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sf_quad_Q5.m File Reference

Description

SF_QUAD_Q5 Biquintic conforming shape function for quadrilaterals (Q5).

[ VBASE, NLDOF, XLDOF, SFUN ] = SF_QUAD_Q5( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming biquintic Q5 shape functions on quadrilaterals with values defined in the nodes, edges, and cell center. XI is [-1..1]^2 reference coordinates.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
i_eval      scalar:  1             Evaluate function values
                    >1             Evaluate values of derivatives
n_sdim      scalar:  2             Number of space dimensions
n_vert      scalar:  4             Number of vertices per cell
i_dof       scalar: 1-36           Local basis function to evaluate
xi          [n_sdim]               Local coordinates of evaluation point
aInvJac     [n,n_sdim*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
sf_quad_Q1

Code listing

 nLDof = [4 16 0 16];
 xLDof = [-1  1 1 -1  -3/5  1   3/5 -1    -1/5  1   1/5 -1     1/5  1   -1/5 -1     3/5  1   -3/5 -1    -3/5  3/5 3/5 -3/5  -1/5  3/5 1/5 -3/5   1/5 3/5 -1/5 -3/5  -1/5  1/5 1/5 -1/5;
          -1 -1 1  1  -1   -3/5 1    3/5  -1   -1/5 1    1/5  -1    1/5  1   -1/5  -1    3/5  1   -3/5  -3/5 -3/5 3/5  3/5  -3/5 -1/5 3/5  1/5  -3/5 1/5  3/5 -1/5  -1/5 -1/5 1/5  1/5];
 sfun  = 'sf_quad_Q5';


 switch i_eval

   case 1

     switch i_dof
       case 1
         vBase = ((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256);
       case 2
         vBase = -((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256);
       case 3
         vBase = ((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256);
       case 4
         vBase = -((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256);
       case 5
         vBase = -((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256);
       case 6
         vBase = ((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
       case 7
         vBase = -((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256);
       case 8
         vBase = ((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
       case 9
         vBase = ((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128);
       case 10
         vBase = -((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
       case 11
         vBase = ((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128);
       case 12
         vBase = -((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
       case 13
         vBase = -((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128);
       case 14
         vBase = ((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
       case 15
         vBase = -((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128);
       case 16
         vBase = ((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
       case 17
         vBase = ((625*xi(2)^5)/768 - (625*xi(2)^4)/768 - (125*xi(2)^3)/384 + (125*xi(2)^2)/384 + (3*xi(2))/256 - 3/256)*((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256);
       case 18
         vBase = -((625*xi(1)^5)/768 + (625*xi(1)^4)/768 - (125*xi(1)^3)/384 - (125*xi(1)^2)/384 + (3*xi(1))/256 + 3/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
       case 19
         vBase = ((625*xi(2)^5)/768 + (625*xi(2)^4)/768 - (125*xi(2)^3)/384 - (125*xi(2)^2)/384 + (3*xi(2))/256 + 3/256)*((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256);
       case 20
         vBase = -((625*xi(1)^5)/768 - (625*xi(1)^4)/768 - (125*xi(1)^3)/384 + (125*xi(1)^2)/384 + (3*xi(1))/256 - 3/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
       case 21
         vBase = ((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
       case 22
         vBase = -((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
       case 23
         vBase = ((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
       case 24
         vBase = -((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
       case 25
         vBase = -((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
       case 26
         vBase = ((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
       case 27
         vBase = -((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
       case 28
         vBase = ((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
       case 29
         vBase = ((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/768 - (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 + (325*xi(2)^2)/128 + (125*xi(2))/768 - 25/256);
       case 30
         vBase = -((3125*xi(1)^5)/768 + (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 - (325*xi(1)^2)/128 + (125*xi(1))/768 + 25/256)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
       case 31
         vBase = ((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/768 + (625*xi(2)^4)/256 - (1625*xi(2)^3)/384 - (325*xi(2)^2)/128 + (125*xi(2))/768 + 25/256);
       case 32
         vBase = -((3125*xi(1)^5)/768 - (625*xi(1)^4)/256 - (1625*xi(1)^3)/384 + (325*xi(1)^2)/128 + (125*xi(1))/768 - 25/256)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
       case 33
         vBase = ((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
       case 34
         vBase = -((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/384 - (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 + (425*xi(2)^2)/192 + (375*xi(2))/128 - 75/128);
       case 35
         vBase = ((3125*xi(1)^5)/384 + (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 - (425*xi(1)^2)/192 + (375*xi(1))/128 + 75/128)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
       case 36
         vBase = -((3125*xi(1)^5)/384 - (625*xi(1)^4)/384 - (2125*xi(1)^3)/192 + (425*xi(1)^2)/192 + (375*xi(1))/128 - 75/128)*((3125*xi(2)^5)/384 + (625*xi(2)^4)/384 - (2125*xi(2)^3)/192 - (425*xi(2)^2)/192 + (375*xi(2))/128 + 75/128);
     end

