An Enhanced Reduced Basis Method for Wideband Finite Element Method Simulations

Abstract

In this paper, we present a novel strategy for selecting expansion points in the reduced basis method. A single computation of the error estimator is used to select a few expansion points in the multi-parameter space simultaneously. The number of selected points is determined adaptively, based on the accuracy of the current reduced model. The reliability and efficiency of this proposed approach are illustrated by numerical tests considering real-life structures, including dielectric resonator filter, H-plane filter, and four-pole dielectric-loaded cavity filter. INDEX TERMS Model-order reduction, a posteriori error estimator, finite element method.

Reduced Order Modeling and Sliding Mode Control of Active Magnetic Bearing

“…The bias current nullifies the weight mg of the AMB system and control current helps for the dynamic movement of this system. Now, subtracting out the equilibrium conditions (2), (3) and (4) from the total expressions (5), (6) and 7, we get the equation for displaced state of the rotor as…”

“…There are different numerical techniques for modeling and analysis of AMB like finite element method, finite difference method, boundary element method, etc. In the case of magnetic field analysis in AMB systems, Finite Element Method (FEM) has been preferred [4]- [6] for its flexibility and versatility. The simulation analysis for three and four coil AMB using FEM has been shown in [7].…”

A Model-Order Reduction Approach for Electromagnetic Problems With Nonaffine Frequency Dependence

“…In the last two decades, many algorithms have been proposed to accelerate frequency-domain FEM simulationsin other words, to perform a so-called fast-frequency sweep (FFS). One of the most popular FFS techniques is based on the concept of model-order reduction (MOR) [2]- [15]. In this approach, a large-scale Finite-element (FE) full-order model (FOM) is projected onto a properly constructed subspace, resulting in a so-called reduced-order model (ROM).…”

“…However, since the size of the ROM is much smaller than the FOM, the frequency sweep with the ROM is much faster. In the reduced-basis method (RBM) family of MOR techniques [6], [14], [15], the projecting basis is composed of a set of field solutions (called snapshots) computed by means of FOM at selected expansion (frequency) points. The number and placement of the expansion points within the frequency range is determined by following a greedy strategy, supported by a residual-based a posteriori error estimator [14].…”

“…The global FEM system of equations is constructed (line 25) and solved (line 26) at this frequency. The computed block V i is orthogonalized using the Gram-Schmidt method, and added to the projection basis V. The algorithm stops once all the expansion points in the sets have been examined (lines [13][14][15]. It is worth noting that the steps 5 and 19 can be performed extremely rapidly using the fast FEM matrix generation approach [33].…”