shcalc.f90

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SUBROUTINE shcalc(shfn, shdx, dv, dvsum, shdx_av, meshpos, &
     ndim,nnode,nintk,xi,eta,zeta,shdxi,wsp2)

!!****f* Rocfrac/Rocfrac/Source/shcalc.f90
!!
!!  NAME
!!     shcalc
!!
!!  FUNCTION
!!     EVALUALTE SHAPE FUNCTION AND ITS DERIVATIVES FOR 4-NODE TET.
!!
!!****

  IMPLICIT NONE
  
  INTEGER ndim, nnode, nintk

  DOUBLE PRECISION shfn(nnode,nintk), shdx(ndim,nnode,nintk), &
       dv(nintk), dvsum, shdx_av(ndim,nnode), &
       meshpos(ndim,nnode),xi(nintk),eta(nintk), &
       zeta(nintk),shdxi(ndim,nnode,nintk)
  
  DOUBLE PRECISION wsp1(3,3),wsp2(3,3),eighth,one,zero
  
  INTEGER igauss, knode, i,j


  one = 1.d0
  eighth = 1.d0/8.d0
  zero = 0.d0

!     fill in shape fn. values and parametric derivatives at Gauss pts.

  igauss = 1
  
  shfn(1,igauss) = zeta(igauss)
  shfn(2,igauss) = xi(igauss) 
  shfn(3,igauss) = one-xi(igauss)-eta(igauss)-zeta(igauss)  
  shfn(4,igauss) = eta(igauss)
  
  shdxi(1,1,igauss) = zero
  shdxi(2,1,igauss) = zero 
  shdxi(3,1,igauss) = one
  
  shdxi(1,2,igauss) = one
  shdxi(2,2,igauss) = zero
  shdxi(3,2,igauss) = zero
  
  shdxi(1,3,igauss) =-one
  shdxi(2,3,igauss) =-one
  shdxi(3,3,igauss) =-one
  
  shdxi(1,4,igauss) = zero
  shdxi(2,4,igauss) = one
  shdxi(3,4,igauss) = zero
  

!    evaluate and store common quantities for all Gauss pts.
!    and shape fn. derivatives w.r.t. spatial coordinates.

  DO i = 1,ndim
     DO j = 1,ndim
        wsp1(i,j) = zero
        DO knode = 1,nnode
           wsp1(i,j) = wsp1(i,j) + meshpos(i,knode)* &
                shdxi(j,knode,igauss)
        END DO
     END DO
  END DO

  CALL ainv(wsp1,wsp2,dv(igauss),ndim)

!        evaluate shape fn. derivatives
  
  DO knode = 1,nnode
     DO i = 1,ndim
        shdx(i,knode,igauss) = zero
        DO j = 1,ndim
           shdx(i,knode,igauss) = shdx(i,knode,igauss) + &
                shdxi(j,knode,igauss)*wsp2(j,i)
        END DO
     END DO
  END DO
  
  RETURN
END SUBROUTINE shcalc