<html><head><meta http-equiv="Content-Type" content="text/html; charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><br class=""></div> Lulu,<div class=""><br class=""></div><div class=""> Sorry for not responding quicker. This question will take a little research to figure out exactly what is needed, I am not sure it is possible. </div><div class=""><br class=""></div><div class=""> I note below you have a <span style="font-family: georgia, serif;" class="">J_{I} is that intentional? If so what does it mean, or is a typo that should be </span><span style="font-family: georgia, serif;" class="">J_{j} as in the next equation?</span></div><div class=""><font face="georgia, serif" class=""><br class=""></font></div><div class=""><font face="georgia, serif" class=""> Barry</font></div><div class=""><font face="georgia, serif" class=""><br class=""></font><div><br class=""><blockquote type="cite" class=""><div class="">On Nov 6, 2021, at 7:19 AM, Lulu Liu <<a href="mailto:lulu.liu@kaust.edu.sa" class="">lulu.liu@kaust.edu.sa</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div class=""><font face="georgia, serif" class="">Hi,</font></div><div class=""><font face="georgia, serif" class="">For ASPIN, the local problem F_{j}(x-T_{j})=0 (j=1,2,...N) is solved. The exact Jacobian of the preconditioned Jacobian is </font></div><div class=""><font face="georgia, serif" class="">J_exact=\sum_{j=1}^{N}J_{I}(x-T_{i})J(x-T_{j}).</font></div><div class=""><font face="georgia, serif" class=""><br class=""></font></div><div class=""><font face="georgia, serif" class="">It seems that PETSc uses the approximate Jacobian, </font></div><div class=""><font face="georgia, serif" class="">J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-\sum_{j=1}^{N}T_{j}).<br class=""></font></div><div class=""><br class=""></div><div class=""><font face="georgia, serif" class="">I want to implement RASPEN, which requires the exact Jacobian of ASPIN. Is</font><span style="font-family:georgia,serif" class=""> there any easy way to compute </span><font face="georgia, serif" class="">J(x-T_{j}) (j=1,2,..N)? How can I get the global vectors like x-T_{j} ? PETSc only provides the vector x-T_{j} on the subdomain now.</font></div><div class=""><span style="font-family:georgia,serif" class=""><br class=""></span></div><div class=""><span style="font-family:georgia,serif" class="">Thanks very much!</span></div><div class=""><br class=""></div>-- <br class=""><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr" class=""><div dir="ltr" class=""><div class="">Best wishes,<br class=""></div><div class=""><font face="arial, helvetica, sans-serif" class="">Lulu Liu</font></div><div class=""><br class=""></div></div></div></div></div>
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