<div> <br></div><blockquote style="padding-left:5px;margin-left:5px;border-left:#a0c6e5 2px solid;margin-right:0px">2011/9/20 Gong Ding <span dir="ltr"><<a href="mailto:gdiso@ustc.edu">gdiso@ustc.edu</a>></span><br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<div>Since the conductance of left part and right part is low, the middle region is floating.<br></div></blockquote><div><br></div><div>Not really floating, just sensitive to parameters. It has a unique value, of physical interest, but if you change the conductivity or thickness of the thin region on either side, then it's value changes significantly. This is an ill-conditioned problem, but it's ill-conditioned for physically meaningful reasons. It's not singular and the smallest singular value has great significance, so a null space method is not appropriate. You could reformulate for a slightly different problem which would have a constant null space, but not for this problem.<br><br>Thanks. Any recommends for solving this type of problems? <br>It's our bottleneck now.<br>Direct solver works, but not efficient for large 3D problem.<br>Krylov space based solver seems not rubost enough. <br>A more exact ILU preconditioner may help? <br><br><br></div>
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