Multi-parametric sweep of large-scale FEM models using the BT-POD

The design and optimization of high-frequency electronic systems such as antenna and microwave devices requires scanning and searching over various design parameter spaces that include frequency, material permittivity, permeability, or excitation (i.e., scan angles). Such sweeps require repeatedly solving the computational model (FEM or BEM) at various different parameter value combinations, leading to very slow computational design cycles. This paper presents a methodology for performing such sweeps in a fast manner. A multi-parametric model order reduction (MOR) scheme based on the recently developed balanced truncation proper orthogonal decomposition (BT-POD) MOR [1], [2] is introduced to handle such sweeps. In contrast to the previous multi-parameter MOR presented in [3] and [4] that are based on Krylov model reduction, this work adopts the SVD-based reduction paradigm of BT-POD. The multi-parameter space sweep in this work is achieved in a two-step procedure: (1) An off-line (learning) stage where a coarse parameter space POD sampling is used to produce the multi-dimensional balancing transformations, followed by (2) an online (sweep) stage that performs the fine sampled parameter-space sweep via the solution of the reduced model. The system gramians [5] approximation involved in this MOR paradigm is obtained through the use of numerical integration over parameter spaces of interest, therefore such MOR technique can be extended to moderately high-dimensional parameter spaces using specialized Monte-Carlo and sparse grid integration strategies. The POD sampling is straightforwardly parallelizable, leading to farther time savings.