enhanced_elem_maps_hex.f90

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subroutine enhanced_elem_maps_hex(mixed_map,enhanced_map)

  implicit none

  integer :: igpt

  REAL*8, DIMENSION(1:8,1:9,1:12) :: mixed_map
  REAL*8, DIMENSION(1:8,1:9,1:9)  :: enhanced_map

  REAL*8, DIMENSION(1:8) :: xi, eta, zeta
  REAL*8, parameter :: one = 1.d0, three = 3.d0
  


  xi   = (/ one/sqrt(three), -one/sqrt(three), -one/sqrt(three), &
       one/sqrt(three),  one/sqrt(three), -one/sqrt(three), &
       -one/sqrt(three),  one/sqrt(three)     /)
  
  eta  = (/ one/sqrt(three),  one/sqrt(three), -one/sqrt(three), &
       -one/sqrt(three),  one/sqrt(three),  one/sqrt(three), &
       -one/sqrt(three), -one/sqrt(three)     /)
  
  zeta = (/ one/sqrt(three),  one/sqrt(three),  one/sqrt(three), &
       one/sqrt(three), -one/sqrt(three), -one/sqrt(three), &  
       -one/sqrt(three), -one/sqrt(three)     /)

!  Compute static things for gauss points

  DO igpt =1, 8

!  Compute mixed mapping matrix <mixed_map> at each gauss point

     mixed_map(igpt,1,1)  = eta(igpt)
     mixed_map(igpt,1,2)  = zeta(igpt)
     mixed_map(igpt,1,3)  = eta(igpt) * zeta(igpt)
     mixed_map(igpt,2,10) = zeta(igpt)
     mixed_map(igpt,3,12) = eta(igpt)
     mixed_map(igpt,4,10) = zeta(igpt)
     mixed_map(igpt,5,4)  = xi(igpt)        
     mixed_map(igpt,5,5)  = zeta(igpt)
     mixed_map(igpt,5,6)  = xi(igpt) * zeta(igpt)
     mixed_map(igpt,6,11) = xi(igpt)
     mixed_map(igpt,7,12) = eta(igpt)
     mixed_map(igpt,8,11) = xi(igpt)
     mixed_map(igpt,9,7)  = xi(igpt)        
     mixed_map(igpt,9,8)  = eta(igpt)
     mixed_map(igpt,9,9)  = xi(igpt) * eta(igpt)

!  Compute enhanced mapping matrix <enhanced_map> at each gauss point

     enhanced_map(igpt,1,1)  = xi(igpt)    
     enhanced_map(igpt,1,2)  = xi(igpt) * eta(igpt)
     enhanced_map(igpt,1,3)  = xi(igpt) * zeta(igpt)
     enhanced_map(igpt,5,4)  = eta(igpt)
     enhanced_map(igpt,5,5)  = eta(igpt) * zeta(igpt)
     enhanced_map(igpt,5,6)  = eta(igpt) * xi(igpt)
     enhanced_map(igpt,9,7)  = zeta(igpt)        
     enhanced_map(igpt,9,8)  = zeta(igpt) * eta(igpt)
     enhanced_map(igpt,9,9)  = zeta(igpt) * xi(igpt)

  END DO


end subroutine enhanced_elem_maps_hex