CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

doi:10.1007/s10473-022-0105-0

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (1): 105-126.doi: 10.1007/s10473-022-0105-0

CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

Minh-Phuong TRAN¹, Thanh-Nhan NGUYEN², Phuoc-Toan HUYNH², Nhu-Binh LY³, Minh-Dang NGUYEN³, Quoc-Anh HO³

1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh city, Vietnam;
2. Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam;
3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh city, Vietnam

收稿日期:2020-08-29 修回日期:2020-12-11 出版日期:2022-02-25 发布日期:2022-02-24
通讯作者: Minh-Phuong TRAN,E-mail:tranminhphuong@tdtu.edu.vn E-mail:tranminhphuong@tdtu.edu.vn
作者简介:Thanh-Nhan NGUYEN,E-mail:nhannt@hcmue.edu.vn;Phuoc-Toan HUYNH,E-mail:huynhphuoctoanhcmup@gmail.com;Nhu-Binh LY,E-mail:lynhubinh2211@gmail.com;Minh-Dang NGUYEN,E-mail:dang.nm1311@gmail.com;Quoc-Anh HO,E-mail:hoquocanh119@gmail.com

CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

Minh-Phuong TRAN¹, Thanh-Nhan NGUYEN², Phuoc-Toan HUYNH², Nhu-Binh LY³, Minh-Dang NGUYEN³, Quoc-Anh HO³

1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh city, Vietnam;
2. Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City, Vietnam;
3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh city, Vietnam

Received:2020-08-29 Revised:2020-12-11 Online:2022-02-25 Published:2022-02-24
Contact: Minh-Phuong TRAN,E-mail:tranminhphuong@tdtu.edu.vn E-mail:tranminhphuong@tdtu.edu.vn

摘要/Abstract

摘要： In this paper, we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem. More precisely, we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions. Then we give a simple method to estimate the new value of parameters in each iteration. The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps. Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.

关键词: domain decomposition method, Schwarz waveform relaxation algorithm, advection reaction diffusion, changing transmission conditions

Abstract: In this paper, we establish a new algorithm to the non-overlapping Schwarz domain decomposition methods with changing transmission conditions for solving one dimensional advection reaction diffusion problem. More precisely, we first describe the new algorithm and prove the convergence results under several natural assumptions on the sequences of parameters which determine the transmission conditions. Then we give a simple method to estimate the new value of parameters in each iteration. The interesting advantage of our method is that one may update the better parameters in each iteration to save the computational cost for optimizing the parameters after many steps. Finally some numerical experiments are performed to show the behavior of the convergence rate for the new method.

Key words: domain decomposition method, Schwarz waveform relaxation algorithm, advection reaction diffusion, changing transmission conditions

中图分类号:

65N55

Minh-Phuong TRAN, Thanh-Nhan NGUYEN, Phuoc-Toan HUYNH, Nhu-Binh LY, Minh-Dang NGUYEN, Quoc-Anh HO. CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS[J]. 数学物理学报(英文版), 2022, 42(1): 105-126.

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CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

CONVERGENCE RESULTS FOR NON-OVERLAP SCHWARZ WAVEFORM RELAXATION ALGORITHM WITH CHANGING TRANSMISSION CONDITIONS

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