A Relation of Preconditioners in Domain Decomposition Method for Magnetostatic Problems-Reference-Cited by-同舟云学术

A Relation of Preconditioners in Domain Decomposition Method for Magnetostatic Problems

Published:2021-02-25 Issue:07 Volume:18 Page:
ISSN:0219-8762
Container-title:International Journal of Computational Methods
language:en
Short-container-title:Int. J. Comput. Methods

Author:

Kanayama Hiroshi¹^ORCID,Ogino Masao²,Sugimoto Shin-Ichiro³,Zheng Hongjie⁴,Yodo Kaworu⁵

Affiliation:

1. Japan Women’s University, Tokyo, Japan

2. Daido University, Nagoya, Japan

3. Hachinohe Institute of Technology, Hachinohe, Japan

4. Toyo University, Tokyo, Japan

5. Toyo University, Kawagoe, Japan Insight Inc., Tokyo, Japan

Abstract

An iterative domain decomposition method is proposed for numerical analysis of three-dimensional (3D) linear magnetostatic problems taking the magnetic vector potential as an unknown function. The iterative domain decomposition method is combined with the preconditioned conjugate gradient (PCG) procedure and the hierarchical domain decomposition method (HDDM) which is adopted in parallel computing. Our previously employed preconditioner was the Neumann–Neumann (NN) preconditioner. Numerical results showed that the method was only effective for problems with a small number of subdomains. In this paper, we show its improvement with the balancing domain decomposition diagonal scaling (BDD-DIAG) preconditioner and show the asymptotic equivalence between BDD-DIAG and the simplified diagonal scaling (diag) preconditioner, which is derived from the following numerical evidences.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Computational Mathematics,Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219876221500158

Reference16 articles.

1. Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics

2. An Introduction to Domain Decomposition Methods

3. On the Coarse Matrix Solver of Preconditioners for Magnetostatic Domain Decomposition Analysis

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. An Element Decomposition Method for Three-Dimensional Solid Mechanics;International Journal of Computational Methods;2023-04-28

2. A condition for positive-definiteness of the coarse matrix in BDD-DIAG of a perturbed magnetostatic problem;Journal of Advanced Simulation in Science and Engineering;2022