Yes.The Roe average is a common method in this area. <br>I couldn't understand well what you said about stashing the quantities. Each residual evaluation is proceeded by a Jacobian one if I choose an Inexact Newton method and freeze Jacobian matrix for some Newton iterations. Please make it for me more clear. <br>
Thanks a lot,<br><br><br><br><br><div class="gmail_quote">On Sat, Nov 12, 2011 at 9:29 PM, Jed Brown <span dir="ltr"><<a href="mailto:jedbrown@mcs.anl.gov">jedbrown@mcs.anl.gov</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div class="gmail_quote"><div class="im">On Sat, Nov 12, 2011 at 11:50, behzad baghapour <span dir="ltr"><<a href="mailto:behzad.baghapour@gmail.com" target="_blank">behzad.baghapour@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
The nonlinear residual and Jacobian matrix are evaluated with a face-based method. Two integrals are involved (the effect of element internal connections and face flux connections). All of my calculations of flow states are solved and stored in arrays of objects called elements.</blockquote>
<div><br></div></div><div>Are you talking about intermediate quantities like Roe averages on face quadrature points? The state X at which the residual is evaluated is different each time, so you would be using old values if you stashed them. The residual might be evaluated multiple times before a Jacobian is requested. Normally the residual is much less expensive than the Jacobian, so it's not worth stashing the intermediate quantities. See also this FAQ:</div>
<div><br></div><div><a href="http://www.mcs.anl.gov/petsc/petsc-as/documentation/faq.html#functionjacobian" target="_blank">http://www.mcs.anl.gov/petsc/petsc-as/documentation/faq.html#functionjacobian</a></div><div><br>
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