Li Ming (State Key Lab of CAD&CG, Zhejiang University)
*Zhao Dengyang (State Key Lab of CAD&CG, Zhejiang University)
This paper mainly focuses on the topology optimization technology for 3-D printing product design. Using traditional topology optimization technology is able to design the optimal structure of a specified physical property. However, usually the designing requirement cannot be fully achieved, particularly in 3D cases, due to the very high computational costs involved it. In order to resolve this issue, the paper presents an approach that drastically accelerates the solution computation of 3-D structural topology optimization problems on a standard PC. The high performance is achieved in two aspects. Firstly, the improvement of computing speed is mainly achieved via a fast FE computation during each step of the optimization process. During each of the finite elements computation, the main costs are due to the stiffness matrix assembly, and solving the large-scaled linear equations. Based on the fact that the stiffness matrix is sparse and symmetric, the conjugate gradient method is applied. Additionally, in order to speed up the computation, a pre-conditioner using multi-grid is applied to decrease the condition number of the stiffness matrix to reduce the iteration numbers. The pre-conditioner is computed once, and used during each step of the optimization process, and thus greatly reduce the computational costs. Secondly, the complex computations are transplanted to the Graphic Processing Unit (GPU) platform implemented via the Compute Unified Device Architecture (CUDA), This is achieved via a parallel implementation of both the stiffness matrix assembly and linear solution computation. Consequently, superfast speed is achieved by executing the computation in parallel and making full use of the shared memory due to its high speed. In the experiment, the performing speed on GPU is more than 50 times faster than on CPU while solving a topology optimization problem on a 150×150×200 mesh grid using conjugate gradient method. Combined the above two techniques, the goal of superfast computation comes true. It is possible to solve the topology optimization problem on a 100×100×100 mesh involving up to billions of degrees of freedom efficiently on GPU. Problems in this order of magnitude is too slow to solve on CPU and is impossible to give the final result. The research is quite meaningful in the sense that a standard PC can solve a large-scaled 3-D topology optimization problem at high precision for the 3-D printing product design.
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