Multilevel Model Order Reduction With Generalized Compression of Boundaries for 3-D Fem Electromagnetic Analysis

Abstract

Abstract-This paper presents a multilevel Model Order Reduction technique for a 3-D electromagnetic Finite Element Method analysis. The reduction process is carried out in a hierarchical way and involves several steps which are repeated at each level. This approach brings about versatility and allows one to efficiently analyze complex electromagnetic structures. In the proposed multilevel reduction the entire computational domain is covered with macro-elements which are subsequently nested, in such a way that size of the problem which has to be reduced at each level is relatively small. In order to increase the speed of the reduction at each level, the electric field at the macro-elements' boundaries is projected onto the subspace spanned by Legendre polynomials and trigonometric functions. The results of the numerical experiments confirm the validity and efficiency of the presented approach.

Efficient Analysis of Structures with Rotatable Elements Using Model Order Reduction

“…MOR is applied locally in such a way, that the subdomains of the computational domain are represented by small dense matrices, called macromodels. The mathematical formulation of this approach is similar to that presented in [10], the main difference being a new technique of incorporating the macromodels within a fixed mesh, that allows for a single macromodel to be either rotated or simultaneously rotated and replicated without the need to regenerate the mesh. This substantially speeds up the computation and makes a fast design tuning possible.…”

“…One of the techniques to improve the efficiency of FEM is to significantly reduce the size of the system matrix by applying the Model Order Reduction (MOR) techniques. The MOR presented in this paper has been thoroughly described in [8], [10]. The main idea is to develop the appropriate transfer functions, which accurately capture the behavior of the electromagnetic field within the selected subdomains.…”

“…S K 1 couples regions Ω 1 and Γ (see [8,10] for details). Note, that the excitation b 1 is applied only to the outer region Ω 1 .…”

“…It combines the meshing techniques from [5] with the model order reduction (MOR), which has been demonstrated previously for FDFD [6], [7], 2D FEM [8], [9] and 3D FEM [10], [11]. MOR is applied locally in such a way, that the subdomains of the computational domain are represented by small dense matrices, called macromodels.…”

“…In order to allow for rotation and at the same time to perform the orthogonal projection technique of [7], [10] we developed a new set of basis functions that is applicable to cylinders. The overall cost of the MOR procedure has been significantly reduced, as the computational domain can be easily decomposed and each region can be meshed independently and the new type of macromodels can be now fully reused and cloned to be placed in different locations.…”