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首页> 外文期刊>SIAM Journal on Control and Optimization >Analysis of shape optimization for magnetic microswimmers
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Analysis of shape optimization for magnetic microswimmers

机译：磁性微泳裤的形状优化分析

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摘要

We analyze an infinite dimensional, geometrically constrained shape optimization problem for magnetically driven microswimmers (locomotors) in three-dimensional (3-D) Stokes flow and give a well-posed descent scheme for computing optimal shapes. The problem is inspired by recent experimental work in this area. We show the existence of a minimizer of the optimization problem using analytical tools for elastic rods that respect the excluded volume constraint. We derive a variational gradient descent method for computing optimal locomotor shapes using the tools of shape differential calculus. The descent direction is obtained by solving a saddle-point system, which we prove is well-posed. We also introduce a finite element approximation of the gradient descent method and prove its stability. We present numerical results illustrating our method and the effect that finite aspect ratio and external cargo can have on the optimal shape. The 3-D Stokes equations are solved by a boundary integral method.
机译：我们分析了三维（3-D）斯托克斯流中的磁驱动微游泳器（运动马达）的无穷维几何约束形状优化问题，并给出了用于计算最佳形状的恰当的下降方案。这个问题是受到最近在该领域的实验工作的启发。我们显示了使用弹性工具的分析工具来优化问题的最小化器，该工具遵循排除的体积约束。我们导出了一种变分梯度下降方法，用于使用形状微积分的工具来计算最佳运动形状。下降方向是通过求解鞍点系统获得的，我们证明它是适当的。我们还介绍了梯度下降法的有限元逼近，并证明了其稳定性。我们提供的数值结果说明了我们的方法以及有限长宽比和外部货物对最佳形状的影响。通过边界积分法求解3-D Stokes方程。

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