A Unified Space–Time Finite Element Solution Framework for Electromagnetic–Mechanical Coupling Problems

<title>Abstract</title> <p>Electromagnetic–mechanical coupling problems are widely encountered in engineering applications. Traditional methods mostly adopt a solution paradigm that combines spatial finite element semi-discretization with temporal integration schemes. This paradigm may introduce numerical dissipation, energy drift, or fail to preserve the underlying symplectic structure during long-term transient simulations. To address these issues, this paper introduces a space–time finite element mesh and establishes a unified space–time discrete variational framework for electromagnetic–mechanical coupling problems, thereby avoiding the conventional treatment that separates spatial discretization from temporal integration. Based on the discrete variational formulation, a unified one-step recursive scheme applicable to both nondissipative and dissipative systems is constructed, enabling the displacement field and electromagnetic fields to be solved within a unified discrete framework. Through three benchmark examples—including pure electromagnetic field problems, elastodynamic problems, and sequentially coupled electromagnetic–mechanical problems—the proposed method demonstrates its capability to accurately solve different types of physical problems within a unified framework and preserve the symplectic structure of nondissipative systems. This paper provides a unified computational approach for electromagnetic 1 fields, structural dynamics, and electromagnetic–mechanical coupling problems, enabling accurate and long-term stable transient simulations.</p>