论文标题
使用Fenics计算螺旋电容器
Spiral capacitor calculation using FEniCS
论文作者
论文摘要
该论文展示了如何使用强大的Python库Fenics优化由圆柱体和螺旋金属条纹组成的水位传感器。它显示了如何使用螺旋坐标系将3D拉普拉斯方程式减少到2D；如何指定开放区域的正确边界条件；如何将部分微分方程转换为fenics的变分形式；以及如何计算电容。然后显示了求解拉普拉斯方程并计算电容的Fenics代码。进一步的数字实验表明，螺旋频率和条纹的宽度是最大化传感器灵敏度的最佳组合。给出了Python代码以计算最佳。
The paper shows how to optimize a water level sensor consisting of a cylinder with spiraling metal stripes on the side, using a powerful Python library FEniCS. It is shown how to reduce a 3D Laplace equation to a 2D, using a spiraling coordinate system; how to specify the correct boundary conditions for an open region; how to convert the partial differential equation to a variational form for FEniCS; and how to calculate the capacitance. Then the FEniCS code is shown that solves the Laplace equation and calculates the capacitance. The further numeric experiments show that there is an optimal combination of the spiral frequency and the width of the stripes that maximizes the sensitivity of the sensor. The Python code is given to calculate the optimum.
