Sarcouncil Journal of Applied Sciences Aims & Scope

Abstract: Finite element methods (FEM) provide a powerful framework for solving Maxwell’s equations in complex domains, supporting advances in electromagnetics, photonics, antenna design, and biomedical applications. Despite their versatility, scalable FEM faces persistent challenges, including the prohibitive computational cost of large-scale 3D discretizations, indefinite and ill-conditioned system matrices, and the need to preserve divergence constraints. This study reviews the mathematical foundations of FEM for Maxwell’s equations, emphasizing weak formulations, edge elements, and strategies for suppressing spurious modes. It also surveys computational bottlenecks such as solver inefficiencies, absorbing boundary conditions, and multiscale geometry representation. Recent progress in preconditioning, multigrid solvers, GPU acceleration, and domain decomposition is highlighted, alongside opportunities in multiphysics integration, adaptive refinement, and machine learning–assisted solvers. Finally, the role of open-source frameworks is discussed as a catalyst for innovation and broad accessibility. The paper concludes that scalable FEM is essential for extending electromagnetic simulation to increasingly complex and high-impact applications.