<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
</head>
<body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">
<br class="">
<div>
<blockquote type="cite" class="">
<div class="">On Feb 4, 2017, at 7:58 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com" class="">knepley@gmail.com</a>> wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div dir="ltr" style="font-family: Verdana; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<div class="gmail_extra">
<div class="gmail_quote">On Sat, Feb 4, 2017 at 7:56 PM, Zhang, Hong<span class="Apple-converted-space"> </span><span dir="ltr" class=""><<a href="mailto:hongzhang@anl.gov" target="_blank" class="">hongzhang@anl.gov</a>></span><span class="Apple-converted-space"> </span>wrote:<br class="">
<blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;">
<div style="word-wrap: break-word;" class="">
<div class="">
<blockquote type="cite" class="">
<div class="">On Feb 4, 2017, at 7:47 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank" class="">knepley@gmail.com</a>> wrote:</div>
<br class="gmail-m_-2078511886790091366Apple-interchange-newline">
<div class="">
<div dir="ltr" class="">
<div class="gmail_extra">
<div class="gmail_quote">On Sat, Feb 4, 2017 at 7:44 PM, Jed Brown<span class="Apple-converted-space"> </span><span dir="ltr" class=""><<a href="mailto:jed@jedbrown.org" target="_blank" class="">jed@jedbrown.org</a>></span><span class="Apple-converted-space"> </span>wrote:<br class="">
<blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;">
<span class="gmail-">Matthew Knepley <<a href="mailto:knepley@gmail.com" target="_blank" class="">knepley@gmail.com</a>> writes:<br class="">
<br class="">
> On Sat, Feb 4, 2017 at 7:24 PM, Zhang, Hong <<a href="mailto:hongzhang@anl.gov" target="_blank" class="">hongzhang@anl.gov</a>> wrote:<br class="">
><br class="">
>> Can you elaborate a bit more on your problem?<br class="">
>><br class="">
>> If your problem is an index-1 DAE, there is no need to use a projection<br class="">
>> method, and it is perfectly fine to set it up as a DAE in PETSc. For<br class="">
>> high-index DAEs, you may have to use TSSetPostStep() to implement your own<br class="">
>> projection algorithm.<br class="">
>><br class="">
><br class="">
> Please define index.<br class="">
<br class="">
</span>Think of it as a measure of singularity of the "mass matrix". Higher<br class="">
index DAE have more complicated constraints on compatibility of initial<br class="">
conditions. It's covered in any book or paper on DAEs.<br class="">
</blockquote>
</div>
<br class="">
Both your explanation and Hong's use of the term do not help Gideon (or me) know whether he has an index-1 DAE. There has</div>
<div class="gmail_extra">to be some simple form you can write down so that we can tell.</div>
</div>
</div>
</blockquote>
<div class=""><br class="">
</div>
<div class="">This is why we need to learn more about Gideon's problem. It is easy to determine the index if he can write down his problem in a simple form. But it is not that easy the other way round.</div>
</div>
</div>
</blockquote>
<div class=""><br class="">
</div>
<div class="">He says</div>
<div class=""><br class="">
</div>
<div class=""> y' = f(y)</div>
<div class=""><br class="">
</div>
<div class=""> 0 = g(y)</div>
<div class=""><br class="">
</div>
which appears to me to be a Hessenberg index-2 DAE. Is that correct?<br class="">
</div>
</div>
</div>
</div>
</blockquote>
<div><br class="">
</div>
<div>This is not a DAE form because neither f() nor g() contains the algebraic variable.</div>
<div><br class="">
</div>
<div>Hong</div>
<br class="">
<blockquote type="cite" class="">
<div class="">
<div dir="ltr" style="font-family: Verdana; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class="">
<div class="gmail_extra">
<div class="gmail_quote"><br class="">
Matt</div>
<div class="gmail_quote"><br class="">
<blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;">
<div style="word-wrap: break-word;" class="">
<div class="">
<div class="">Hong </div>
<div class=""><br class="">
</div>
<blockquote type="cite" class="">
<div class="">
<div dir="ltr" class="">
<div class="gmail_extra"><br class="">
</div>
<div class="gmail_extra"> Matt<span class="gmail-"><br clear="all" class="">
<div class=""><br class="">
</div>
--<span class="Apple-converted-space"> </span><br class="">
<div class="gmail-m_-2078511886790091366gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">
-- Norbert Wiener</div>
</span></div>
</div>
</div>
</blockquote>
</div>
<br class="">
</div>
</blockquote>
</div>
<br class="">
<br clear="all" class="">
<div class=""><br class="">
</div>
--<span class="Apple-converted-space"> </span><br class="">
<div class="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br class="">
-- Norbert Wiener</div>
</div>
</div>
</div>
</blockquote>
</div>
<br class="">
</body>
</html>