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

The Partial Element Equivalent Circuit (PEEC) method has gained significant 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 effectively reduce their size while preserving accuracy. Model order reduction (MOR) serves as a highly effective approach to accomplish this objective. This paper presents two MOR techniques based on proper orthogonal decomposition (POD) for PEEC models described by neutral delayed differential 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 differential 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 efficiency of the proposed PEEC-MOR methods are demonstrated through multiple relevant numerical results in both the frequency-domain and time-domain.