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FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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FEATool Multiphysics
v1.17.1
Finite Element Analysis Toolbox
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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
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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
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