Diagonalized Macromodels in Finite Element Method for Fast Electromagnetic Analysis of Waveguide Components

Abstract

A new technique of local model-order reduction (MOR) in 3-D finite element method (FEM) for frequency-domain electromagnetic analysis of waveguide components is proposed in this paper. It resolves the problem of increasing solution time of the reduced-order system assembled from macromodels created in the subdomains, into which an analyzed structure is partitioned. This problem becomes particularly relevant for growing size and count of the macromodels, and when they are cloned in multiple locations of the structures or are used repeatedly in a tuning and optimization process. To significantly reduce the solution time, the diagonalized macromodels are created by means of the simultaneous diagonalization and subsequently assembled in the global system. For the resulting partially diagonal matrix, an efficient dedicated solver based on the Schur complement technique is proposed. The employed MOR method preserves frequency independence of the macromodels, which is essential for efficient diagonalization, as it can be performed once for the whole analysis bandwidth. The numerical validation of the proposed procedures with respect to accuracy and speed was carried out for varying size and count of macromodels. An exemplary finite periodical waveguide structure was chosen to investigate the influence of macromodel cloning on the resultant efficiency. The results show that the use of the diagonalized macromodels provided a significant solution speedup without any loss of accuracy.

Recursive Domain Decomposition Approach in 2-D Time-Harmonic Wireless Power Transfer Simulations Considering Litz Wires

“…This results in the term −L W i in (22). The matrix L W u contains strand current mappings (5) for each subdomain block which map all the subdomain voltages to the global strand voltages…”

“…the end winding parts. By changing the block rows corresponding to u W g and i W g in (22), and the number of voltages and currents we can change the connection topology of the winding to e.g. parallelly connected turns.…”

“…The approach is based on a non-overlapping domain decomposition technique called Schur complement method [15], [16] which is sometimes called reduction to the interface, or, especially in mechanics, iterative substructuring [17], [18], and also shares similarities with static condensation [19], and macro element methods [20], [21], [22]. The relationships of the methods are discussed in [23].…”

On the Use of Quadrilateral Meshes for Enhanced Analysis of Waveguide Devices with Manhattan-Type Geometry Cross-Sections

“…The Finite Element Method (FEM) is a long-known well-established numerical method [1,2]. FEM has proven to be a powerful tool in all fields of engineering [3][4][5]. Specifically, in the arena of applied electromagnetics, FEM is a commonly used technique in the analysis and design of a wide variety of high-frequency components such as microwave circuits or antennas [6,7], either as a standalone tool or hybridized with other analytical or numerical methods.…”