Model reduction for linear and nonlinear magneto‐quasistatic equations

We consider model reduction for magneto‐quasistatic field equations in the vector potential formulation. A finite element discretization of such equations leads to large‐scale differential‐algebraic equations of special structure. For model reduction of linear systems, we employ a balanced truncation approach, whereas nonlinear systems are reduced using a proper orthogonal decomposition method combined with a discrete empirical interpolation technique. We will exploit the special block structure of the underlying problem to improve the performance of the model reduction algorithms. Furthermore, we discuss an efficient evaluation of the Jacobi matrix required in nonlinear time integration of the reduced models. Copyright © 2017 John Wiley & Sons, Ltd.