Dear Arvind, Your computation is correct except
FF = N'*F; which have to be completed by FF = N'*F-N'*K*U0'; since you solve your system on the new unknown U-U0. Yves. Arvind Ajoy <[email protected]> a écrit : > Dear users, > > 1 . I am trying to understand the null-space method for imposing constraints > HU=R > on a system KU=F. I find that the convention used in the documentation is > different under the section for [H,R] = > gf_asm('dirichlet',bnum,mim,mf_u,mf_d,Hd,Rd) > at http://download.gna.org/getfem/doc/getfem_matlab/gfm_50.html and > the example at http://download.gna.org/getfem/doc/getfem_matlab/gfm_13.html. > Specifically, > the matrix N and N' seem to be interchanged. > > Could someone please direct me to a reference where I can understand the > theory behind > the null-space technique? > > =================================================================== > > 2. In order to figure out more, I tried a simple problem to solve \frac{d^2 > u}{dx^2} = 1 on [0,1] > with boundary conditions u(0) = u(1) =2. However, the solution I obtain is > wrong. The dirichlet conditions > are not imposed correctly. The code is as under > > clear all; > gf_workspace('clear'); > > M = gf_mesh('cartesian',[0:0.025:1]); > MFU = gf_mesh_fem(M,1); > gf_mesh_fem_set(MFU,'fem',gf_fem('FEM_PK(1,1)')); > MIM = gf_mesh_im(M,gf_integ('IM_NC(1,1)')); > > nbd = gf_mesh_fem_get(MFU,'nbdof'); > > > A = gf_mesh_fem_get(MFU, 'eval', {-1}) ; > K = gf_asm('laplacian',MIM,MFU,MFU,A) ; > F = gf_asm('volumic source', MIM, MFU, MFU, -A) ; > > border = gf_mesh_get(M,'outer faces'); > gf_mesh_set(M,'boundary',100,border); > [H,R] = gf_asm('dirichlet',100,MIM,MFU,MFU,ones(1,nbd),2*ones(1,nbd)); > [N,U0]=gf_spmat_get(H,'dirichlet_nullspace',R) > > KK = N'*K*N; > FF = N'*F; > > UU = KK \ FF; > U = (N * UU)' + U0; > > x = linspace(0,1,100); > plot(x,0.5*x.^2 - 0.5*x + 2,'b'); > > hold on; > plot([0:0.025:1],U,'r+'); > > ================================================================ > > Thanks for any help! > > > Regards > Arvind > > PhD Student, Indian Institute of Technology Madras > _______________________________________________ Getfem-users mailing list [email protected] https://mail.gna.org/listinfo/getfem-users
