<html><body><div style="color:#000; background-color:#fff; font-family:verdana, helvetica, sans-serif;font-size:10pt">Thank you for reply! <br>I didnt get , what does it mean by applying the preconditioner to the right hand side, making it look just like a smoother ?<br><br>More simply, how can I implement Prec = \bar C b + (b - \bar A \bar C b)<br>where \bar C = P (M_H^-1 A_H)^-1 R<br>and \bar A = M^-1 A. <br><span style="font-weight: bold;">Note: we know how to implement Prec = C b + (b - A C b). </span><br><br>Many thanks, Abdul <br><br><div><blockquote style="border-left: 2px solid rgb(16, 16, 255); margin-left: 5px; margin-top: 5px; padding-left: 5px;"> <div style="font-family: verdana, helvetica, sans-serif; font-size: 10pt;"> <div style="font-family: times new roman, new york, times, serif; font-size: 12pt;"> <div dir="ltr"> <font size="2" face="Arial"> <hr size="1"> <b><span style="font-weight:bold;">From:</span></b> Jed Brown
<jedbrown@mcs.anl.gov><br> <b><span style="font-weight: bold;">To:</span></b> Abdul Hanan Sheikh <hanangul12@yahoo.co.uk> <br><b><span style="font-weight: bold;">Cc:</span></b> PETSc users list <petsc-users@mcs.anl.gov> <br> <b><span style="font-weight: bold;">Sent:</span></b> Friday, 15 June 2012, 21:36<br> <b><span style="font-weight: bold;">Subject:</span></b> Re: [petsc-users] How to implement projection preconditioner?<br> </font> </div> <br><div id="yiv702936839"><div class="yiv702936839gmail_quote">On Fri, Jun 15, 2012 at 2:23 PM, Abdul Hanan Sheikh <span dir="ltr"><<a rel="nofollow" ymailto="mailto:hanangul12@yahoo.co.uk" target="_blank" href="mailto:hanangul12@yahoo.co.uk">hanangul12@yahoo.co.uk</a>></span> wrote:<br><blockquote class="yiv702936839gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div style="font-family:verdana, helvetica, sans-serif;"><span>I recall my previous thread; copy and paste here, and then I try to ask: <br></span></div><div style="font-family:verdana, helvetica, sans-serif;"><br></div><div style="font-family:verdana, helvetica, sans-serif;font-weight:bold;">
Suppose C = P*A_H^{-1}*R is the coarse grid
solver. Then with a post-smoother S, application of the preconditioner
to the vector "b" would be C b + S (b - A C b). If we drop the
post-smoother by setting S = I, We get Prec = C b + b - A C b. Note that there is no presmoother. <br></div><div style="font-family:verdana, helvetica, sans-serif;"><br></div><div style="font-family:verdana, helvetica, sans-serif;">
This is the preconditioner I have used before, in PCMG framework, with no pre-smoothing and Richardson(without any preconditioner) as post smoother. </div><div style="font-family:verdana, helvetica, sans-serif;"><br></div><div style="font-family:verdana, helvetica, sans-serif;">
I need to apply the updated version of above Prec = C b + (b - A C b), where A is replaced by M^-1 A , and A_H by M_H^-1 A_H . <br></div></blockquote><div><br></div><div>With left preconditioning, you also have to apply the preconditioner to the right hand side, thus making it look just like a smoother.</div>
<div> </div><blockquote class="yiv702936839gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="font-family:verdana, helvetica, sans-serif;"></div><div><font face="'courier new', monospace"><br style="font-family:verdana, helvetica, sans-serif;">
<span style="font-family:verdana, helvetica, sans-serif;">Now does it make sense :<br><br>1) incorporating M as only preconditioner in presmoother will replace A by M^-1 A in Prec = C b + (b - A C b) ?<br></span></font></div>
</blockquote><div><br></div><div>No, it uses the preconditioner the way that preconditioners work, see above.</div><div> </div><blockquote class="yiv702936839gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div><font face="'courier new', monospace"><span style="font-family:verdana, helvetica, sans-serif;">2)
incorporating M as preconditioner to CG-solver will replace A_H by (M_H^-1 A_H ) ? <span style="font-weight:bold;">I am kinda of sure about this point 2.</span> </span></font></div></blockquote></div><br><div>C already contains A_H^{-1}. Replacing that by M_H^{-1} is an approximate coarse level solve (that's okay and seems to be what you want, just not what you have written, which is not a consistent method).</div>
</div><br><br> </div> </div> </blockquote></div> </div></body></html>