Description

EX_EDDYCURRENTS2 3D Eddy currents test example.

[ FEA, OUT ] = EX_EDDYCURRENTS2( VARARGIN ) 3D Eddy currents test example for vector elements (Nedelec). Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
icase       integer 1/{1}          Predefined test case
hmax        scalar {0.05}          Grid cell size
sfun        string {sf_simp_N1}    Vector shape function (Nedelec)
iplot       scalar 0/{1}           Plot solution (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = { 'icase',    1;
             'hmax',     0.05;
             'sfun',     'sf_simp_N1';
             'iplot',    1;
             'tol',      0.01;
             'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});


% Geometry and grid generation.
 fea.sdim = {'x','y','z'};
 fea.geom.objects = { gobj_rectangle() };
 fea.grid = hex2tet( blockgrid(ceil(1/opt.hmax)), 2 );


% Problem definition.
 fea = addphys( fea, @customeqn, {'E'} );
 fea.phys.ce.eqn.seqn = {'Ec_c + E_t = 0'};
 fea.phys.ce.sfun = {opt.sfun};
 if( opt.icase==2 )   % Set homogenous Neumann BCs.
   [fea.phys.ce.bdr.coef{5}{:}] = deal(0);
 end

% Parse problem.
 fea = parsephys( fea );
 fea = parseprob( fea );

% Define manual source term with rank 3 to each vector compnent.
 switch( opt.icase )
   case 1
     f1 = '0';
     f2 = '0';
     f3 = '(2*pi^2 + 1)*sin(pi*x)*sin(pi*y)';
 end
 fea.eqn.f.form{1} = 1;
 fea.eqn.f.coef{1} = {cat(3,{f1},{f2},{f3})};


% Solve problem.
 fea.sol.u = solvestat( fea, 'fid', opt.fid );


% Postprocessing.
 if( opt.iplot )
   postplot( fea, 'sliceexpr', 'Ec#1' )
   title( 'Curl solution #1')
 end


% Error checking.
 switch( opt.icase )
   case 1
     refsol = { '0', ...
                '0', ...
                'sin(pi*x)*sin(pi*y)', ...
                'pi*cos(pi*y)*sin(pi*x)', ...
                '-pi*cos(pi*x)*sin(pi*y)', ...
                '0' };
 end
 out.err = [ intsubd(['(',refsol{1},'-E#1)^2'],fea), ...
             intsubd(['(',refsol{2},'-E#2)^2'],fea), ...
             intsubd(['(',refsol{3},'-E#3)^2'],fea), ...
             intsubd(['(',refsol{4},'-Ec#1)^2'],fea), ...
             intsubd(['(',refsol{5},'-Ec#2)^2'],fea), ...
             intsubd(['(',refsol{6},'-Ec#3)^2'],fea) ];
 out.pass = all( out.err < opt.tol );
 if( nargout==0 )
   clear fea out
 end