Reduced-order modeling of large linear subcircuits via a block Lanczos algorithm
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Matrix algorithms
The Quadratic Eigenvalue Problem
SIAM Review
Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
SIAM Journal on Matrix Analysis and Applications
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Mathematics and Computers in Simulation
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Abstract: Numerical simulations of the behavior of machine tools are usually based on a finite element (FE) discretization of their mechanical structure. After linearization one obtains a second-order system of ordinary differential equations. In order to capture all necessary details the system that inevitable arises is too complex to meet the expediency requirements of real time simulation and control. In commercial FE simulation software often modal reduction is used to obtain a model of lower order which allows for faster simulation. In recent years new methods to reduce large and sparse dynamical systems emerged. This work concentrates on the reduction of certain FE systems arising in machine tool simulation with Krylov subspace methods. The main goal of this work is to discuss whether these methods are suitable for the type of application considered here. Several Krylov subspace methods for first or second-order systems were tested. Numerical examples comparing our results to modal reduction are presented.