A New Type of Macro-Elements for Efficient Two-Dimensional FEM Analysis

Efficient Model Order Reduction for Fem Analysis of Waveguide Structures and Resonators

“…First, we shall present extension of model order reduction procedure, proposed in [10] for 2-D, to 3-D vector problems. To this end a simple waveguide structure (Figure 1) is considered.…”

“…In order to compress Ω 1 , Ω 2 into macro-elements by means of model order reduction (MOR) [10] using the ENOR algorithm [3], Equation (4) have to be transformed to the following form:…”

“…They are generated by applying model order reduction locally in selected subdomains that require strong mesh refinement. The efficiency of the macromodeling technique was demonstrated for finite difference methods in time or frequency domain [6][7][8], as well as for the finite element method [9][10][11].…”

“…This paper addresses the problem of applying model order reduction locally via macro-elements in a three-dimensional finite element analysis of waveguide structures and resonators. It is based on the general idea presented in [10], where 2-D scalar FEM method and macro-elements reduced by the ENOR algorithm [3] were used. In this reduction technique, selected parts of FEM matrices are compressed one by one by projecting their relevant blocks onto a subspace spanned by an orthonormal basis, which is generated by the ENOR algorithm for one, arbitrarily chosen frequency.…”

“…This is an important distinguishing feature of our approach, which implies two fundamental advantages: it is sufficient to make the reduction only once for wide frequency sweeps and, moreover, this approach can be employed in eigenvalue problems in order to allow for their solving solely, by means of standard techniques. So far we have demonstrated the application of the new type of frequency-independent macroelements in 2-D FEM [10]. A direct extension of the 2-D method to the 3-D analysis requires introducing 3-D vectorial FEM formulation.…”