scholarly journals Model reduction methods based on Krylov subspaces

Acta Numerica ◽  
2003 ◽  
Vol 12 ◽  
pp. 267-319 ◽  
Author(s):  
Roland W. Freund
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Circuit Simulation ◽  
Krylov Subspaces ◽  
Lanczos Algorithm ◽  
Linear Dynamical Systems ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Reduction Methods ◽  
Modelling Techniques

In recent years, reduced-order modelling techniques based on Krylov-subspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools for tackling the large-scale time-invariant linear dynamical systems that arise in the simulation of electronic circuits. This paper reviews the main ideas of reduced-order modelling techniques based on Krylov subspaces and describes some applications of reduced-order modelling in circuit simulation.

scholarly journals Lanczos Model Reduction for Switched Linear Systems

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Krylov Subspace ◽  
Linear Time ◽  
Lanczos Algorithm ◽  
Linear Time Invariant ◽  
New Methods ◽  
Reduction Methods ◽  
Non Linear System ◽  
Time Invariant

In today the methods reduction of large-scale linear time invariant and complexe systems are very many, the best choices today is the used of the krylov subspace methods based on moment matching. As hybrid dynamical systems are of rising spread and complexity, for these reasons, we present in this paper two model reduction methods applied to linear switched system. Which is an important class of hybrid and non linear system. Tow methods for reduction systems are present. In first part we present the modified non symmetric Lanczos algorithm, which is numerically efficient and applicable of any order. In second part we present the modified global lanczos algorithm, it is also numerically efficient, applicable of any order and having a best numerical stability. The effectivity and suitability of these new methods is illustrated by one simulation example.

The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations

2021 ◽  
Vol 8 (3) ◽  
pp. 526-536
Author(s):  
L. Sadek ◽  
◽  
H. Talibi Alaoui ◽  
Keyword(s):  
Matrix Equation ◽  
Large Scale ◽  
Krylov Subspace ◽  
Low Rank ◽  
Lyapunov Equations ◽  
Lanczos Algorithm ◽  
Lyapunov Matrix ◽  
Block Lanczos ◽  
Low Dimensional ◽  
Differential Lyapunov Equations

In this paper, we present a new approach for solving large-scale differential Lyapunov equations. The proposed approach is based on projection of the initial problem onto an extended block Krylov subspace by using extended nonsymmetric block Lanczos algorithm then, we get a low-dimensional differential Lyapunov matrix equation. The latter differential matrix equation is solved by the Backward Differentiation Formula method (BDF) or Rosenbrock method (ROS), the obtained solution allows to build a low-rank approximate solution of the original problem. Moreover, we also give some theoretical results. The numerical results demonstrate the performance of our approach.

scholarly journals A Broadband Enhanced Structure-Preserving Reduced-Order Interconnect Macromodeling Method for Large-Scale Equation Sets of Transient Interconnect Circuit Problems

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5746
Author(s):  
Ning Wang ◽  
Huifang Wang ◽  
Shiyou Yang
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Equivalent Circuit Model ◽  
Order Reduction ◽  
Wide Band ◽  
Circuit Model ◽  
Band Frequency ◽  
Reduced Order ◽  
Structure Preserving ◽  
Expansion Point

In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature. Compared to other MOR methods, the structure-preserving reduced-order interconnect macromodeling (SPRIM) based on Krylov subspaces will achieve a higher reduction radio and precision for large multi-port Resistor-Capacitor-Inductor (RCL) circuits. However, for very wide band frequency transients, the performance of a Krylov subspace-based MOR method is not satisfactory. Moreover, the selection of the expansion point in this method has not been comprehensively studied in the literature. From this point of view, a broadband enhanced structure-preserving reduced-order interconnect macromodeling (SPRIM) method is proposed to reduce the order of equation sets of a transient interconnect circuit model. In addition, a method is introduced to determine the optimal expansion point at each frequency in the proposed method. The proposed method is validated by the numerical results on a transient problem of an insulated-gate bipolar transistor (IGBT)-based inverter busbar under different exciting conditions.

Development of Reduced Order Modelling Techniques for Downhole Logging Sensor Design

2015 ◽  
Author(s):  
Qiong Zhang ◽  
Freddy Mendez ◽  
John Longo ◽  
Sandeep Gade ◽  
Jean Peyaud
Keyword(s):  
Sensor Design ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Modelling Techniques

scholarly journals Circuit realization method for reduced order inductive PEEC modeling circuits

2016 ◽  
Vol 35 (3) ◽  
Author(s):  
Trung-Son Nguyen ◽  
Tung Le Duc ◽  
Son Thanh Tran ◽  
Jean-Michel Guichon ◽  
Olivier Chadebec
Keyword(s):  
Equivalent Circuit ◽  
Design Methodology ◽  
Large Scale ◽  
Circuit Simulation ◽  
Fast Multipole Method ◽  
Synthesis Method ◽  
Reduced Order Model ◽  
Order Model ◽  
Circuit Realization ◽  
Reduced Order

Purpose To synthesize equivalent circuit obtained from reduced order model of large scale inductive PEEC circuits. Design/methodology/approach This paper describes an original approach for reducing and synthesizing large parasitic RLM electrical circuits coming from inductive Partial Element Equivalent Circuit (PEEC) models. The proposed technique enables the re-use of the reduced order model in the time domain circuit simulation context. Findings The paper shows how to use a synthesis method to realize an equivalent circuit issued from compressed PEEC circuits. Originality/value The coupling between methods PEEC and a compressed method as Fast Multipole Method (FMM) in order to reduce time and space consuming are well-known. The innovation here is to realise a smaller circuit equivalent with the original large scale PEEC circuits to use in temporal simulation tools. Moreover, this synthesis method reduces time and memories for modelling industrial application while maintaining high accuracy.

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