Topology optimization is a computational method that optimally distributes materials within a design domain. The method is becoming popular in the initial stages of design. As opposed to the traditional mechanics, topology optimization is now being used in an array of engineering domains. Some approaches have been used in the topology optimization including the level set method. Unlike other approaches that implement explicit material representation, the level set method-based topology optimization models geometric constraints through implicit boundary description.
However, implicit boundary description comes with a problem depending on the initial guess. In a majority of conventional level set-based approaches implementing the finite difference method, the time step size must be restrained to some condition in a bid to ensure numerical stability of the time-marching process. Above all, it calls for re-initialization of the level-set function if gets too flat or too steep. This normally reduce the efficiency of the topology optimization.
Researchers led by professor Yingjun Wang from South China University of Technology, China, studied the parallelization of the topology optimization problem domain with level set method as well as isogeometric analysis. They discussed the computational procedure of every step of the optimization approach. Their work is published in peer-reviewed journal, Structural and Multidisciplinary Optimization.
The authors verified the performance of the parallel topology optimization algorithm implementing the isogeometric analysis as well as non-uniform rational B-splines-based parameterized level set method through three benchmarks. The three benchmarks were; the quarter annulus problem, Messerschmidt-Bölkow-Blohm beam, and the cantilever beam problem.
The authors set the default test parameters. The elastic modulus of the solid material was set as 1.0 and that of weak material at 0.0001. The Poisson’s ratio was set at 0.3. The terminal criterion was picked as the relative difference of the objective function values between successive iterations (0.0001). The volume ratio was set at 0.5.
Graphics Processing Unit (GPU) parallel method indicated relatively high speedups for the initial design domain, sensitivity analysis, stiffness matrix assembly, and the update scheme in the topology optimization. The authors used the cantilever beam problem with varying mesh scales to validate the effectiveness of the GPU approach for the level set method-based topology optimization implementing the isogeometric analysis by comparing it with the CPU.
Messerschmidt-Bölkow-Blohm beam was implemented to analyze the impact of the mesh scale on the topology. In addition, the authors implemented the quarter annulus problem with a curve design domain to analyze the inherent errors between the GPU and the CPU. These examples indicated that the GPU could effectively solve the topology optimization problems.
The extent of this paper focused on the minimum compliance problem of the topology optimization, however, the proposed parallel approach will not be restricted to this specific problem but it will be extended to deal other problems. Above all, it can be improved further in the aspects of multiple GPU devices as well as distributed parallel computing with MPI.
Zhaohui Xia1, Yingjun Wang2, Qifu Wang3, Chao Mei3.GPU parallel strategy for parameterized LSM-based topology optimization using isogeometric analysis. Struct Multidisc Optim (2017). doi:10.1007/s00158-017-1672-xShow Affiliations
- Center for Modeling, Simulation and Imaging in Medicine (CeMSIM)Rensselaer Polytechnic Institute, Troy, USA
- School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, China
- National CAD Support Software Engineering Research Center, Huazhong University of Science and Technology, Wuhan, China
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