Strongly Coupled Simulation of Magnetic Rigid Bodies

We present a strongly coupled method for the robust simulation of linear magnetic rigid bodies. Our approach describes the magnetic effects as part of an incremental potential function. This potential is inserted into the reformulation of the equations of motion for rigid bodies as an optimization p...

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Bibliographic Details
Published in:Computer graphics forum Vol. 43; no. 8
Main Authors: Westhofen, L., Fernández‐Fernández, J. A., Jeske, S. R., Bender, J.
Format: Journal Article
Language:English
Published: Oxford Blackwell Publishing Ltd 01.12.2024
Subjects:
Equations of motion
Magnetic effects
Magnets
Optimization
Potential energy
Rigid structures
Robustness
Simulation
Systems stability
Time integration
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary:We present a strongly coupled method for the robust simulation of linear magnetic rigid bodies. Our approach describes the magnetic effects as part of an incremental potential function. This potential is inserted into the reformulation of the equations of motion for rigid bodies as an optimization problem. For handling collision and friction, we lean on the Incremental Potential Contact (IPC) method. Furthermore, we provide a novel, hybrid explicit / implicit time integration scheme for the magnetic potential based on a distance criterion. This reduces the fill‐in of the energy Hessian in cases where the change in magnetic potential energy is small, leading to a simulation speedup without compromising the stability of the system. The resulting system yields a strongly coupled method for the robust simulation of magnetic effects. We showcase the robustness in theory by analyzing the behavior of the magnetic attraction against the contact resolution. Furthermore, we display stability in practice by simulating exceedingly strong and arbitrarily shaped magnets. The results are free of artifacts like bouncing for time step sizes larger than with the equivalent weakly coupled approach. Finally, we showcase the utility of our method in different scenarios with complex joints and numerous magnets.
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ISSN:0167-7055
1467-8659
DOI:10.1111/cgf.15185