Description

EX_MAGNETOSTATICS2 Magnetic field around a horseshoe magnet.

[ FEA, OUT ] = EX_MAGNETOSTATICS2( VARARGIN ) Magnetic field around a horseshoe magnet.

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
sfun        string {sflag2}        Shape function for pressure
hmax        scalar {0.01}          Grid size
iorient     scalar 0/{1,2,3}       Magnet orientation (top, right, bottom, left)
iplot       scalar 0/{1}           Plot solution (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = { 'sfun',     'sflag2';
             'hmax',     0.01;
             'iorient',  0;
             'iplot',    1;
             'tol',      1e-1;
             'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


% Geometry and grid generation.
 fea.sdim = { 'x' 'y' };
 fea.geom.objects = { gobj_circle([0 0],0.05,'C1'), ...
                      gobj_circle([0 0],0.025,'C2'), ...
                      gobj_rectangle(-0.06,0.06,0,0.06,'R1'), ...
                      gobj_rectangle(-0.05,-0.025,0,0.06,'R2'), ...
                      gobj_rectangle(0.025,0.05,0,0.06,'R3'), ...
                      gobj_rectangle(-0.15,0.15,-0.2,0.2,'R4') };
 fea = geom_apply_formula( fea, 'C1-C2-R1' );
 fea.grid = gridgen( fea, 'hmax', opt.hmax, 'fid', opt.fid );
 fea.grid = gridrotate( fea.grid, -pi/2*opt.iorient );


% Problem definition.
 fea = addphys( fea, @magnetostatics );
 switch( opt.iorient )
   case 0
     fea.phys.ms.eqn.coef{4,end} = { 1 -1 0 0 };
   case 1
     fea.phys.ms.eqn.coef{3,end} = { 1 -1 0 0 };
   case 2
     fea.phys.ms.eqn.coef{4,end} = { -1 1 0 0 };
   case 3
     fea.phys.ms.eqn.coef{3,end} = { -1 1 0 0 };
 end
 fea.phys.ms.sfun = { opt.sfun };


% Parse and solve problem.
 fea       = parsephys( fea );
 fea       = parseprob( fea );
 fea.sol.u = solvestat( fea, 'fid', opt.fid );   % Call to stationary solver.


% Postprocessing.
 if( opt.iplot>0 )
   figure
   postplot( fea, 'surfexpr', 'Az', ...
             'isoexpr', 'Az', 'isolev', 25, ...
             'arrowexpr', fea.phys.ms.eqn.vars{9,2}, 'arrowcolor', 'w', 'arrowspacing', [45 30] )
   title( 'Magnetic potential (surface, iso), and flux density (arrows) ' )
 end


% Error checking.
 Az   = intsubd( fea.phys.ms.eqn.vars{1,2}, fea );
 Mf   = intsubd( fea.phys.ms.eqn.vars{2,2}, fea );
 gAzb = intbdr(  fea.phys.ms.eqn.vars{5,2}, fea, 1:4 );
 Scb1 = intbdr(  fea.phys.ms.bdr.vars{2,2}, fea, 1 );
 Scb2 = intbdr(  fea.phys.ms.bdr.vars{2,2}, fea, 2 );
 Scb3 = intbdr(  fea.phys.ms.bdr.vars{2,2}, fea, 3 );
 Scb4 = intbdr(  fea.phys.ms.bdr.vars{2,2}, fea, 4 );
 out.err = [ abs(Az+9.637833e-11)/9.637833e-11;
             abs(Mf-0.005108)/0.005108;
             abs(gAzb-1.15859e-8)/1.15859e-8;
             abs(Scb1-0.001326)/0.001326;
             abs(Scb2+0.001865)/0.001865;
             abs(Scb3-0.002403)/0.002403;
             abs(Scb4+0.001865)/0.001865 ];
 out.pass = all( out.err < opt.tol );


 if ( nargout==0 )
   clear fea out
 end