Simulation of Rigid Magnets in Motion
움직이는 강체 자석의 시뮬레이션
- 주제(키워드) Magnet simulation
- 발행기관 고려대학교 대학원
- 지도교수 한정현
- 발행년도 2021
- 학위수여년월 2021. 2
- 학위구분 박사
- 학과 대학원 컴퓨터학과(정보대학)
- 세부전공 소프트웨어
- 원문페이지 85 p
- UCI I804:11009-000000235785
- DOI 10.23186/korea.000000235785.11009.0001157
- 본문언어 영어
- 제출원본 000046071894
초록/요약
Since the first rigid magnet simulation is researched in the computer graphics field in 2008, rigid magnet simulations have been ecently studied. This thesis introduces how to simulate the interactions between rigid magnets in an effective, efficient and stable way. Firstly, it is investigated how to magnetize rigid magnets in an effective way. The scheme is based on magnetization dynamics showing the temporal behavior of magnetic moments. For magnetization dynamics, we adopted the Landau-Lifshitz-Gilbert equation, which is widely used in micromagnetics. It is extended into the macroscopic scale to be incorporated with rigid-body dynamics. Thanks to the properties of the Landau-Lifshitz-Gilbert equation, magnetic mutual induction and remanence can be effectively simulated. Secondly, we also demonstrate how to accelerate rigid magnets with given magnetic strengths. It is based on analytic solutions of the magnetic vector potential and flux density, which induce the magnetic forces and torques calculated using them and they seldom diverge. Therefore, the rigid magnet simulations can be stable although magnets are in close proximity or penetrate each other. Thanks to the stability, our method can simulate magnets of any shapes. Another strength of our method is that the time complexities for computing the magnetic forces and torques are significantly reduced, compared to the previous methods. Our method is easily integrated with classic rigid-body simulators. The experiment results presented in this thesis prove the stability and efficiency of our method.
more목차
1 Introduction 1
2 Related work 7
3 Equivalent Dipole Method 10
3.1 Magnetization and Magnetic Moment 10
3.2 Magnetic Force and Magnetic Torque 11
4 Magnetization Dynamics using Overlapped Magnetic Moments 13
4.1 Micromagnetics 13
4.1.1 Effective Magnetic Field 14
4.1.2 Landau-Lifshitz-Gilbert Equation 15
4.1.3 Numerical Integration for Magnetization Dynamics 18
4.2 Macro-scale Magnetization Simulation 20
4.2.1 Cell Decomposition and Magnetic Moments 20
4.2.2 Effective Magnetic Field at the Macro Scale 20
4.2.3 Saturated Magnetization 22
4.2.4 Magnet Modeling and Simulation 24
4.2.5 Magnetic Simulation + Rigid-body Simulation 29
4.2.6 Magnetic Remanence 30
4.3 Experimental Results and Discussions 32
4.3.1 Validation of Magnetization Curve 32
4.3.2 Mutual Induction 33
4.3.3 Magnetic Remanence 34
4.3.4 Performance 35
4.3.5 Simulation Stability 36
5 Magnetic Boundary Method 40
5.1 Magnetic Boundary Method 41
5.1.1 Magnetic Vector Potential and Flux Density 41
5.1.2 Magnetic Force and Torque 43
5.1.3 Magnetic Induction 47
5.2 Implementation 48
5.3 Experiment Results and Discussions 50
5.3.1 Mathematical Evaluation 51
5.3.2 Simulation 52
6 Conclusions 60
Appendix A Convergence of Net Magnetization of Multiple Magnetic Moments 62
Appendix B Closed-form Expressions of Wp(r) and ∇Wp(r) 65
Appendix C Closed-form Expression of ωe(r) 69
Bibliography 71
