<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""> <div class=""> What is your A00 operator? ILU is almost never a good choice for large scale problems. If it is an elliptic operator that using a PC of gamg may work well for the A00 preconditioner instead of ILU.</div><div class=""><br class=""></div><div class=""> Barry</div><div class=""><br class=""></div><div class=""> For moderate size problems you can use a PC type LU for AOO to help you understand the best preconditioner to use for the A11 (the Schur complement block), once you have a good preconditioner for the A11 block you would then go back and determine a good preconditioner for the A00 block.<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Sep 26, 2022, at 10:08 AM, 晓峰 何 <<a href="mailto:tlanyan@hotmail.com" class="">tlanyan@hotmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
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Hello Jed,
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<div class="">The saddle point is due to Lagrange multipliers, thus the size of A11 is much smaller than A00.</div>
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<div class="">Best Regards,</div>
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<div class="">Xiaofeng</div>
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<div class="">On Sep 26, 2022, at 21:03, Jed Brown <<a href="mailto:jed@jedbrown.org" class="">jed@jedbrown.org</a>> wrote:</div>
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<div class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Lagrange
multipliers</span></div>
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