BT-POD: A parallel and error-controllable wideband model reduction method for frequency-domain simulations

Abstract

Ultra Wide Band (UWB) electromagnetic (EM) systems are ubiquitous in computing, communication and sensing applications. The design of such systems is often performed with time-domain or model order reduction (MOR) frequency-domain computational EM techniques. This paper will present a new MOR method that will be used in conjunction with the tangential vector finite elements (TVFEM) for the analysis of lossless, lossy, and infinitely periodic EM systems. Among MOR methods the Krylov subspace (or moment matching) techniques [1] have attracted much of the CEM community's attention because they are computationally efficient. Unfortunately, these methods do not offer error controls and indicators, and the inherent orthogonalization of the relatively large basis set often brakes-down and is difficult to parallelize. On the other extreme, the singular value decomposition (SVD) MOR methods [2] are very robust and offer error controls, but are computationally prohibitive since they require the solution of two Lyapunov equations. This paper introduces a hybrid SVD-Krylov technique based on the Balanced Truncation - Proper Orthogonal Decomposition (BT-POD). The method combines the best features of the two categories, namely offers error controls and indicators while preserving the efficiency of Krylov MOR. The most time consuming step related to the POD sampling is embarrassingly parallel, making the method suitable for multi-core computing. The method is related to the Principal Component Analysis (PCA) of pattern recognition and machine learning, and shares the same spirit with the low-rank POD of Willcox et.al. [3], Phillips' poor-man's TBR [4]. and the Choleski Factor -Alternating Direction Implicit (CF-ADI) algorithm [5].