GPU-Based Topology Optimization Using Matrix-Free Conjugate Gradient Finite Element Solver with Customized Nodal Connectivity Storage

Ratnakar, Shashi Kant; Sanfui, Subhajit; Sharma, Deepak

doi:10.1007/978-981-15-9956-9_9

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…However, when unstructured meshes are used, the elemental stiffness matrix for each element must be computed. In such case, EbE À strategy is preferable because it can ensure equal computational load among GPU threads and can prevent redundant data accesses associated with NbN and DbD strategies (Ratnakar et al, 2021a). However, an appropriate measure has to be taken to avoid "race condition" (Cecka et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Unstructured meshes, on the other hand, need to compute and store the elemental stiffness matrices of all mesh elements on GPU. Ratnakar et al (2021a) presented an EbE À based implementation of CG solver for 3D unstructured meshes. The atomic operations of CUDA (Nvidia, 2011) were used to alleviate the issue of "race condition" while storing the results of SpMV.…”

Section: Introductionmentioning

confidence: 99%

“…Unstructured meshes, on the other hand, need to compute and store the elemental stiffness matrices of all mesh elements on GPU. Ratnakar et al. (2021a) presented an EbE − based implementation of CG solver for 3D unstructured meshes.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ratnakar

Kiran²,

Sharma³

2022

Self Cite

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Graphics Processing Unit-Based Element-by-Element Strategies for Accelerating Topology Optimization of Three-Dimensional Continuum Structures Using Unstructured All-Hexahedral Mesh

Ratnakar

Sanfui

Sharma

2021

Journal of Computing and Information Science in Engineering

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Topology optimization has been successful in generating optimal topologies of various structures arising in real-world applications. Since these applications can have complex and large domains, topology optimization suffers from a high computational cost because of the use of unstructured meshes for discretization of these domains and their finite element analysis (FEA). This paper addresses this challenge by developing three GPU-based element-by-element strategies targeting unstructured all-hexahedral mesh for the matrix-free precondition conjugate gradient (PCG) finite element solver. These strategies mainly perform sparse matrix multiplication (SpMV) arising with the FEA solver by allocating more compute threads of GPU per element. Moreover, the strategies are developed to use shared memory of GPU for efficient memory transactions. The proposed strategies are tested with solid isotropic material with penalization (SIMP) method on four examples of 3D structural topology optimization. Results demonstrate that the proposed strategies achieve speedup up to 8.2× over the standard GPU-based SpMV strategies from the literature.

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GPU-Based Topology Optimization Using Matrix-Free Conjugate Gradient Finite Element Solver with Customized Nodal Connectivity Storage

Cited by 2 publications

References 10 publications

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

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

Graphics Processing Unit-Based Element-by-Element Strategies for Accelerating Topology Optimization of Three-Dimensional Continuum Structures Using Unstructured All-Hexahedral Mesh

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