Model reduction for linear and nonlinear magneto‐quasistatic equations. (14th February 2017)

• Record Type: Journal Article
• Authors: Kerler‐Back, Johanna; Stykel, Tatjana
• Is Part Of: International journal for numerical methods in engineering. Volume 111:Number 13(2017)
• Page Start: 1274
• Page End: 1299
• Publication Date: 2017-02-14
• Subjects: Maxwell's equations -- magneto‐quasistatic problems -- model order reduction -- balanced truncation -- proper orthogonal decomposition -- discrete empirical interpolation method; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5507
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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.