VP5-13 Topology Optimization for a Magnetic Actuator Using Different Gradient-Based Solvers
Creators: Mohamed Reda Mahmoud
Mohamed N. Ibrahim
and Peter Sergeant
Publisher: name: IEEE
Year: 2025

This paper presents a comparative study on density based topology optimization for a magnetic actuator using different gradient-based solvers. The applied solvers are method of moving asymptotes (MMA), interior point optimizer (IPOPT), and sparse nonlinear optimizer (SNOPT). The objective is to enhance the performance of the magnetic actuator in terms of maximizing the electromagnetic force by optimizing material distribution. The objective function is formulated using Maxwell stress tensor to calculate the force exerted on the armature. Density based method is implemented based on Solid Isotropic Material with Penalization (SIMP) as material interpolating scheme, Helmholtz filtering and hyperbolic tangent projection method. This study investigates the convergence behaviour, computational time, solution quality, and sensitivity for filtering and projection schemes of each solver. The results provide valuable insights into the strengths and limitations of MMA, IPOPT, and SNOPT in solving complex topology optimization problems, and offering guidance for selecting appropriate solvers. The results proved that applying topology optimization enhanced the performance of the magnetic actuator by increasing the force and reducing the amount of the material of optimal designs comparing to the initial c-core actuator. The obtained results proved that SNOPT is suitable for large scale problem as it has a robust convergence. However, it needs both filtering and projection to avoid the mechanical strength problems. MMA performance is robust gradient solver with low computational time and efficient solution. Efficient solutions can be achieved using IPOPT without high sensitivity for filtering and projection but not suitable for large-scale problems due to high computation time.References: [1] S. i. Park, S. Min, S. Yamasaki, S. Nishiwaki, and J. Yoo, "Magnetic Actuator Design Using Level Set Based Topology Optimization," IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 4037-4040, 2008. [2] S. Lim, T. Yamada, S. Min, and S. Nishiwaki, "Topology Optimization of a Magnetic Actuator Based on a Level Set and Phase-Field Approach," IEEE Transactions on Magnetics, vol. 47, no. 5, pp. 1318-1321, 2011. [3] C. Midha, M. H. Mohammadi, R. C. P. Silva, and D. A. Lowther, "Selection of Spatial Filters for ON/OFF Based Topology Optimization of a C-Core Electromagnetic Actuator," IEEE Transactions on Magnetics, vol. 55, no. 10, pp. 1-4, 2019.
This paper presents a comparative study on density based topology optimization for a magnetic actuator using different gradient-based solvers. The applied solvers are method of moving asymptotes (MMA), interior point optimizer (IPOPT), and sparse nonlinear optimizer (SNOPT). The objective is to enhance the performance of the magnetic actuator in terms of maximizing the electromagnetic force by optimizing material distribution. The objective function is formulated using Maxwell stress tensor to calculate the force exerted on the armature. Density based method is implemented based on Solid Isotropic Material with Penalization (SIMP) as material interpolating scheme, Helmholtz filtering and hyperbolic tangent projection method. This study investigates the convergence behaviour, computational time, solution quality, and sensitivity for filtering and projection schemes of each solver. The results provide valuable insights into the strengths and limitations of MMA, IPOPT, and SNOPT in solving complex topology optimization problems, and offering guidance for selecting appropriate solvers. The results proved that applying topology optimization enhanced the performance of the magnetic actuator by increasing the force and reducing the amount of the material of optimal designs comparing to the initial c-core actuator. The obtained results proved that SNOPT is suitable for large scale problem as it has a robust convergence. However, it needs both filtering and projection to avoid the mechanical strength problems. MMA performance is robust gradient solver with low computational time and efficient solution. Efficient solutions can be achieved using IPOPT without high sensitivity for filtering and projection but not suitable for large-scale problems due to high computation time.References: [1] S. i. Park, S. Min, S. Yamasaki, S. Nishiwaki, and J. Yoo, "Magnetic Actuator Design Using Level Set Based Topology Optimization," IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 4037-4040, 2008. [2] S. Lim, T. Yamada, S. Min, and S. Nishiwaki, "Topology Optimization of a Magnetic Actuator Based on a Level Set and Phase-Field Approach," IEEE Transactions on Magnetics, vol. 47, no. 5, pp. 1318-1321, 2011. [3] C. Midha, M. H. Mohammadi, R. C. P. Silva, and D. A. Lowther, "Selection of Spatial Filters for ON/OFF Based Topology Optimization of a C-Core Electromagnetic Actuator," IEEE Transactions on Magnetics, vol. 55, no. 10, pp. 1-4, 2019.