Description

SF_SIMP_P1 Linear Lagrange shape function for simplices (P1).

[ VBASE, NLDOF, XLDOF, SFUN ] = SF_SIMP_P1( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming linear P1 Lagrange shape functions on simplices with values defined in the nodes. XI is Barycentric coordinates.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
i_eval      scalar:  1             Evaluate function values
                    >1             Evaluate values of derivatives
n_sdim      scalar: 1-3            Number of space dimensions
n_vert      scalar: 2-4            Number of vertices per cell
i_dof       scalar: 1-n_ldof       Local basis function to evaluate
xi          [n_sdim+1]             Local coordinates of evaluation point
aInvJac     [n,n_sdim+1*n_sdim]    Inverse of transformation Jacobian
vBase       [n]                    Preallocated output vector
                                                                                  .
Output      Value/[Size]           Description
-----------------------------------------------------------------------------------
vBase       [n]                    Evaluated function values
nLDof       [4]                    Number of local degrees of freedom on
                                   vertices, edges, faces, and cell interiors
xLDof       [n_sdim,n_ldof]        Local coordinates of local dofs
sfun        string                 Function name of called shape function

See also: sflag1

Code listing

 nLDof = [n_vert 0 0 0];
 if( n_vert==4 )
   xLDof = [1 0 0 0; 0 1 0 0; 0 0 1 0; 0 0 0 1];
 elseif( n_vert==3 )
   xLDof = [1 0 0; 0 1 0; 0 0 1];
 else
   xLDof = [1 0; 0 1];
 end
 sfun  = 'sf_simp_P1';


 switch i_eval    % Evaluation type flag.

   case 1         % Evaluation of function values.

     vBase = xi(i_dof);

   case {2,3,4}   % Evaluation of first derivatives.

     i_col = i_dof+(i_eval-2)*n_vert;

     vBase = aInvJac(:,i_col);

   otherwise
     vBase = 0;

 end