Yep, that's right, use the RB method to solve for u'. Note that you put a(u0,v) on the right-hand side, since u0 is known (it's the "lifting function").
David On 01/24/2013 11:34 PM, Kyunghoon Lee wrote: > Thanks for clearing it up. Then I guess we just solve for u' > > a(u',v) + a(u0,v) = f(v) > > and attach assemblies a(u',v), a(u0,v), and f(v) as usual, then restore u > by u = u' + u0. > > K. Lee. > > On Fri, Jan 25, 2013 at 12:17 PM, David Knezevic <[email protected] >> wrote: >> Hi K, >> >> heterogeneously_constrain_element_matrix_and_vector is not relevant to >> Reduced Basis stuff. For Reduced Basis formulations, you have to >> transform the problem using a lifting function so that it has zero >> Dirichlet BC's --- this is essential since you want your Reduced Basis >> space to be a vector space, i.e. it must contain 0 (which would be not >> be the case with non-zero Dirichlet BCs). This lifting function approach >> is what you described in your email already, so that's fine. >> >> Once you've transformed your problem using a lifting function, then you >> just proceed as normal, e.g. as in reduced_basis_ex1. The only trick is >> you have to add your lifting function back on at the end to recover u >> from u'. >> >> David >> >> >> >> On 01/24/2013 11:10 PM, Kyunghoon Lee wrote: >>> Hi all, >>> >>> In my previous email regarding inhomogeneous Dirichlet boundary >> conditions, >>> David suggested using heterogenously_constrain_element_matrix_and_vector >> in >>> introduction_ex4, but I'm not sure of how to deal with inhomogeneous >>> Dirichlet BCs in connection with reduced basis models. Suppose we have a >>> simple steady state heat conduction model whose BCs are u = T on \Gamma >> and >>> u = 0 on the rest surfaces. After variable change, we solve >>> >>> a(u',v) = f(v) - a(u0,v) >>> >>> where 1) u' = u - T on \Gamma and u' = u on the rest surfaces; and 2) u0 >> = >>> T on \Gamma and u0 = zero on the rest surfaces. I thought we build the >> LHS >>> then call attach_F_assembly to attach it, but in that case, I'm not sure >>> how heterogenously_constrain_element_matrix_and_vector can be used. Or >>> should we attach a(u',v) and f(v) as usual then call >>> heterogenously_constrain_element_matrix_and_vector to impose - a(u0,v) on >>> the LHS? I'd appreciate if someone can briefly describe how the function >>> work. >>> >>> Regards, >>> K. Lee. >>> >> ------------------------------------------------------------------------------ >>> Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS, >>> MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current >>> with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft >>> MVPs and experts. ON SALE this month only -- learn more at: >>> http://p.sf.net/sfu/learnnow-d2d >>> _______________________________________________ >>> Libmesh-users mailing list >>> [email protected] >>> https://lists.sourceforge.net/lists/listinfo/libmesh-users >> >> >> ------------------------------------------------------------------------------ >> Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS, >> MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current >> with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft >> MVPs and experts. ON SALE this month only -- learn more at: >> http://p.sf.net/sfu/learnnow-d2d >> _______________________________________________ >> Libmesh-users mailing list >> [email protected] >> https://lists.sourceforge.net/lists/listinfo/libmesh-users >> > ------------------------------------------------------------------------------ > Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS, > MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current > with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft > MVPs and experts. ON SALE this month only -- learn more at: > http://p.sf.net/sfu/learnnow-d2d > _______________________________________________ > Libmesh-users mailing list > [email protected] > https://lists.sourceforge.net/lists/listinfo/libmesh-users ------------------------------------------------------------------------------ Master Visual Studio, SharePoint, SQL, ASP.NET, C# 2012, HTML5, CSS, MVC, Windows 8 Apps, JavaScript and much more. Keep your skills current with LearnDevNow - 3,200 step-by-step video tutorials by Microsoft MVPs and experts. ON SALE this month only -- learn more at: http://p.sf.net/sfu/learnnow-d2d _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
