Getfem Matlab Interface

• Introduction
• Installation
• Preliminary
• Changes from the getfem-interface-1.7
• Getfem-matlab organization
• Functions
• Objects
• Examples
• A step-by-step basic example
• Another Laplacian with exact solution
• Linear and non-linear elasticity
• Avoiding the bricks framework
• Other examples
• Using Matlab Object-Oriented features
• Command reference
• Types
• gf_workspace
• gf_delete
• gf_util
• gf_geotrans
• gf_geotrans_get
• gf_cvstruct_get
• gf_mesh, gfMesh
• gf_mesh_get
• gf_mesh_set
• gf_eltm
• gf_fem
• gf_fem_get
• gf_integ
• gf_integ_get
• gf_mesh_fem
• gf_mesh_fem_get
• gf_mesh_fem_set
• gf_mesh_im
• gf_mesh_im_get
• gf_mesh_im_set
• gf_mdbrick
• gf_mdbrick_get
• gf_mdbrick_set
• gf_mdstate
• gf_mdstate_get
• gf_mdstate_set
• gf_slice
• gf_slice_get
• gf_slice_set
• gf_asm
• gf_spmat
• gf_spmat_get
• gf_spmat_set
• gf_precond
• gf_precond_get
• gf_linsolve
• gf_solve
• gf_compute
• gf_plot
• gf_plot_1D
• gf_plot_mesh
• gf_plot_slice
• getfem-matlab OO-commands
• Index

Avoiding the bricks framework

The model bricks are very convenient, as they hide most of the details of the assembly of the final linear systems. However it is also possible to stay at a lower level, and handle the assembly of linear systems, and their resolution, directly in matlab. For example, the demonstration demo_tripod_alt.m is very similar to the demo_tripod.m except that the assembly is explicit:

nbd=get(mfd, 'nbdof');
F = gf_asm('boundary_source', 1, mim, mfu, mfd, repmat([0;-10;0],1,nbd));
K = gf_asm('linear_elasticity', mim, mfu, mfd, ...
	   lambda*ones(1,nbd),mu*ones(1,nbd));

% handle Dirichlet condition
[H,R]=gf_asm('dirichlet', 2, mim, mfu, mfd, repmat(eye(3),[1,1,nbd]), zeros(3, nbd));
[N,U0]=gf_spmat_get(H, 'dirichlet_nullspace', R);
KK=N'*K*N;
FF=N'*F;
% solve ...
disp('solving...'); t0 = cputime;
lsolver = 1 % change this to compare the different solvers
if (lsolver == 1),     % conjugate gradient
  P=gfPrecond('ildlt',KK);
  UU=gf_linsolve('cg',KK,FF,P,'noisy','res',1e-9);
elseif (lsolver == 2), % superlu
  UU=gf_linsolve('superlu',KK,FF);
else                   % the matlab "slash" operator 
  UU=KK \ FF;
end;
disp(sprintf('linear system solved in %.2f sec', cputime-t0));
U=(N*UU).'+U0;

In getfem-interface, the assembly of vectors, and matrices is done via the gf_asm function. The Dirichlet condition u(x) = r(x) is handled in the weak form ∫(h(x)u(x)).v(x) = ∫r(x).v(x) forall v (where h(x) is a 3×3 matrix field - here it is constant and equal to the identity). The reduced system KK UU = FF is then built via the elimination of Dirichlet constraints from the original system. Note that it might be more efficient (and simpler) to deal with Dirichlet condition via a penalization technique.