2011-08-25 23:48:38 +05:30
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!$Id$
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!all function below are taken from math.f90
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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module math
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real*8, parameter :: pi = 3.14159265358979323846264338327950288419716939937510
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! *** 3x3 Identity ***
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real*8, dimension(3,3), parameter :: math_I3 = &
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reshape( (/ &
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1.0,0.0,0.0, &
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0.0,1.0,0.0, &
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0.0,0.0,1.0 /),(/3,3/))
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contains
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!**************************************************************************
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! matrix multiplication 33x33 = 3x3
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!**************************************************************************
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pure function math_mul33x33(A,B)
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implicit none
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integer i,j
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real*8, dimension(3,3), intent(in) :: A,B
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real*8, dimension(3,3) :: math_mul33x33
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forall (i=1:3,j=1:3) math_mul33x33(i,j) = &
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A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j)
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return
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end function math_mul33x33
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!**************************************************************************
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! Cramer inversion of 3x3 matrix (subroutine)
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!**************************************************************************
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PURE SUBROUTINE math_invert3x3(A, InvA, DetA, error)
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! Bestimmung der Determinanten und Inversen einer 3x3-Matrix
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! A = Matrix A
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! InvA = Inverse of A
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! DetA = Determinant of A
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! error = logical
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implicit none
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logical, intent(out) :: error
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real*8,dimension(3,3),intent(in) :: A
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real*8,dimension(3,3),intent(out) :: InvA
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real*8, intent(out) :: DetA
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DetA = A(1,1) * ( A(2,2) * A(3,3) - A(2,3) * A(3,2) )&
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- A(1,2) * ( A(2,1) * A(3,3) - A(2,3) * A(3,1) )&
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+ A(1,3) * ( A(2,1) * A(3,2) - A(2,2) * A(3,1) )
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if (DetA <= tiny(DetA)) then
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error = .true.
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else
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InvA(1,1) = ( A(2,2) * A(3,3) - A(2,3) * A(3,2) ) / DetA
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InvA(2,1) = ( -A(2,1) * A(3,3) + A(2,3) * A(3,1) ) / DetA
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InvA(3,1) = ( A(2,1) * A(3,2) - A(2,2) * A(3,1) ) / DetA
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InvA(1,2) = ( -A(1,2) * A(3,3) + A(1,3) * A(3,2) ) / DetA
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InvA(2,2) = ( A(1,1) * A(3,3) - A(1,3) * A(3,1) ) / DetA
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InvA(3,2) = ( -A(1,1) * A(3,2) + A(1,2) * A(3,1) ) / DetA
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InvA(1,3) = ( A(1,2) * A(2,3) - A(1,3) * A(2,2) ) / DetA
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InvA(2,3) = ( -A(1,1) * A(2,3) + A(1,3) * A(2,1) ) / DetA
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InvA(3,3) = ( A(1,1) * A(2,2) - A(1,2) * A(2,1) ) / DetA
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error = .false.
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endif
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return
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END SUBROUTINE math_invert3x3
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!********************************************************************
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! determinant of a 3x3 matrix
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!********************************************************************
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pure function math_det3x3(m)
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implicit none
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real*8, dimension(3,3), intent(in) :: m
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real*8 math_det3x3
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math_det3x3 = m(1,1)*(m(2,2)*m(3,3)-m(2,3)*m(3,2)) &
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-m(1,2)*(m(2,1)*m(3,3)-m(2,3)*m(3,1)) &
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+m(1,3)*(m(2,1)*m(3,2)-m(2,2)*m(3,1))
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return
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end function math_det3x3
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!****************************************************************
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pure subroutine math_pDecomposition(FE,U,R,error)
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!-----FE = R.U
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!****************************************************************
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implicit none
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real*8, intent(in) :: FE(3,3)
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real*8, intent(out) :: R(3,3), U(3,3)
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logical, intent(out) :: error
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real*8 CE(3,3),EW1,EW2,EW3,EB1(3,3),EB2(3,3),EB3(3,3),UI(3,3),det
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error = .false.
