Model reduction using the Routh stability criterion and the Padé approximation technique

1975 ◽  
Vol 21 (3) ◽  
pp. 475-484 ◽  
Author(s):  
Y. SHAMASH
Keyword(s):  
Model Reduction ◽  
Stability Criterion ◽  
Padé Approximation ◽  
Approximation Technique ◽  
Pade Approximation

Model Reduction of Transfer Functions Using a Dominant Root Method

1990 ◽  
Vol 112 (3) ◽  
pp. 547-554 ◽  
Author(s):  
J. E. Seem ◽  
S. A. Klein ◽  
W. A. Beckman ◽  
J. W. Mitchell
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Model Reduction ◽  
Transfer Functions ◽  
Linear Time ◽  
Padé Approximation ◽  
Computational Effort ◽  
Pade Approximation ◽  
Bilinear Transformation ◽  
Transfer Problems

Transfer function methods are more efficient for solving long-time transient heat transfer problems than Euler, Crank-Nicolson, or other classical techniques. Transfer functions relate the output of a linear, time-invariant system to a time series of current and past inputs, and past outputs. Inputs are modeled by a continuous, piecewise linear curve. The computational effort required to perform a simulation with transfer functions can be significantly decreased by using the Pade´ approximation and bilinear transformation to determine transfer functions with fewer coefficients. This paper presents a new model reduction method for reducing the number of coefficients in transfer functions that are used to solve heat transfer problems. There are two advantages of this method over the Pade´ approximation and bilinear transformation. First, if the original transfer function is stable, then the reduced transfer function will also be stable. Second, reduced multiple-input single-output transfer functions can be determined by this method.

Convergence analysis of Padé approximations for Helmholtz frequency response problems

2018 ◽  
Vol 52 (4) ◽  
pp. 1261-1284 ◽  
Author(s):  
Francesca Bonizzoni ◽  
Fabio Nobile ◽  
Ilaria Perugia
Keyword(s):  
Hilbert Space ◽  
Boundary Value Problem ◽  
Padé Approximation ◽  
Approximation Error ◽  
Approximation Technique ◽  
Pade Approximation ◽  
Solution Map ◽  
Type Approximation ◽  
Numerical Tests ◽  
The Laplace Operator

The present work concerns the approximation of the solution map S associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution of the Helmholtz equation. We introduce a least squares rational Padé-type approximation technique applicable to any meromorphic Hilbert space-valued univariate map, and we prove the uniform convergence of the Padé approximation error on any compact subset of the interval of interest that excludes any pole. This general result is then applied to the Helmholtz solution map S, which is proven to be meromorphic in ℂ, with a pole of order one in every (single or multiple) eigenvalue of the Laplace operator with the considered boundary conditions. Numerical tests are provided that confirm the theoretical upper bound on the Padé approximation error for the Helmholtz solution map.

Sign in / Sign up

Export Citation Format

Share Document