Magnetic Modeling and Simulation for Computer Graphics

Abstract Physics‐based modeling and simulation have long been central to computer graphics, enabling the creation of realistic and expressive digital worlds. While extensive progress has been made in simulating physical phenomena of various materials, magnetic interactions, characterized by their long‐range, nonlinear, and material‐dependent nature, have only recently attracted sustained attention. Emerging research has explored magnetic effects across rigid bodies, deformable solids, ferrofluids, and magneto‐viscoelastic materials, leading to a diverse set of models and solvers. However, these efforts have often evolved in isolation, leaving the broader landscape fragmented. This survey provides the first consolidated perspective on magnetic modeling and simulation for computer graphics. We begin by revisiting the fundamentals of magnetostatics and magneto‐mechanical coupling, summarizing the governing equations that underlie existing methods. Building on this foundation, we review numerical algorithms in two complementary aspects: those addressing magnetic fields and magnetization, and those focused on force computation and integration with simulation frameworks. By clarifying common principles and comparing methodological choices, we discuss the successes and challenges of existing literature and outline promising directions for advancing the modeling and simulation of magnetic phenomena.