Application of a model order reduction method based on the Krylov subspace to finite element transient analysis imposing several kinds of boundary condition

N. M. Amin, M. Asai, Y. Sonoda

研究成果: ジャーナルへの寄稿Conference article

抄録

Model order reduction (MOR) via Krylov subspace (KS-MOR) is one of projection-based reduction method for spatially discretized time differential equation. This paper presents a treatment of KS-MOR incorporating with finite element method for structure dynamics. KS-MOR needs basis vectors for the projection into Krylov subspace. In this context, Arnoldi and/or Lanczos method are typical techniques to generate basis vectors, and these techniques requires the information of right hand side (RHS) vector, which is the loading pattern vector in structure dynamics. In this study, we propose a treatment of Dirichlet boundary problem by generating an equivalent blocked system equation including three RHS vectors. In order to solve the multiple RHS vector problem, Block Second Order Arnoldi (BSOAR) is utilized in this paper. After projection, time integration of the projected small system equations was performed by the conventional Newmark-β method. In order to show the performance of KS-MOR, several numerical simulations are conducted. The numerical results show less than 1% of the original degrees of freedoms (DOFs) are necessary to get the accurate results for all of our numerical examples, and the CPU time is less than 2% of the conventional FE calculation.

元の言語英語
記事番号012118
ジャーナルIOP Conference Series: Materials Science and Engineering
10
発行部数1
DOI
出版物ステータス出版済み - 1 1 2014
イベント9th World Congress on Computational Mechanics, WCCM 2010, Held in Conjuction with the 4th Asian Pacific Congress on Computational Mechanics, APCOM 2010 - Sydney, オーストラリア
継続期間: 7 19 20107 23 2010

Fingerprint

Transient analysis
Boundary conditions
Program processors
Differential equations
Finite element method
Computer simulation

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Engineering(all)

これを引用

@article{abe2a1b5a6aa469d9c4a33108d0c7c0b,
title = "Application of a model order reduction method based on the Krylov subspace to finite element transient analysis imposing several kinds of boundary condition",
abstract = "Model order reduction (MOR) via Krylov subspace (KS-MOR) is one of projection-based reduction method for spatially discretized time differential equation. This paper presents a treatment of KS-MOR incorporating with finite element method for structure dynamics. KS-MOR needs basis vectors for the projection into Krylov subspace. In this context, Arnoldi and/or Lanczos method are typical techniques to generate basis vectors, and these techniques requires the information of right hand side (RHS) vector, which is the loading pattern vector in structure dynamics. In this study, we propose a treatment of Dirichlet boundary problem by generating an equivalent blocked system equation including three RHS vectors. In order to solve the multiple RHS vector problem, Block Second Order Arnoldi (BSOAR) is utilized in this paper. After projection, time integration of the projected small system equations was performed by the conventional Newmark-β method. In order to show the performance of KS-MOR, several numerical simulations are conducted. The numerical results show less than 1{\%} of the original degrees of freedoms (DOFs) are necessary to get the accurate results for all of our numerical examples, and the CPU time is less than 2{\%} of the conventional FE calculation.",
author = "Amin, {N. M.} and M. Asai and Y. Sonoda",
year = "2014",
month = "1",
day = "1",
doi = "10.1088/1757-899X/10/1/012118",
language = "English",
volume = "10",
journal = "IOP Conference Series: Materials Science and Engineering",
issn = "1757-8981",
publisher = "IOP Publishing Ltd.",
number = "1",

}

TY - JOUR

T1 - Application of a model order reduction method based on the Krylov subspace to finite element transient analysis imposing several kinds of boundary condition

AU - Amin, N. M.

AU - Asai, M.

AU - Sonoda, Y.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Model order reduction (MOR) via Krylov subspace (KS-MOR) is one of projection-based reduction method for spatially discretized time differential equation. This paper presents a treatment of KS-MOR incorporating with finite element method for structure dynamics. KS-MOR needs basis vectors for the projection into Krylov subspace. In this context, Arnoldi and/or Lanczos method are typical techniques to generate basis vectors, and these techniques requires the information of right hand side (RHS) vector, which is the loading pattern vector in structure dynamics. In this study, we propose a treatment of Dirichlet boundary problem by generating an equivalent blocked system equation including three RHS vectors. In order to solve the multiple RHS vector problem, Block Second Order Arnoldi (BSOAR) is utilized in this paper. After projection, time integration of the projected small system equations was performed by the conventional Newmark-β method. In order to show the performance of KS-MOR, several numerical simulations are conducted. The numerical results show less than 1% of the original degrees of freedoms (DOFs) are necessary to get the accurate results for all of our numerical examples, and the CPU time is less than 2% of the conventional FE calculation.

AB - Model order reduction (MOR) via Krylov subspace (KS-MOR) is one of projection-based reduction method for spatially discretized time differential equation. This paper presents a treatment of KS-MOR incorporating with finite element method for structure dynamics. KS-MOR needs basis vectors for the projection into Krylov subspace. In this context, Arnoldi and/or Lanczos method are typical techniques to generate basis vectors, and these techniques requires the information of right hand side (RHS) vector, which is the loading pattern vector in structure dynamics. In this study, we propose a treatment of Dirichlet boundary problem by generating an equivalent blocked system equation including three RHS vectors. In order to solve the multiple RHS vector problem, Block Second Order Arnoldi (BSOAR) is utilized in this paper. After projection, time integration of the projected small system equations was performed by the conventional Newmark-β method. In order to show the performance of KS-MOR, several numerical simulations are conducted. The numerical results show less than 1% of the original degrees of freedoms (DOFs) are necessary to get the accurate results for all of our numerical examples, and the CPU time is less than 2% of the conventional FE calculation.

UR - http://www.scopus.com/inward/record.url?scp=84907699849&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907699849&partnerID=8YFLogxK

U2 - 10.1088/1757-899X/10/1/012118

DO - 10.1088/1757-899X/10/1/012118

M3 - Conference article

AN - SCOPUS:84907699849

VL - 10

JO - IOP Conference Series: Materials Science and Engineering

JF - IOP Conference Series: Materials Science and Engineering

SN - 1757-8981

IS - 1

M1 - 012118

ER -