Proper Orthogonal Decomposition-Based Model Order Reduction of Delayed PEEC Models

The Partial Element Equivalent Circuit (PEEC) method is an electromagnetic computational method that has attracted a lot of attention for its capability to represent electromagnetic phenomena by equivalent circuits. This allows combining mixed EM-circuit problems in a straightforward manner, which proves to be very useful for mixed EM-circuit problems. However, the PEEC models can result of large size and therefore it becomes important to have modeling techniques that can compress the size of these models while retaining accuracy. Model order reduction (MOR) is a very effective way to achieve this goal. In this paper, we present a proper orthogonal decomposition (POD) based MOR for PEEC models that are described by neutral delayed differential equations (NDDEs). NDDEs require dedicated MOR schemes since the form of those equations is definitely more complex that standard quasi-static PEEC models described by standard (non-delayed) differential equations. The proposed PEEC-MOR method is validated by pertinent numerical results.