shapefunction_quad_lin

PURPOSE ^

SHAPEFUNCTION_QUAD Evaluates the linearized basis function on the reference square

SYNOPSIS ^

function phi=shapefunction_quad_lin(z,quadnode)

DESCRIPTION ^

SHAPEFUNCTION_QUAD   Evaluates the linearized basis function on the reference square
   PHI = SHAPEFUNCTION_QUAD(Z, QUADNODE)
   Evaluates the linearized basis function phi(x) on the reference (macro)
   square, where the linearization is based on the point quadnode.

   Z is a 2 x 1 vector containing the x and y coordinates in the reference
   square.
    
   QUADNODE is a 2 x 1 vector containing the x and y coordinates of the 
   quadrature node the linearization is based on in the reference square.

   PHI contains the evaluated function value.


   This function should not be modified.


   The code is available at http://anmc.epfl.ch/ and described in 
   further detail in 

   A. Abdulle and A. Nonnenmacher
   "A short and versatile finite element multiscale code for
   homogenization problems"
   Computer Methods in Applied Mechanics and Engineering,
   http://dx.doi.org/10.1016/j.cma.2009.03.019

   Please cite this article in any publication describing research
   performed using the software.


   Email           : assyr.abdulle@epfl.ch and achim.nonnenmacher@epfl.ch
   Last updated    : 04/29/2009 with MATLAB 7.4

   FE_HMM2D is Copyright (C) 2009 A. Abdulle and A. Nonnenmacher. 
   The software is provided free for non-commercial use unter the terms of 
   the GNU General Public License. See "copyright.m" for full details.

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function phi=shapefunction_quad_lin(z,quadnode)
0002 %SHAPEFUNCTION_QUAD   Evaluates the linearized basis function on the reference square
0003 %   PHI = SHAPEFUNCTION_QUAD(Z, QUADNODE)
0004 %   Evaluates the linearized basis function phi(x) on the reference (macro)
0005 %   square, where the linearization is based on the point quadnode.
0006 %
0007 %   Z is a 2 x 1 vector containing the x and y coordinates in the reference
0008 %   square.
0009 %
0010 %   QUADNODE is a 2 x 1 vector containing the x and y coordinates of the
0011 %   quadrature node the linearization is based on in the reference square.
0012 %
0013 %   PHI contains the evaluated function value.
0014 %
0015 %
0016 %   This function should not be modified.
0017 %
0018 %
0019 %   The code is available at http://anmc.epfl.ch/ and described in
0020 %   further detail in
0021 %
0022 %   A. Abdulle and A. Nonnenmacher
0023 %   "A short and versatile finite element multiscale code for
0024 %   homogenization problems"
0025 %   Computer Methods in Applied Mechanics and Engineering,
0026 %   http://dx.doi.org/10.1016/j.cma.2009.03.019
0027 %
0028 %   Please cite this article in any publication describing research
0029 %   performed using the software.
0030 %
0031 %
0032 %   Email           : assyr.abdulle@epfl.ch and achim.nonnenmacher@epfl.ch
0033 %   Last updated    : 04/29/2009 with MATLAB 7.4
0034 %
0035 %   FE_HMM2D is Copyright (C) 2009 A. Abdulle and A. Nonnenmacher.
0036 %   The software is provided free for non-commercial use unter the terms of
0037 %   the GNU General Public License. See "copyright.m" for full details.
0038 
0039 %
0040 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0041 
0042 
0043 % quadrature node, repeated
0044 quadnode_rep=repmat(quadnode', size(z,1), 1);
0045 x=quadnode_rep(:,1); y=quadnode_rep(:,2);
0046 
0047 % quadrature node, single
0048 xq=quadnode(1); yq=quadnode(2);
0049 
0050 % dx, dy for all the points
0051 dz=z-quadnode_rep;
0052 
0053 phi(:,1)= (1-x).*(1-y)+ dz(:,1) *(yq-1) + dz(:,2)* (xq-1);
0054 phi(:,2)=   x.*(1-y)  + dz(:,1) *(1-yq) + dz(:,2)* ( -xq);
0055 phi(:,3)=   x.*y      + dz(:,1) *(  yq) + dz(:,2)* (  xq);
0056 phi(:,4)= (1-x).*y    + dz(:,1) *( -yq) + dz(:,2)* (1-xq);
0057 
0058 end

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