The alternating active-phase algorithm has recently been used to solve multi-material topology optimization (TO) problems. The algorithm splits the multi-material problem into several two-material problems that are inexactly solved in a sequential way, using a nonlinear programming method. The coupling of the solutions is done using a Gauss-Seidel scheme, which means that, form materials, m(m - 1)/2 subproblems need to be solved at each iteration, resulting in a high computational cost when the problem is very large. Besides, algorithm convergence depends on reducing the filter radius, which can also increase computational cost. In this work, we propose a new alternating active-phase algorithm for solving multi-material TO problems. The new algorithm solves m subproblems with one material per iteration, using the non-monotonic spectral projected gradient method. This combination greatly reduces the overall time required to solve the problem. Furthermore, the convergence of the proposed algorithm does not depend on reducing the filter radius. The efficiency of the new method is supported by experiments with some classical topological optimization problems.
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机译:交变有源相算法最近被用于解决多材料拓扑优化(TO)问题。该算法使用非线性规划方法将多材料问题拆分为几个双材料问题,这些问题以顺序方式不精确求解。解的耦合是使用高斯-塞德尔方案完成的,这意味着,在每次迭代中都需要求解 m(m - 1)/2 个子问题,当问题非常大时,计算成本很高。此外,算法收敛依赖于滤波半径的减小,这也会增加计算成本。在这项工作中,我们提出了一种新的交变有源相位算法,用于求解多材料TO问题。新算法使用非单调光谱投影梯度方法,每次迭代用一种材料求解 m 个子问题。这种组合大大减少了解决问题所需的总时间。此外,所提算法的收敛性不依赖于滤波半径的减小。通过一些经典拓扑优化问题的实验,支持了新方法的效率。
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