[petsc-users] double orthogonalization for modified gram schmidt in KSPGMRES

[shenren_xu at nwpu.edu.cn]

Dear PETSC moderator,




I found there are classical and modified gram-schmidt options for KSPGMRES solver. For classical GS, one could define

additional orthogonalization sweeps, while for modified GS there is no such option. I got the impression that PETSC

GMRES implementation assumes that the MGS is so robust that double orthogonalization is unnecessary. However, our

recent experience indicated that even for MGS, double orth. is nenecessary. Otherwise, GMRES would produce an increase

residual convergence history. 

I'm emailing for clarification on this: was it because I did not use the option correctly with some misunderstanding

about the user guide, or is this indeed the current situation for the KSPGMRES solver implemention?




As a side note, it was written in Yousef Saad's book 'Iterative methods for sparse linear systems, second editon' 

(page 162) that

"However, there are cases where cancellations are so severe in the orthogonalization steps that even

the Modified Gram-Schmidt option is inadequate." It seems that Prof Saad was well aware of this, which backs

our finding.




Thanks and look forward to further discussion on this.




Best regards,

Shenren




徐慎忍
西北工业大学动力与能源学院 副教授/博导
手机/微信：18762660364
电子邮箱：shenren_xu at nwpu.edu.cn
个人主页：https://urldefense.us/v3/__https://teacher.nwpu.edu.cn/xushenren.html__;!!G_uCfscf7eWS!ZQPNzqIpQl_f9D2grHzxnPVMeys4fV6pumRzr-GoGSdYnvlc6af7refw2J_yHEC2AJewkzY4oRv6Z4fmyMum0-iAy1Lk4Q$ 

Shenren Xu, PhD
Associate Professor
School of Power and Energy
Northwestern Polytechnical University
Xi'an 710129 , China P.R.
Tel: +86-18762660364
Web: https://urldefense.us/v3/__https://teacher.nwpu.edu.cn/xushenren.html__;!!G_uCfscf7eWS!ZQPNzqIpQl_f9D2grHzxnPVMeys4fV6pumRzr-GoGSdYnvlc6af7refw2J_yHEC2AJewkzY4oRv6Z4fmyMum0-iAy1Lk4Q$ 
Email: shenren_xu at nwpu.edu.cn


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