   case {2,3}

     switch i_dof
       case 1
         dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
       case 2
         dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
       case 3
         dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
       case 4
         dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
       case 5
         dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
       case 6
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
       case 7
         dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
       case 8
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
       case 9
         dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/384;
       case 10
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/384;
         dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
       case 11
         dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = (25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/384;
       case 12
         dNdxi1 = -(25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/384;
         dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
       case 13
         dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = -(25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/384;
       case 14
         dNdxi1 = (25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/384;
         dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
       case 15
         dNdxi1 = -((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/384;
       case 16
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/384;
         dNdxi2 = ((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
       case 17
         dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 - (625*xi(2)^3)/192 - (125*xi(2)^2)/128 + (125*xi(2))/192 + 3/256))/768;
       case 18
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 + (625*xi(1)^3)/192 - (125*xi(1)^2)/128 - (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
       case 19
         dNdxi1 = ((5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((3125*xi(2)^4)/768 + (625*xi(2)^3)/192 - (125*xi(2)^2)/128 - (125*xi(2))/192 + 3/256))/768;
       case 20
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((3125*xi(1)^4)/768 - (625*xi(1)^3)/192 - (125*xi(1)^2)/128 + (125*xi(1))/192 + 3/256))/768;
         dNdxi2 = -((5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
       case 21
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
       case 22
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/768;
       case 23
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
       case 24
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/768;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/768;
       case 25
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/384;
       case 26
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/384;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
       case 27
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = -(25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/384;
       case 28
         dNdxi1 = (25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/384;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
       case 29
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) - 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = (25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 - (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 + (325*xi(2))/64 + 125/768))/384;
       case 30
         dNdxi1 = -(25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 + (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 - (325*xi(1))/64 + 125/768))/384;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/768;
       case 31
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) + 1)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/768;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/768 + (625*xi(2)^3)/64 - (1625*xi(2)^2)/128 - (325*xi(2))/64 + 125/768))/384;
       case 32
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/768 - (625*xi(1)^3)/64 - (1625*xi(1)^2)/128 + (325*xi(1))/64 + 125/768))/384;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) + 1)*(5*xi(1) - 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/768;
       case 33
         dNdxi1 = (25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/384;
         dNdxi2 = (25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/384;
       case 34
         dNdxi1 = -(25*(5*xi(2) - 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/384;
         dNdxi2 = -(25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 - (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 + (425*xi(2))/96 + 375/128))/384;
       case 35
         dNdxi1 = (25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 + (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 - (425*xi(1))/96 + 375/128))/384;
         dNdxi2 = (25*(5*xi(1) + 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/384;
       case 36
         dNdxi1 = -(25*(5*xi(2) + 1)*(5*xi(2) - 3)*(5*xi(2) + 3)*(xi(2) - 1)*(xi(2) + 1)*((15625*xi(1)^4)/384 - (625*xi(1)^3)/96 - (2125*xi(1)^2)/64 + (425*xi(1))/96 + 375/128))/384;
         dNdxi2 = -(25*(5*xi(1) - 1)*(5*xi(1) - 3)*(5*xi(1) + 3)*(xi(1) - 1)*(xi(1) + 1)*((15625*xi(2)^4)/384 + (625*xi(2)^3)/96 - (2125*xi(2)^2)/64 - (425*xi(2))/96 + 375/128))/384;
     end

     if( i_eval==2 )
       vBase = aInvJac(:,1).*dNdxi1 + aInvJac(:,2).*dNdxi2;
     else
       vBase = aInvJac(:,3).*dNdxi1 + aInvJac(:,4).*dNdxi2;
     end

   case {22,23,32,33}   % Evaluation of second order derivatives.
     error('sf_quad_Q5: second order derivative evaluation not supported.')

   otherwise
     vBase = 0;

 end