<div dir="ltr">Dear Barry,<div><div><br></div><div>Yes, J_{I} is the typo, and it should be J_{j}. <span style="font-family:georgia,serif">The exact Jacobian of the preconditioned Jacobian is </span><br></div><div><div><font face="georgia, serif">J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-T_{j}) (1)</font></div><div><font face="georgia, serif"><br></font></div><div><font face="georgia, serif">It seems that PETSc uses the approximate Jacobian, </font></div><div><font face="georgia, serif">J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-\sum_{j=1}^{N}T_{j}) (2)</font></div></div><div><font face="georgia, serif"><br></font></div><div><br></div><div><font face="georgia, serif">In the RASPEN algorithm, it requires the exact Jacobian of ASPIN in the equation (1). Currently, the J_{j}(x-T_{i}) is only computed on each processor in PETSc, how can I get the global term J(x-T_{j})</font><span style="font-family:georgia,serif">(j=1,2,..N)?</span><span style="font-family:georgia,serif"> </span></div><div><span style="font-family:georgia,serif"><br></span></div><div><span style="font-family:georgia,serif">Thanks.</span></div><div><font face="georgia, serif"><br></font></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Nov 9, 2021 at 11:18 AM Barry Smith <<a href="mailto:bsmith@petsc.dev">bsmith@petsc.dev</a>> wrote:<br></div><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;line-break:after-white-space"><div><br></div> Lulu,<div><br></div><div> 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><br></div><div> I note below you have a <span style="font-family:georgia,serif">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">J_{j} as in the next equation?</span></div><div><font face="georgia, serif"><br></font></div><div><font face="georgia, serif"> Barry</font></div><div><font face="georgia, serif"><br></font><div><br><blockquote type="cite"><div>On Nov 6, 2021, at 7:19 AM, Lulu Liu <<a href="mailto:lulu.liu@kaust.edu.sa" target="_blank">lulu.liu@kaust.edu.sa</a>> wrote:</div><br><div><div dir="ltr"><div><font face="georgia, serif">Hi,</font></div><div><font face="georgia, serif">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><font face="georgia, serif">J_exact=\sum_{j=1}^{N}J_{I}(x-T_{i})J(x-T_{j}).</font></div><div><font face="georgia, serif"><br></font></div><div><font face="georgia, serif">It seems that PETSc uses the approximate Jacobian, </font></div><div><font face="georgia, serif">J_exact=\sum_{j=1}^{N}J_{j}(x-T_{i})J(x-\sum_{j=1}^{N}T_{j}).<br></font></div><div><br></div><div><font face="georgia, serif">I want to implement RASPEN, which requires the exact Jacobian of ASPIN. Is</font><span style="font-family:georgia,serif"> there any easy way to compute </span><font face="georgia, serif">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><span style="font-family:georgia,serif"><br></span></div><div><span style="font-family:georgia,serif">Thanks very much!</span></div><div><br></div>-- <br><div dir="ltr"><div dir="ltr"><div dir="ltr"><div>Best wishes,<br></div><div><font face="arial, helvetica, sans-serif">Lulu Liu</font></div><div><br></div></div></div></div></div>
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<div>King Abdullah University of Science and Technology<br>Tel：＋966－0544701599</div></div></div></div></div>
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