<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><br></div> We could possibly provide the equivalent of PCFieldSplit for nonlinear problems? These could be accelerated via the various non-linear accelerates or even via matrix-free Newton?<div><br><div><br></div><div> Barry</div><div><br><div><br><div>Begin forwarded message:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>From: </b></span><span style="font-family:'Helvetica'; font-size:medium;">Jed Brown <<a href="mailto:jedbrown@mcs.anl.gov">jedbrown@mcs.anl.gov</a>><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>Subject: </b></span><span style="font-family:'Helvetica'; font-size:medium;"><b>Re: Is there any example that allows time-integration provided by users</b><br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>Date: </b></span><span style="font-family:'Helvetica'; font-size:medium;">December 13, 2012 11:06:29 AM CST<br></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px;"><span style="font-family:'Helvetica'; font-size:medium; color:rgba(0, 0, 0, 1.0);"><b>To: </b></span><span style="font-family:'Helvetica'; font-size:medium;">Lulu Liu <<a href="mailto:lulu.liu@kaust.edu.sa">lulu.liu@kaust.edu.sa</a>>, Barry Smith <<a href="mailto:bsmith@mcs.anl.gov">bsmith@mcs.anl.gov</a>><br></span></div><br>It sounds like you want to do classical operator splitting (which is notoriously inaccurate). The literature on these methods is rife with special-purpose band-aids that I'd rather not try to support all of in PETSc.<br>
<br>My preference would be to write your method as an ARKIMEX, with "trivial" implicit part on the "part" of the equation that you wanted to treat explicitly, or if you wanted to solve both implicitly (but decoupled) then do the appropriate incomplete solve. Can you be more specific about what problem you want to solve?<div class="gmail_extra">
<br><br><div class="gmail_quote">On Wed, Dec 12, 2012 at 7:42 AM, Lulu Liu <span dir="ltr"><<a href="mailto:lulu.liu@kaust.edu.sa" target="_blank">lulu.liu@kaust.edu.sa</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr"><div>There is two equations in my system, and I want solve the first one, and then solve the second equation. Is there any example that allows me to solve equations one by one?</div>
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<div>I want to solve nonlinear system on every time level, but it is feasible if I could provide the time discretization schemes by myself. Is there any example about this?</div>
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<div>Thank you!<span class="HOEnZb"><font color="#888888"><br clear="all"><br>-- <br></font></span></div><span class="HOEnZb"><font color="#888888">
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<div>Best wishes,<br>Lulu Liu<br>Applied Mathematics and Computational Science</div>
<div>King Abdullah University of Science and Technology<br>Tel：<a href="tel:%EF%BC%8B966%EF%BC%8D0544701599" value="+966544701599" target="_blank">＋966－0544701599</a></div></div><br></font></span></div><span class="HOEnZb"><font color="#888888">
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