<div class="gmail_quote">On Mon, Dec 19, 2011 at 18:48, Mohamad M. Nasr-Azadani <span dir="ltr"><<a href="mailto:mmnasr@gmail.com">mmnasr@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>I have been using BoomerAMG as a preconditioner joint with an iterative solver, e.g. GMRES of BiCGs for regular 3D CFD problems. </div><div>On the top of my head, I can not remember if I had the strong scaling tests done (I will look into it and let you know if you found any), but for the weak-scaling case, I definitely saw some scaling issues. </div>
<div>As the size of the system increases, the number of iterations does also increase (somewhat significantly for my test problem, i.e. incompressible N-S with complex geometry) which ultimately deteriorates the weak-scaling behaviors. </div>
</blockquote><div><br></div><div>It is very dangerous to use AMG directly on the indefinite problem produced by most discretizations of incompressible flow. For example, for mixed finite element methods, I have on multiple occasions observed BoomerAMG produce a singular preconditioner (with huge null space), leading to the appearance of convergence in the preconditioned norm, but no actual convergence.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div><br></div><div>This is also reported in the reports given by the hypre team, cf. </div><div><a href="https://computation.llnl.gov/casc/linear_solvers/pubs/pmis_report.pdf" target="_blank">https://computation.llnl.gov/casc/linear_solvers/pubs/pmis_report.pdf</a></div>
<div><br></div><div>(cf. see Table 6.1 for the Stokes flow simulation results and scaling). </div></blockquote></div><br><div>This table is for a very special discretization, First Order System Least Squares (FOSLS). Advocates of FOSLS like to point out that the method does not require inf-sup compatibility between velocity and pressure spaces, so equal-order spaces can, in principle, be used, without harming the "optimal" convergence rates. The problem is that equal order spaces, which are almost always used in practice, cause systematic conservation errors. Even for very simple geometries, "incompressible" flow solutions can exhibit more than 90% mass loss. If you look at the literature, you will notice that many of the most prominent advocates of FOSLS were not forthcoming about this "detail" for the first decade of their publications. In the last five years, they have published on "enhanced mass conservation" techniques, with which, still for simple, well-resolved flow problems, they manage to get less than 20% mass loss with linear elements and less than 1% by using higher order elements (up to quartic). I have yet to meet an engineer who would consider such systematic mass loss acceptable.</div>