Model Order Reduction for Magneto-Quasistatic Equations

Dynamic iteration and model order reduction for magneto-quasistatic systems

“…The algebraic constraints should be treated carefully when approximating the system. A naive application of the existing model reduction methods to DAEs may lead to an inaccurate approximation and physically meaningless results [GSW13, KS15,Sty11]. We will exploit the special block structure of the semidiscretized MQS system to transform it into a system of ODEs.…”

Model reduction for linear and nonlinear magneto‐quasistatic equations

“…Multiplying system (58) from the left with the orthogonal matrix T as in (18) and taking into account that Y T X 2 = 0 and YY T + ZZ T = I, we have…”

“…in blocks according to T in (18) and computing the SVD where Σ a 1 ∈ R r 1 ,r 1 contains the dominant singular values of X a 1 . Then the reduced-order model is obtained by projectingẼ…”

“…They should be treated carefully when approximating the system. A naive application of the existing model reduction methods to DAEs may lead to an inaccurate approximation and physically meaningless results . We will exploit the special block structure of the semidiscretized MQS system to transform it into a system of ordinary differential equations (ODEs).…”

“…First note that the differential and algebraic components of the state vector x are mixed in the reduced‐order model . Secondly, the reduction of the algebraic components and the algebraic constraints in DAEs may lead to inaccurate and physically meaningless results, see .…”