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ce = math_mul33x33(transpose(FE),FE)
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CALL math_spectral1(CE,EW1,EW2,EW3,EB1,EB2,EB3)
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U=DSQRT(EW1)*EB1+DSQRT(EW2)*EB2+DSQRT(EW3)*EB3
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call math_invert3x3(U,UI,det,error)
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if (.not. error) R = math_mul33x33(FE,UI)
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return
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end subroutine math_pDecomposition
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!**************************************************************************
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! Cramer inversion of 3x3 matrix (function)
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!**************************************************************************
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pure function math_inv3x3(A)
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! direct Cramer inversion of matrix A.
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! returns all zeroes if not possible, i.e. if det close to zero
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implicit none
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real*8,dimension(3,3),intent(in) :: A
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real*8 DetA
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real*8,dimension(3,3) :: math_inv3x3
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math_inv3x3 = 0.0
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DetA = A(1,1) * ( A(2,2) * A(3,3) - A(2,3) * A(3,2) )&
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- A(1,2) * ( A(2,1) * A(3,3) - A(2,3) * A(3,1) )&
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+ A(1,3) * ( A(2,1) * A(3,2) - A(2,2) * A(3,1) )
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if (DetA > tiny(DetA)) then
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math_inv3x3(1,1) = ( A(2,2) * A(3,3) - A(2,3) * A(3,2) ) / DetA
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math_inv3x3(2,1) = ( -A(2,1) * A(3,3) + A(2,3) * A(3,1) ) / DetA
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math_inv3x3(3,1) = ( A(2,1) * A(3,2) - A(2,2) * A(3,1) ) / DetA
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math_inv3x3(1,2) = ( -A(1,2) * A(3,3) + A(1,3) * A(3,2) ) / DetA
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math_inv3x3(2,2) = ( A(1,1) * A(3,3) - A(1,3) * A(3,1) ) / DetA
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math_inv3x3(3,2) = ( -A(1,1) * A(3,2) + A(1,2) * A(3,1) ) / DetA
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math_inv3x3(1,3) = ( A(1,2) * A(2,3) - A(1,3) * A(2,2) ) / DetA
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math_inv3x3(2,3) = ( -A(1,1) * A(2,3) + A(1,3) * A(2,1) ) / DetA
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math_inv3x3(3,3) = ( A(1,1) * A(2,2) - A(1,2) * A(2,1) ) / DetA
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endif
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return
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end function math_inv3x3
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!**********************************************************************
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! HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M
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!**********************************************************************
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PURE SUBROUTINE math_hi(M,HI1M,HI2M,HI3M)
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implicit none
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real*8, intent(in) :: M(3,3)
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real*8, intent(out) :: HI1M, HI2M, HI3M
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HI1M=M(1,1)+M(2,2)+M(3,3)
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HI2M=HI1M**2/2.0-(M(1,1)**2+M(2,2)**2+M(3,3)**2)/2.0-M(1,2)*M(2,1)-M(1,3)*M(3,1)-M(2,3)*M(3,2)
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HI3M=math_det3x3(M)
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! QUESTION: is 3rd equiv det(M) ?? if yes, use function math_det !agreed on YES
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return
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END SUBROUTINE math_hi
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!**********************************************************************
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pure subroutine math_spectral1(M,EW1,EW2,EW3,EB1,EB2,EB3)
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!**** EIGENWERTE UND EIGENWERTBASIS DER SYMMETRISCHEN 3X3 MATRIX M
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implicit none
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real*8, intent(in) :: M(3,3)
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real*8, intent(out) :: EB1(3,3),EB2(3,3),EB3(3,3),EW1,EW2,EW3
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real*8 HI1M,HI2M,HI3M,TOL,R,S,T,P,Q,RHO,PHI,Y1,Y2,Y3,D1,D2,D3
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real*8 C1,C2,C3,M1(3,3),M2(3,3),M3(3,3),arg
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TOL=1.e-14
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CALL math_hi(M,HI1M,HI2M,HI3M)
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R=-HI1M
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S= HI2M
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T=-HI3M
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P=S-R**2.0/3.0
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Q=2.0/27.0*R**3.0-R*S/3.0+T
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EB1=0.0
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EB2=0.0
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EB3=0.0
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IF((ABS(P).LT.TOL).AND.(ABS(Q).LT.TOL))THEN
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! DREI GLEICHE EIGENWERTE
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EW1=HI1M/3.0
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EW2=EW1
