Higher-Order Time-Domain Simulations of Maxwell's Equations Using Krylov-Subspace Methods

2007 ◽  
Vol 4 (3) ◽  
pp. 627-634 ◽  
Author(s):  
Jens Niegemann ◽  
Lasha Tkeshelashvili ◽  
Kurt Busch
Keyword(s):  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Higher Order ◽  
Subspace Methods

The Error Bound of Timing Domain in Model Order Reduction by Krylov Subspace Methods

2018 ◽  
Vol 27 (06) ◽  
pp. 1850093 ◽  
Author(s):  
Xinsheng Wang ◽  
Mingyan Yu
Keyword(s):  
Error Bound ◽  
Time Domain ◽  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Auxiliary Variable ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Model Order ◽  
Error System

In this paper, we present four different error bound estimates of timing domain in model order reduction by Krylov subspace methods. Firstly, we give integral method based on the impulse response in time domain. The second method is to use small sample statistical method to estimate the error bound based on an error system. The error induced by model order reduction process is constructed by an independent system output. We next present the error bound based on frequency domain error bound transformed into time domain method. The final method is reconstructing an error system, which is factorized to the sum of two parts, resulting from model order reduction by Krylov subspace. It is shown that the first factor is of the reduced order system except for subtracting an auxiliary variable, while the second factor is of the original system except for adding an auxiliary variable. In addition, we also give the analysis of the four methods. A few numerical examples are used to show the efficiency of the four different error bound estimate methods.

scholarly journals Krylov subspace methods for estimating operator-vector multiplications in Hilbert spaces

2021 ◽  
Author(s):  
Yuka Hashimoto ◽  
Takashi Nodera
Keyword(s):  
Krylov Subspace ◽  
Time Series Data ◽  
Linear Equations ◽  
Transfer Operator ◽  
Krylov Subspace Methods ◽  
Krylov Subspace Method ◽  
Linear Operators ◽  
Series Data ◽  
Subspace Method ◽  
Subspace Methods

AbstractThe Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.

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