The Finite Element Method (FEM) is a fundamental technique for solving large-scale and complex engineering problems. During the construction of the system equations, the efficiency of finite element matrix assembly plays a crucial role in the overall performance. However, existing approaches often overlook the sensitivity of assembly algorithm performance to mesh characteristics, making it difficult to achieve optimal performance across diverse problems. In this work, we propose a novel pattern-aware FEM matrix assembly method on GPUs. To this end, we thoroughly analyze the key factors affecting performance and extract a set of potentially influential mesh features and density representations. Based on this, we construct a Deep learning-based prediction model that fully captures the input mesh characteristics to predict the performance-optimal assembly strategy. Experimental results on mesh datasets with a wide range of feature variations demonstrate that our method achieves remarkable prediction accuracy and delivers up to$7.34 \times$speedup in execution time compared to state-of-the-art approaches. To the best of our knowledge, this is the first work that introduces auto-tuning for the FEM matrix assembly process.

Graph community detection is widely applied in fields such as genetic engineering and social network analysis.As the scale of input graphs continues to grow and multi-GPU platforms become increasingly prevalent, utilizing the storage capacity and computational power of these platforms to scale graph community detection algorithms has become more feasible.However, existing multi-GPU graph community detection methods are constrained by the traditional CPUdominated communication model, and fail to simultaneously account for the irregular sparse memory access patterns and the latency disparities between local and remote communication.Consequently, they do not fully exploit modern high-speed GPU interconnect technologies.Furthermore, while current solutions propose various strategies to mitigate the decline in clustering quality during parallelization, these approaches are often inefficient or compromise clustering quality.Finally, to address the high memory overhead of the algorithms, existing Multi-GPU solutions extend the graph size limit at the cost of reduced performance.To address these challenges, we propose MG-𝛼GCD, a novel graph community detection algorithm designed for multi-GPU platforms.First, MG-𝛼GCD introduces a loading balancing and latency-aware computation-communication pipeline that effectively mitigates the overhead of highlatency remote communication.Second, MG-𝛼GCD incorporates a bidirectional probing heuristic to enhance execution efficiency while outperforming existing methods in clustering quality.Lastly, MG-𝛼GCD employs a two-phase graph coarsening algorithm consisting of a symbolic phase and a numeric phase, which significantly reduces GPU peak memory usage and minimizes data transfers between CPU and

Sparse General Matrix-Matrix Multiplication (SpGEMM) serves as a fundamental operation in the domains of sparse linear algebra and graph data processing. The majority of existing research predominantly concentrates on optimizing SpGEMM in the context of single GPU scenarios. Nevertheless, the growing prevalence of multi-GPU systems offers opportunities to harness the computational capabilities of multiple GPUs, thereby enhancing the performance of sparse general matrix-matrix multiplication. The efficacy of multi-GPU SpGEMM is chiefly constrained by two factors: (1) the irregular sparse pattern of sparse matrices, and (2) the load imbalance among multiple GPUs. To address these challenges, this paper presents DeltaSPARSE, the first algorithm to achieve significant speed-up for large-scale SpGEMM on multiple GPUs, to the best of our knowledge. Our algorithm incorporates hybrid accumulators, which dynamically choose the most suitable accumulator algorithm for rows exhibiting varying levels of sparsity. Moreover, we suggest a hierarchical task scheduling approach to partition and allocate tasks across diverse levels of parallel hardware, such as GPU s, blocks, warps, and threads. Experimental outcomes utilizing the SuiteS parse matrix dataset reveal that DeltaSPARSE displays near-linear scalability in multi-GPU configurations. Furthermore, it attains substantial speed enhancements in comparison to the present state-of-the-art single GPU SpGEMM methods, including NSPARSE, spECK, bhSPARSE, and cuSPARSE, across matrices with various sparse characteristics.