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EW3=EW1
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! this is not really correct, but this way U is calculated
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! correctly in PDECOMPOSITION (correct is EB?=I)
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EB1(1,1)=1.0
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EB2(2,2)=1.0
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EB3(3,3)=1.0
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ELSE
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RHO=DSQRT(-3.0*P**3.0)/9.0
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arg=-Q/RHO/2.0
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if(arg.GT.1) arg=1
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if(arg.LT.-1) arg=-1
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PHI=DACOS(arg)
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Y1=2*RHO**(1.0/3.0)*DCOS(PHI/3.0)
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Y2=2*RHO**(1.0/3.0)*DCOS(PHI/3.0+2.0/3.0*PI)
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Y3=2*RHO**(1.0/3.0)*DCOS(PHI/3.0+4.0/3.0*PI)
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EW1=Y1-R/3.0
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EW2=Y2-R/3.0
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EW3=Y3-R/3.0
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C1=ABS(EW1-EW2)
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C2=ABS(EW2-EW3)
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C3=ABS(EW3-EW1)
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IF(C1.LT.TOL) THEN
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! EW1 is equal to EW2
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D3=1.0/(EW3-EW1)/(EW3-EW2)
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M1=M-EW1*math_I3
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M2=M-EW2*math_I3
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EB3=math_mul33x33(M1,M2)*D3
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EB1=math_I3-EB3
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! both EB2 and EW2 are set to zero so that they do not
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! contribute to U in PDECOMPOSITION
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EW2=0.0
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ELSE IF(C2.LT.TOL) THEN
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! EW2 is equal to EW3
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D1=1.0/(EW1-EW2)/(EW1-EW3)
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M2=M-math_I3*EW2
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M3=M-math_I3*EW3
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EB1=math_mul33x33(M2,M3)*D1
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EB2=math_I3-EB1
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! both EB3 and EW3 are set to zero so that they do not
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! contribute to U in PDECOMPOSITION
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EW3=0.0
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ELSE IF(C3.LT.TOL) THEN
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! EW1 is equal to EW3
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D2=1.0/(EW2-EW1)/(EW2-EW3)
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M1=M-math_I3*EW1
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M3=M-math_I3*EW3
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EB2=math_mul33x33(M1,M3)*D2
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EB1=math_I3-EB2
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! both EB3 and EW3 are set to zero so that they do not
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! contribute to U in PDECOMPOSITION
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EW3=0.0
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ELSE
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! all three eigenvectors are different
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D1=1.0/(EW1-EW2)/(EW1-EW3)
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D2=1.0/(EW2-EW1)/(EW2-EW3)
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D3=1.0/(EW3-EW1)/(EW3-EW2)
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M1=M-EW1*math_I3
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M2=M-EW2*math_I3
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M3=M-EW3*math_I3
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EB1=math_mul33x33(M2,M3)*D1
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EB2=math_mul33x33(M1,M3)*D2
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EB3=math_mul33x33(M1,M2)*D3
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END IF
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END IF
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RETURN
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END SUBROUTINE math_spectral1
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!**************************************************************************
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! volume of tetrahedron given by four vertices
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!**************************************************************************
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pure function math_volTetrahedron(v1,v2,v3,v4)
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implicit none
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real*8 math_volTetrahedron
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real*8, dimension (3), intent(in) :: v1,v2,v3,v4
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real*8, dimension (3,3) :: m
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m(:,1) = v1-v2
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m(:,2) = v2-v3
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m(:,3) = v3-v4
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math_volTetrahedron = math_det3x3(m)/6.0
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end function math_volTetrahedron
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!subroutines below are for postprocessing with python
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!two small helper functions for indexing
