FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation

Abstract The full Maxwell equations in the unbounded three-dimensional space coupled to Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials. We propose weak formulation of system based on boundary integral exterior equations. show existence and partial uniqueness solution new numerical algorithm finite elements spatial discretization with backward Euler convolution quadrature time domain. This is first which able deal Maxwell’s without any simplifications like quasi-static approximations (e.g. eddy current model) restrictions shape domain convexity). well-posedness convergence under minimal assumptions regularity solution. particularly important there are few results available one generally expects be non-smooth. Numerical experiments illustrate expand theoretical results.