Efficient Frequency and Time-Domain Simulations of Delayed PEEC Models With Proper Orthogonal Decomposition Techniques

Abstract

The Partial Element Equivalent Circuit (PEEC) method has gained signicant recognition as an electromagnetic computational technique known for its ability to represent electromagnetic phenomena using equivalent circuits. This feature makes it particularly valuable for addressing mixed EM-circuit problems. However, PEEC models often exhibit large dimensions, necessitating modeling techniques that can eectively reduce their size while preserving accuracy. Model order reduction (MOR) serves as a highly eective approach to accomplish this objective. This paper presents two MOR techniques based on proper orthogonal decomposition (POD) for PEEC models described by neutral delayed dierential equations (NDDEs). The unique characteristics of NDDEs demand specialized MOR approaches, as their formulation is inherently more complex compared to standard quasi-static PEEC models described by non-delayed dierential equations. In addition to a traditional one-shot singular value decomposition (SVD), this paper also presents an incrementally computed SVD to evaluate the orthogonal matrix needed to generate the reduced order matrices. The accuracy and eciency of the proposed PEEC-MOR methods are demonstrated through multiple relevant numerical results in both the frequency-domain and time-domain.INDEX TERMS Partial element equivalent circuit (PEEC) method, model order reduction, proper orthogonal decomposition, frequency-domain analysis, and time-domain analysis.

Mixed Riccati–Lyapunov Balanced Truncation for Order Reduction of Electrical Circuit Systems

“…To reduce the order of electrical and electronic circuit systems, there are several groups of methods and algorithms to mention, such as the Krylov subspace methods group [5]; techniques related to the iterative rational Krylov algorithm (IRKA) such as Asymptotic Waveform Evaluation (AWE) [6], Lanczos and the Arnold-algorithm [7], Padé approximation [8], etc. ; the Proper Orthogonal Decomposition (POD) [9] group of methods and similar algorithms such as Principal Component Analysis (PCA) [10], etc. ; the group of algorithms on Modal Truncation (MT) [11,12] and improved technique Subspace Accelerated Dominant Pole Algorithm (SADPA) [13]; and the technical group on Gramian balance, represented by balanced truncation (BT) [14], with improved algorithms such as frequencylimited balanced truncation [15], time-limited balanced truncation [16], bounded-real balanced truncation [17], positive-real balanced truncation (PRBT) [18], balanced stochastic truncation [19], linear-quadratic Gaussian balanced truncation [20], H-infinity balanced truncation [21], Hankel-norm approximation [22], etc.…”