GPGPU-based parallel computing applied in the FEM using the conjugate gradient algorithm: a review

Abstract

Parallelization of the finite-element method (FEM) has been contemplated by the scientific and high-performance computing community for over a decade. Most of the computations in the FEM are related to linear algebra that includes matrix and vector computations. These operations have the single-instruction multiple-data (SIMD) computation pattern, which is beneficial for shared-memory parallel architectures. General-purpose graphics processing units (GPGPUs) have been effectively utilized for the parallelization of FEM computations ever since 2007. The solver step of the FEM is often carried out using conjugate gradient (CG)type iterative methods because of their larger convergence rates and greater opportunities for parallelization. Although the SIMD computation patterns in the FEM are intrinsic for GPU computing, there are some pitfalls, such as the underutilization of threads, uncoalesced memory access, lower arithmetic intensity, limited faster memories on GPUs and synchronizations. Nevertheless, FEM applications have been successfully deployed on GPUs over the last 10 years to achieve a significant performance improvement. This paper presents a comprehensive review of the parallel optimization strategies applied in each step of the FEM. The pitfalls and tradeoffs linked to each step in the FEM are also discussed in this paper. Furthermore, some extraordinary methods that exploit the tremendous amount of computing power of a GPU are also discussed. The proposed review is not limited to a single field of engineering. Rather, it is applicable to all fields of engineering and science in which FEM-based simulations are necessary.

GPU Finite Element Method Computation Strategy Without Mesh Coloring

“…The CG method adapted to GPU [1], [10], [12], [18] is used in this work, whose computational cost is smaller and optimized than its EbE-FEM counterpart when the data is processed in the assembled matrix. The solver steps can be decomposed into variables initialization, inner products, vector updates and matrix-vector multiplications, operations with properties that can be exploited under parallel computing environments.…”

Accelerating the finite element analysis of functionally graded materials using fixed‐grid strategy on CUDA‐enabled GPUs

“…The parallelization in FEM has been carried out over two decades on multi‐core and many‐core architectures . There are some parallel libraries available to accelerate the performance of the FEM based applications, such as ParaFEM .…”

Node-to-Node Realization of Meshless Local Petrov Galerkin (MLPG) Fully in GPU

“…For meshless methods there are already partial solutions to the shape functions construction, numerical integration, interdependence relation among nodes, and application of boundary conditions [17], [18]. However, to the best of our knowledge, there is no meshless implementation that addresses the end-to-end problem, equivalent to the finiteelement method Element per Element -EbE-FEM [19], [20]. The most significant complication is that, in addition to calculating the node's contributions, it is also necessary to solve the equations system before it is entirely formed in memory.…”

“…An alternative, equivalent to the proposal for the EbE-FEM [19], [20] but applied to meshless methods, is to work with the individual node's contributions without building the system integrally. In the Meshless Local Petrov-Galerkin (MLPG) method [24] this is possible due to the property that each node subdomain can be integrated independently of the others [4], [17], [25].…”

“…FIGURE19. Time execution comparison between the knn-BF (''brute force'') algorithm (versions CPU, single thread, and GPU, many threads) and GPU knn-Grid (section III).…”