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! CAREFULL, index and location runs from 0 to N-1 (python style)
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function mesh_location(idx,resolution)
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integer, intent(in) :: idx
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integer, intent(in) :: resolution(3)
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integer :: mesh_location(3)
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mesh_location = (/modulo(idx/ resolution(3) / resolution(2),resolution(1)), &
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modulo(idx/ resolution(3), resolution(2)), &
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modulo(idx, resolution(3))/)
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end function mesh_location
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function mesh_index(location,resolution)
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integer, intent(in) :: location(3)
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integer, intent(in) :: resolution(3)
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integer :: mesh_index
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mesh_index = modulo(location(3), resolution(3)) +&
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(modulo(location(2), resolution(2)))*resolution(3) +&
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(modulo(location(1), resolution(1)))*resolution(3)*resolution(2)
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end function mesh_index
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end module math
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine mesh(res_x,res_y,res_z,geomdim,defgrad_av,centroids,nodes)
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! Routine to build a regular mesh of cubes for given coordinates (= center of the cubes)
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!
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implicit none
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real*8 geomdim(3)
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integer res_x, res_y, res_z
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real*8 wrappedCentroids(res_x+2,res_y+2,res_z+2,3)
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real*8 nodes(res_x+1,res_y+1,res_z+1,3)
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real*8 centroids(res_x ,res_y ,res_z ,3)
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integer, dimension(3,8) :: neighbor = reshape((/ &
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0, 0, 0, &
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1, 0, 0, &
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1, 1, 0, &
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0, 1, 0, &
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0, 0, 1, &
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1, 0, 1, &
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1, 1, 1, &
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0, 1, 1 &
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/), &
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(/3,8/))
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integer i,j,k,n
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real*8, dimension(3,3) :: defgrad_av
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integer, dimension(3) :: diag, shift, lookup, me, res
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nodes = 0.0
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diag = 1
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shift = 0
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lookup = 0
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res = (/res_x,res_y,res_z/)
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wrappedCentroids = 0.0
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wrappedCentroids(2:res_x+1,2:res_y+1,2:res_z+1,:) = centroids
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do k = 0,res_z+1
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do j = 0,res_y+1
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do i = 0,res_x+1
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if (k==0 .or. k==res_z+1 .or. & ! z skin
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j==0 .or. j==res_y+1 .or. & ! y skin
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i==0 .or. i==res_x+1 ) then ! x skin
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me = (/i,j,k/) ! me on skin
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shift = sign(abs(res+diag-2*me)/(res+diag),res+diag-2*me)
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lookup = me-diag+shift*res
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wrappedCentroids(i+1,j+1,k+1,:) = centroids(lookup(1)+1,lookup(2)+1,lookup(3)+1,:) - &
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matmul(defgrad_av, shift*geomdim)
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endif
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enddo; enddo; enddo
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do k = 0,res_z
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do j = 0,res_y
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do i = 0,res_x
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do n = 1,8
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nodes(i+1,j+1,k+1,:) = nodes(i+1,j+1,k+1,:) + wrappedCentroids(i+1+neighbor(1,n), &
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j+1+neighbor(2,n), &
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k+1+neighbor(3,n), :)
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enddo; enddo; enddo; enddo
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nodes = nodes/8.0
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end subroutine mesh
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine deformed(res_x,res_y,res_z,geomdim,defgrad,defgrad_av,coord_avgCorner)
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! Routine to calculate coordinates in current configuration for given defgrad
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! using linear interpolation (blurres out high frequency defomation)
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!
