A two-kernel based strategy for performing assembly in FEA on the graphics processing unit

Sanfui, Subhajit; Sharma, Deepak

doi:10.1109/amiams.2017.8069221

Cited by 9 publications

(3 citation statements)

References 19 publications

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“…Based on this observation, the authors concluded that the LMA approach is suitable for a GPU and that the Addto approach is suitable for a CPU. Recently, Sanfui and Sharma [46] proposed a modified Addto approach for a GPU using two kernels. For 3D domain discretization, each node is associated with 3 DoFs.…”

Section: Assembly To Form Global Matrixmentioning

confidence: 99%

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

2018

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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.

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Section: Assembly To Form Global Matrixmentioning

confidence: 99%

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

2018

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“…GPU has been utilized to accelerate various computational tasks of FEA, such as computation of elemental matrices (Sanfui and Sharma, 2018, 2020), assembling the global stiffness matrix (Sanfui and Sharma, 2017, 2019; Kiran et al. , 2019) and solution of a system of linear equations (Kiran et al.…”

Section: Introductionmentioning

confidence: 99%

Acceleration of structural topology optimization using symmetric element-by-element strategy for unstructured meshes on GPU

Ratnakar

Kiran²,

Sharma³

2022

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PurposeStructural topology optimization is computationally expensive due to the involvement of high-resolution mesh and repetitive use of finite element analysis (FEA) for computing the structural response. Since FEA consumes most of the computational time in each optimization iteration, a novel GPU-based parallel strategy for FEA is presented and applied to the large-scale structural topology optimization of 3D continuum structures.Design/methodology/approachA matrix-free solver based on preconditioned conjugate gradient (PCG) method is proposed to minimize the computational time associated with solution of linear system of equations in FEA. The proposed solver uses an innovative strategy to utilize only symmetric half of elemental stiffness matrices for implementation of the element-by-element matrix-free solver on GPU.FindingsUsing solid isotropic material with penalization (SIMP) method, the proposed matrix-free solver is tested over three 3D structural optimization problems that are discretized using all hexahedral structured and unstructured meshes. Results show that the proposed strategy demonstrates 3.1× –3.3× speedup for the FEA solver stage and overall speedup of 2.9× –3.3× over the standard element-by-element strategy on the GPU. Moreover, the proposed strategy requires almost 1.8× less GPU memory than the standard element-by-element strategy.Originality/valueThe proposed GPU-based matrix-free element-by-element solver takes a more general approach to the symmetry concept than previous works. It stores only symmetric half of the elemental matrices in memory and performs matrix-free sparse matrix-vector multiplication (SpMV) without any inter-thread communication. A customized data storage format is also proposed to store and access only symmetric half of elemental stiffness matrices for coalesced read and write operations on GPU over the unstructured mesh.

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“…Sanfui and Sharma [16] developed an advance version of addTo GPU based two kernel approach. In descertization of 3D domain, each DOF was further connected with three DOFs.…”

Section: Introductionmentioning

confidence: 99%

Performance Comparison of GPU-Based Jacobi Solvers Using CUDA Provided Synchronization Methods

et al. 2020

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In this manuscript, variants of Jacobi solver implementation on general purpose graphical processing units (GPGPU) have been purposed and compared. During this work, parallel implementation of finite element method (FEM) using Poisson's equation on shared memory architecture as well as on GPGPUs has been observed to identify computationally most expensive part of FEM software, which is linear algebra Jacobi solver. Sparse matrices were used for system of linear equations. Nine implementations of Jacobi solver have been developed and compared using various synchronization and computation methods like atomicAdd, atomicAdd_block, butterfly communication, grid synchronization, hybrid and whole GPU based computation methods, respectively. Experiments have showed that Jacobi implementations based on our implemented Butterfly communication method have outperformed CUDA 10.0 provided critical execution methods like atomicAdd, atomicAdd_block and grid methods. The GPU has achieved a max speedup of 46 times using GTX 1060 and 60 times using Quadro P4000 with double precision computations when compared with sequential implementation on Core-i7 8750H. All the developments were performed using C/C++ GNU compiler 7.3.0 on Ubuntu 18.04 and CUDA 10.0.

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A two-kernel based strategy for performing assembly in FEA on the graphics processing unit

Cited by 9 publications

References 19 publications

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

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

Acceleration of structural topology optimization using symmetric element-by-element strategy for unstructured meshes on GPU

Performance Comparison of GPU-Based Jacobi Solvers Using CUDA Provided Synchronization Methods

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