## libmesh-users

 [Libmesh-users] inhomogeneous Dirichlet boundary conditions for reduced basis From: Kyunghoon Lee - 2013-01-25 04:11:06 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.
 Re: [Libmesh-users] inhomogeneous Dirichlet boundary conditions for reduced basis From: David Knezevic - 2013-01-25 04:18:10 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 > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users