On Sun, Nov 4, 2012 at 7:52 PM, w_ang_temp <span dir="ltr"><<a href="mailto:w_ang_temp@163.com" target="_blank">w_ang_temp@163.com</a>></span> wrote:<br><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="line-height:1.7;font-size:14px;font-family:arial"><div class="im"><div><br> </div>>At 2012-11-04 21:52:23,"Mark F. Adams" <<a href="mailto:mark.adams@columbia.edu" target="_blank">mark.adams@columbia.edu</a>> wrote:<br>
</div><blockquote style="BORDER-LEFT:#ccc 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex"><div class="im">>Just to add to Jed and Matt's comments:
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<div>>1) What are your equations (I really don't care what physics you are modeling, its the equations that we see). Is is a scalar div (alpha(x) grad ) u?</div>
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</div><div>The linear system Ax=b is resulted from the finite element discretization. It is a algebraic equation, based from a elliptic equation, my opinion.</div></blockquote></div></blockquote><div><br></div><div>If you use the formulation in the first cited reference, then you have a saddle point problem. This is extremely important and explains why naive application of algebraic multigrid did not work. AMG can handle the variable coefficients (and "ill-conditioning"), but it can't "automatically" handle the saddle. You can use PCFIELDSPLIT for these problems, but it's not a black box and it requires that you _understand_ what you are trying to do.</div>
<div><br></div><div>You need to choose a respectable reference on preconditioners for saddle point problems. Best would be a review paper written since 2000 and with more than 100 citations. (There are a handful, almost any will be fine.) Read it first, then read a couple papers specific to poroelasticity and frame those methods in the context from the saddle point paper. Also read section 4.5 of the PETSc user's manual on PCFIELDSPLIT.</div>
<div><br></div><div>Yes, this takes time, but if you want to solve these problems robustly, you have to understand enough about the methods to troubleshoot.</div><div><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>>2) Try using hyper (-pc_type hyper -pc_hypre_type boomeramg). Look at "<span style="LINE-HEIGHT:23px;FONT-FAMILY:arial;FONT-SIZE:14px">PCApply 448</span>", this should be like 10-20. Configure your systems with -->download-hyper=1 if you do not have it.</div>
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<div>>3) Why do you say it is ill conditioned? Stretched grids? large jumps in material coefficients? Why do you think it is illoconditioned?</div>
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</div><div>Pragmatic geotechnical problems often involve materials with highly varied material zones, such as in soil-structure interaction problems or soil-water<br>coupled problems.([1]summary;[2-4])</div>
<div>Reference:<br>[1]Krishna Bahadur Chaudhary. Preconditioners for soil-structure interaction problems with significant material stiffness contrast[D]. <br>[2]S.H.Chan. A modified Jacobi preconditioner for solving ill-conditioned Biot's consolidation equations using symmetric quasi-minimal residual </div>
<div>method.International journal for numerical and analytical methods in geomechanics[J].<br>[3]Kok-Kwang Phoon. Iterative solution of large-scale consolidation and constraint finite element equations for 3D problems.International e-Conference on </div>
<div>Modern Trends in Foundation Engineering[J].<br>[4]Massimiliano, etc. Ill-conditioning of finite element poroelasticity equations. International Journal of Solids and Structures[J].</div>
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<div>Thanks.</div>
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<div> Jim<br><br></div>
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