A Proper Generalized Decomposition-Based Solver for Nonlinear Magnetothermal Problems

This paper investigates solving coupled magnetothermal problems through a proper generalized decomposition-based non-incremental approach. The magnetodynamic and thermodynamic problems are strongly coupled as the electric material property changes with the temperature while the temperature field evolves due to the Joule heat generated by induced currents. A challenge to solve the coupled problem is that the electric time constant can be several orders of magnitude smaller than the thermal one. Solution through a classical time integration approach requires too many time steps, especially when a long duration needs to be simulated, hence making the problem size too large to be handled. The proposed solver overcomes this difficulty through decomposing unknown dynamic fields into the space and time modes and solving the linearized systems in space and time iteratively, using the finite element method. The material nonlinearity can be incorporated in a straightforward way. The advantages of the proposed solver are demonstrated in solving an academic problem.