<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#0563C1;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:#954F72;
text-decoration:underline;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
span.E-MailFormatvorlage18
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="DE" link="#0563C1" vlink="#954F72">
<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Hi Barry,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">thanks for the reply. We are not using any operator splitting method. Can I take from your answer that the initial residual norm is not recommended then?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">We are solving a diffusion equation with FD and implicit time stepping (mostly euler, sometimes crank Nicholson.)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Regards,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Daniel<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<div>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b>Von:</b> Barry Smith <bsmith@petsc.dev> <br>
<b>Gesendet:</b> Montag, 3. <span lang="EN-US">Februar 2025 17:17<br>
<b>An:</b> Abele, Daniel <Daniel.Abele@dlr.de><br>
<b>Cc:</b> petsc-users@mcs.anl.gov<br>
<b>Betreff:</b> Re: [petsc-users] KSP: when to use initial residual norm (ksp_converged_use_initial_residual_norm)<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<div>
<p class="MsoNormal"><span lang="EN-US"><br>
<br>
<o:p></o:p></span></p>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<p class="MsoNormal"><span lang="EN-US">On Feb 2, 2025, at 1:09 PM, Daniel.Abele--- via petsc-users <</span><a href="mailto:petsc-users@mcs.anl.gov"><span lang="EN-US">petsc-users@mcs.anl.gov</span></a><span lang="EN-US">> wrote:<o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<div>
<div>
<p class="MsoNormal"><span lang="EN-US">Hi,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US">we are solving a time dependent problem with a single KSP in every time step. We are debating which convergence criterion to use. Is there general guidance around when to use one of the norms with initial residual (ksp_converged_use_initial_residual_norm
or ksp_converged_use_min_initial_residual_norm) over the default norm?<o:p></o:p></span></p>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<p class="MsoNormal"><span lang="EN-US"><br>
<br>
<o:p></o:p></span></p>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal"><span lang="EN-US">If I understand the formulas correctly, the initial residual norm “norm(b – A * x0)” (maybe add preconditioning) means that if you have a very good initial guess (as is often the case in time dependent problems if you
can use the result if the last time step as initial guess), the norm is much stricter than the default norm “norm(b)”.<o:p></o:p></span></p>
</div>
</div>
</blockquote>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<p class="MsoNormal"><span lang="EN-US"> The above statement is correct.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><br>
<br>
<o:p></o:p></span></p>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<div>
<div>
<p class="MsoNormal"><span lang="EN-US">Is this meant as a way to control error accumulation over time? Or does it have some other purpose?<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US">Thanks and Regards,<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US">Daniel<o:p></o:p></span></p>
</div>
</div>
</blockquote>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> For splitting-type methods, you want the error in the linear system solve, e, to be on the same order as the maximum error from the splitting, the explicit time-step discretization, and the implicit time-step discretization.
So you need some estimate of that value.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US">Now<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> || e ||_2 < || B(b - Ax) ||_2 <o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> -------------------<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> \lambda_min(BA).<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> For this you need a handle on \lambda_min(BA) which you can obtain with Lanczo using -ksp_monitor_singular_values. So the converge criteria should really depend on setting the -ksp_atol using the required bound on
|| e ||_2 and \lambda_min(BA). <o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> PETSc should provide this convergence test but no one has gotten around to adding it.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span lang="EN-US"> </span>Barry<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</body>
</html>