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sf_hex_Q3.m File Reference

Description

SF_HEX_Q3 Tricubic conforming shape function for hexahedrons (Q3).

[ VBASE, NLDOF, XLDOF, SFUN ] = SF_HEX_Q3( I_EVAL, N_SDIM, N_VERT, I_DOF, XI, AINVJAC, VBASE ) Evaluates conforming tricubic Q3 shape functions on hexahedrons with values defined in the nodes, edges, faces, and cell center. XI is [-1..1]^3 reference coordinates.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
i_eval      scalar:  1             Evaluate function values
                    >1             Evaluate values of derivatives
n_sdim      scalar:  3             Number of space dimensions
n_vert      scalar:  8             Number of vertices per cell
i_dof       scalar: 1-n_ldof       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
sflag3, sf_hex_Q1

Code listing

 nLDof = [8 24 24 8];
 xLDof = [ -1  1  1 -1 -1  1  1 -1  -1/3 1   1/3 -1   -1    1    1   -1  -1/3 1   1/3 -1    1/3 1   -1/3 -1   -1   1   1  -1   1/3 1  -1/3 -1   -1/3 -1/3  1    1/3 -1   -1/3  1/3  1/3  1   -1/3 -1    1/3  1/3  1/3 1   -1/3 -1   1/3 -1/3 -1/3  1   1/3 -1  -1/3   -1/3  1/3  1/3 -1/3 -1/3  1/3  1/3 -1/3 ;
           -1 -1  1  1 -1 -1  1  1  -1  -1/3 1    1/3 -1   -1    1    1  -1  -1/3 1    1/3 -1   1/3  1   -1/3 -1  -1   1   1  -1   1/3 1   -1/3 -1/3 -1   -1/3  1    1/3 -1/3 -1/3 -1    1/3  1   -1/3 -1/3  1/3 -1   1/3  1   -1/3 1/3  1/3 -1   -1/3 1    1/3 1/3   -1/3 -1/3  1/3  1/3 -1/3 -1/3  1/3  1/3 ;
           -1 -1 -1 -1  1  1  1  1  -1  -1  -1   -1   -1/3 -1/3 -1/3 -1/3 1   1   1    1   -1  -1   -1   -1    1/3 1/3 1/3 1/3 1   1   1    1   -1   -1/3 -1/3 -1/3 -1/3  1   -1   -1/3 -1/3 -1/3 -1/3  1   -1    1/3 1/3  1/3  1/3 1   -1    1/3  1/3 1/3  1/3 1     -1/3 -1/3 -1/3 -1/3  1/3  1/3  1/3  1/3 ];
 sfun  = 'sf_hex_Q3';


 switch i_eval

   case 1

     switch i_dof
       case 1
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 2
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 3
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 4
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 5
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 6
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 7
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
       case 8
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
       case 9
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 10
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 11
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 12
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 13
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 14
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 15
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 16
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 17
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 18
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 19
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
       case 20
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 21
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 22
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 23
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 24
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 25
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 26
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 27
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 28
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 29
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 30
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 31
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) + 1)/4096;
       case 32
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 33
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 34
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 35
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 36
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 37
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 38
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 39
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 40
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 41
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 42
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 43
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 44
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 45
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 46
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 47
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 48
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 49
         vBase = (3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 50
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 51
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 52
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 53
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) + 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 54
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) + 1)*(xi(3) - 1)/4096;
       case 55
         vBase = -(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 56
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) + 1)/4096;
       case 57
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 58
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 59
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 60
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) - 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 61
         vBase = -(3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 62
         vBase = (3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) - 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 63
         vBase = -(3*xi(1) + 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
       case 64
         vBase = (3*xi(1) - 1)*(9*xi(1) + 9)*(3*xi(2) + 1)*(9*xi(2) + 9)*(3*xi(3) + 1)*(9*xi(3) + 9)*(xi(1) - 1)*(xi(2) - 1)*(xi(3) - 1)/4096;
     end