Sparse general matrix-matrix multiplication (SpGEMM) is challenging especially on graphic accelerators. Existing solutions do not fully utilize the shared memory of the graphics accelerator. Our proposal could effectively utilize the graphics accelerator's on-chip shared memory and dynamically assign the device resources by grouping the rows based on a hybrid strategy for load balancing. Experiments show that our proposal achieves speedups of up to x7.43 in double precision compared to existing SpGEMM libraries. Our implementation is fully general and our optimization strategy adaptively processes the SpGEMM workload row-wise to substantially improve performance by decreasing the work complexity and utilizing the memory hierarchy more effectively.

Time-series waveform data widely exist in various industrial fields, such as equipment monitoring and fault diagnosis. The current time series representation methods have limitations when dealing with industrial abnormal time-series waveforms, such as limited applicability, semantic ambiguity, and time distortion. This work proposes a novel shape reference-based representation method for industrial abnormal time-series waveform (ShapeRef), which takes the shape of the standard waveform as a reference to represent the anomaly deviation. Specifically, ShapeRef first establishes a time-series shape reference frame, then proposes the minimum shape difference-based mapping method to describe the mapping process of coordinates, and finally reduces multi-intersection points in the mapping process to achieve uniform mapping of the abnormal time-series waveform. Experimental results show that ShapeRef can effectively represent abnormal time-series waveforms and outperforms several baseline methods in the clustering task of a real industrial equipment waveform dataset. This work enhances the accuracy and reliability of industrial equipment monitoring and fault diagnosis, which could have significant practical implications.

Large-scale finite element equations are usually solved by the Preconditioned Conjugate Gradient (PCG) iterative method, and the computational hotspots are sparse matrix-vector multiplication and inner product, which requires local and global communication. But, the latency of the high-performance cluster is too long for the PCG algorithm. This paper proposes a new asynchronous algorithm that could reduce the number of communication among cluster nodes to improve the scalability of finite element solvers. The performance could be improved up to 6.31 x.

SpMV (Sparse Matrix-Vector multiplication), in its simplest form y = Ax, multiplies a sparse matrix with a dense vector and is a widely used computing primitive in the domain of HPC. On the newly SW26010 many-core platform, we propose a highly efficient CSR (Compressed Storage Row) based implementation of parallel SpMV, referred to as SWCSR-SpMV in the sequel. SpMV in the CSR format can be trivially parallelized but its performance is majorly impeded by memory access efficiency, and therefore to leverage high-throughput memory access mechanism while avoiding redundant bandwidth usage becomes the major goal of designing high performance SpMV on the target platform. The original problem is sequentially partitioned into row-slices, each of which can reside in the fast scratchpad memory, so that the loaded x'es can be reused; meanwhile, a dynamic look-ahead scheme is applied to avoid redundant memory access; we split the many-core mesh into smaller communication scope to facilitate the sharing of the common data across the working threads via the high speed on-mesh data bus. Beyond the above, to leverage massive parallelism balanced workload is ensured by both static and dynamic means. Performance evaluation is done on a benchmark of 36 frequently used sparse matrices in the fields of graph computing, data mining, computational fluid dynamics, etc.. While the performance upper-bound is defined by the ratio between the minimal data access volume required against the practically optimal bandwidth, ignoring the computing overhead, SWCSR-SpMV can achieve an efficiency of nearly 87%, maintaining over 75% for 1/3 of the testing matrices. SWCSR-SpMV is further applied in a PETSc based application, a 1.75x-2.6x speedup is sustained in a multi-process environment on the Sunway TaiHuLight supercomputer.

In this paper we discuss about our experiences in improving the performance of GEMM (both single and double precision) on Fermi architecture using CUDA, and how the new features of Fermi such as cache affect performance. It is found that the addition of cache in GPU on one hand helps the processers take advantage of data locality occurred in runtime but on the other hand renders the dependency of performance on algorithmic parameters less predictable. Auto tuning then becomes a useful technique to address this issue. Our auto-tuned SGEMM and DGEMM reach 563 GFlops and 253 GFlops respectively on Tesla C2050. The design and implementation entirely use CUDA and C and have not benefited from tuning at the level of binary code.