (SpGEMM) is widely used in a variety of applications. However, research on optimizing SpGEMM for high-performance digital signal processors (DSPs) has been limited. We present VES, a method to accelerate SpGEMM on multi-core DSPs, using the FT-M7032 platform as a case study. Based on the ESC algorithm, VES enhances computational efficiency through vectorized expansion operations, a double-buffering strategy, and an optimized vectorized sorting method. We provide an in-depth analysis of the bottlenecks in vectorized sorting and introduce an efficient vectorized reduction method that significantly improves instruction-level pipeline throughput. Experimental results show that VES outperforms existing methods HASH, ESC, and SPA by an average of 1.12×, 1.90×, and 22.34× on 1,931 sparse matrices, with maximum speedups of 8.69×, 65.9×, and 821.6×, respectively.

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this challenge by dynamically relocating mesh nodes to rapidly-varying regions, enhancing both simulation accuracy and computational efficiency. However, traditional approaches suffer from high computational complexity and geometric inflexibility, limiting their applicability, and existing supervised learning-based approaches face challenges in zero-shot generalization across diverse PDEs and mesh topologies. In this paper, we present an $\textbf{U}$nsupervised and $\textbf{G}$eneralizable $\textbf{M}$esh $\textbf{M}$ovement $\textbf{N}$etwork (UGM2N). We first introduce unsupervised mesh adaptation through localized geometric feature learning, eliminating the dependency on pre-adapted meshes. We then develop a physics-constrained loss function, M-Uniform loss, that enforces mesh equidistribution at the nodal level. Experimental results demonstrate that the proposed network exhibits equation-agnostic generalization and geometric independence in efficient mesh adaptation. It demonstrates consistent superiority over existing methods, including robust performance across diverse PDEs and mesh geometries, scalability to multi-scale resolutions and guaranteed error reduction without mesh tangling.

Turbulence, a complex multi-scale phenomenon inherent in fluid flow systems, presents critical challenges and opportunities for understanding physical mechanisms across scientific and engineering domains. Although high-resolution (HR) turbulence data remain indispensable for advancing both theoretical insights and engineering solutions, their acquisition is severely limited by prohibitively high computational costs. While deep learning architectures show transformative potential in reconstructing high-fidelity flow representations from sparse measurements, current methodologies suffer from two inherent constraints: strict reliance on perfectly paired training data and inability to perform multi-scale reconstruction within a unified framework. To address these challenges, we propose HADF, a hash-adaptive dynamic fusion implicit network for turbulence reconstruction. Specifically, we develop a low-resolution (LR) consistency loss that facilitates effective model training under conditions of missing paired data, eliminating the conventional requirement for fully matched LR and HR datasets. We further employ hash-adaptive spatial encoding and dynamic feature fusion to extract turbulence features, mapping them with implicit neural representations for reconstruction at arbitrary resolutions. Experimental results demonstrate that HADF achieves superior performance in global reconstruction accuracy and local physical properties compared to state-of-the-art models. It precisely recovers fine turbulence details for partially unpaired data conditions and diverse resolutions by training only once while maintaining robustness against noise.