   case {2,3,4}

     switch i_dof
       case 1
         dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 2
         dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 3
         dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 4
         dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 5
         dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 6
         dNdxi1 = -((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 7
         dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = ((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 8
         dNdxi1 = ((3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -((3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 9
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 10
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 11
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -(9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 12
         dNdxi1 = (9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 13
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 14
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 15
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 16
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 17
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 18
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 19
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -(9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 20
         dNdxi1 = -(9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 21
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = (9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 22
         dNdxi1 = (9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 23
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 24
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 25
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 26
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 27
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 28
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 29
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(9*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = (9*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 30
         dNdxi1 = -(9*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 31
         dNdxi1 = -(9*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = (9*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 32
         dNdxi1 = (9*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = (9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(9*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 33
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 34
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 35
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 36
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 37
         dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 38
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 39
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 40
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 41
         dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 42
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 43
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 44
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 45
         dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 46
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = -(81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 47
         dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 48
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 49
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 50
         dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 51
         dNdxi1 = -(81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 27*xi(3)^2 + 18*xi(3) + 1))/4096;
       case 52
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(2)^2 + 18*xi(2) + 1))/4096;
         dNdxi3 = (81*(3*xi(1) - 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 53
         dNdxi1 = -(81*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(1)^2 + 18*xi(1) - 1))/4096;
         dNdxi2 = (81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 54
         dNdxi1 = (81*(3*xi(2) - 1)*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (81*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(27*xi(2)^2 + 18*xi(2) - 1))/4096;
         dNdxi3 = (81*(3*xi(1) + 1)*(3*xi(2) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 55
         dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 27*xi(1)^2 + 18*xi(1) + 1))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 56
         dNdxi1 = (81*(3*xi(2) + 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(81*(3*xi(1) - 1)*(3*xi(3) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(81*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(27*xi(3)^2 + 18*xi(3) - 1))/4096;
       case 57
         dNdxi1 = -(729*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(729*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(729*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 58
         dNdxi1 = -(729*(3*xi(2) - 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (729*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (729*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 59
         dNdxi1 = (729*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = (729*(3*xi(1) + 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(729*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 60
         dNdxi1 = (729*(3*xi(2) + 1)*(3*xi(3) - 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = -(729*(3*xi(1) - 1)*(3*xi(3) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (729*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(- 9*xi(3)^2 + 2*xi(3) + 3))/4096;
       case 61
         dNdxi1 = (729*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (729*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = -(729*(3*xi(1) - 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 62
         dNdxi1 = (729*(3*xi(2) - 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(729*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(2)^2 + 2*xi(2) + 3))/4096;
         dNdxi3 = (729*(3*xi(1) + 1)*(3*xi(2) - 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 63
         dNdxi1 = -(729*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(1)^2 + 2*xi(1) - 3))/4096;
         dNdxi2 = -(729*(3*xi(1) + 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = -(729*(3*xi(1) + 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
       case 64
         dNdxi1 = -(729*(3*xi(2) + 1)*(3*xi(3) + 1)*(xi(2) - 1)*(xi(2) + 1)*(xi(3) - 1)*(xi(3) + 1)*(- 9*xi(1)^2 + 2*xi(1) + 3))/4096;
         dNdxi2 = (729*(3*xi(1) - 1)*(3*xi(3) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(3) - 1)*(xi(3) + 1)*(9*xi(2)^2 + 2*xi(2) - 3))/4096;
         dNdxi3 = (729*(3*xi(1) - 1)*(3*xi(2) + 1)*(xi(1) - 1)*(xi(1) + 1)*(xi(2) - 1)*(xi(2) + 1)*(9*xi(3)^2 + 2*xi(3) - 3))/4096;
     end

     if     ( i_eval==2 )   % x-derivative.

       vBase = aInvJac(:,1)*dNdxi1 + aInvJac(:,2)*dNdxi2 + aInvJac(:,3)*dNdxi3;

     elseif ( i_eval==3 )   % y-derivative.

       vBase = aInvJac(:,4)*dNdxi1 + aInvJac(:,5)*dNdxi2 + aInvJac(:,6)*dNdxi3;

     elseif ( i_eval==4 )   % z-derivative.

       vBase = aInvJac(:,7)*dNdxi1 + aInvJac(:,8)*dNdxi2 + aInvJac(:,9)*dNdxi3;
     end

   case {22,23,24,32,33,34,42,43,44}   % Evaluation of second order derivatives.
     error('sf_hex_Q3: second order derivative evaluation not supported.')

   otherwise
     vBase = 0;

 end