article published Jan Bohn author Michael Feischl author Balázs Kovács author 1004410000-0001-9872-3474 841 department <jats:title>Abstract</jats:title> <jats:p>The full Maxwell equations in the unbounded three-dimensional space coupled to the Landau–Lifshitz–Gilbert equation serve as a well-tested model for ferromagnetic materials. We propose a weak formulation of the coupled system based on the boundary integral formulation of the exterior Maxwell equations. We show existence and partial uniqueness of a weak solution and propose a new numerical algorithm based on finite elements and boundary elements as spatial discretization with backward Euler and convolution quadrature for the time domain. This is the first numerical algorithm which is able to deal with the coupled system of Landau–Lifshitz–Gilbert equation and full Maxwell’s equations without any simplifications like quasi-static approximations (e.g. eddy current model) and without restrictions on the shape of the domain (e.g. convexity). We show well-posedness and convergence of the numerical algorithm under minimal assumptions on the regularity of the solution. This is particularly important as there are few regularity results available and one generally expects the solution to be non-smooth. Numerical experiments illustrate and expand on the theoretical results.</jats:p> Walter de Gruyter GmbH2022 eng Applied MathematicsComputational MathematicsNumerical Analysis 1609-4840 1609-938910.1515/cmam-2022-0145 23119-48 Bohn, Jan, Michael Feischl, and Balázs Kovács. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” <i>Computational Methods in Applied Mathematics</i> 23, no. 1 (2022): 19–48. <a href="https://doi.org/10.1515/cmam-2022-0145">https://doi.org/10.1515/cmam-2022-0145</a>. J. Bohn, M. Feischl, and B. Kovács, “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation,” <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, pp. 19–48, 2022, doi: <a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>. Bohn J, Feischl M, Kovács B. FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational Methods in Applied Mathematics</i>. 2022;23(1):19-48. doi:<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a> @article{Bohn_Feischl_Kovács_2022, title={FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation}, volume={23}, DOI={<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>}, number={1}, journal={Computational Methods in Applied Mathematics}, publisher={Walter de Gruyter GmbH}, author={Bohn, Jan and Feischl, Michael and Kovács, Balázs}, year={2022}, pages={19–48} } Bohn, Jan, et al. “FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation.” <i>Computational Methods in Applied Mathematics</i>, vol. 23, no. 1, Walter de Gruyter GmbH, 2022, pp. 19–48, doi:<a href="https://doi.org/10.1515/cmam-2022-0145">10.1515/cmam-2022-0145</a>. J. Bohn, M. Feischl, B. Kovács, Computational Methods in Applied Mathematics 23 (2022) 19–48. Bohn, J., Feischl, M., &#38; Kovács, B. (2022). FEM-BEM Coupling for the Maxwell–Landau–Lifshitz–Gilbert Equations via Convolution Quadrature: Weak Form and Numerical Approximation. <i>Computational Methods in Applied Mathematics</i>, <i>23</i>(1), 19–48. <a href="https://doi.org/10.1515/cmam-2022-0145">https://doi.org/10.1515/cmam-2022-0145</a> 459562023-07-10T11:43:13Z2024-04-03T09:20:30Z