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implicit none
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real*8 geomdim(3)
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integer res_x, res_y, res_z
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real*8 coord(8,6,res_x,res_y,res_z,3)
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real*8 coord_avgOrder(8,res_x,res_y,res_z,3)
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real*8 coord_avgCorner(res_x,res_y,res_z,3)
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real*8 defgrad(res_x,res_y,res_z,3,3)
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integer, dimension(3,8) :: corner = reshape((/ &
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0, 0, 0,&
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1, 0, 0,&
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1, 1, 0,&
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0, 1, 0,&
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1, 1, 1,&
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0, 1, 1,&
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0, 0, 1,&
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1, 0, 1 &
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/), &
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(/3,8/))
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integer, dimension(3,8) :: step = reshape((/ &
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1, 1, 1,&
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-1, 1, 1,&
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-1,-1, 1,&
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1,-1, 1,&
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-1,-1,-1,&
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1,-1,-1,&
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1, 1,-1,&
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-1, 1,-1 &
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/), &
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(/3,8/))
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integer, dimension(3,6) :: order = reshape((/ &
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1, 2, 3,&
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1, 3, 2,&
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2, 1, 3,&
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2, 3, 1,&
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3, 1, 2,&
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3, 2, 1 &
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/), &
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(/3,6/))
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real*8 myStep(3), fones(3), parameter_coords(3)
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real*8 defgrad_av(3,3)
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real*8 negative(3), positive(3)
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integer rear(3), init(3), ones(3), oppo(3), me(3), res(3)
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integer i, j, k, s, o
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print*, 'Restore geometry using linear integration'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res_x,res_y,res_z
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ones = 1
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fones = 1.0
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coord_avgOrder=0.0
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res = (/res_x,res_y,res_z/)
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do s = 0, 7 ! corners (from 0 to 7)
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init = corner(:,s+1)*(res-ones) +ones
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oppo = corner(:,mod((s+4),8)+1)*(res-ones) +ones
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do o=1,6 ! orders ! from 1 to 6)
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do k = init(order(3,o)), oppo(order(3,o)), step(order(3,o),s+1)
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rear(order(2,o)) = init(order(2,o))
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do j = init(order(2,o)), oppo(order(2,o)), step(order(2,o),s+1)
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rear(order(1,o)) = init(order(1,o))
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do i = init(order(1,o)), oppo(order(1,o)), step(order(1,o),s+1)
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me(order(1,o)) = i
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me(order(2,o)) = j
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me(order(3,o)) = k
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if ( (me(1)==init(1)).and.(me(2)==init(2)).and. (me(3)==init(3)) ) then
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coord(s+1,o,me(1),me(2),me(3),:) = geomdim * (matmul(defgrad_av,corner(:,s+1)) + &
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matmul(defgrad(me(1),me(2),me(3),:,:),0.5*step(:,s+1)/res))
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else
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myStep = (me-rear)*geomdim/res
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coord(s+1,o,me(1),me(2),me(3),:) = coord(s+1,o,rear(1),rear(2),rear(3),:) + &
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0.5*matmul(defgrad(me(1),me(2),me(3),:,:) + &
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defgrad(rear(1),rear(2),rear(3),:,:),myStep)
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endif
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rear = me
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enddo; enddo; enddo; enddo
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do i=1,6
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coord_avgOrder(s+1,:,:,:,:) = coord_avgOrder(s+1,:,:,:,:) + coord(s+1,i,:,:,:,:)/6.0
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enddo
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enddo
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do k=0, res_z-1
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do j=0, res_y-1
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do i=0, res_x-1
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parameter_coords = (2.0*(/i+0.0,j+0.0,k+0.0/)-real(res)+fones)/(real(res)-fones)
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positive = fones + parameter_coords
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negative = fones - parameter_coords
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coord_avgCorner(i+1,j+1,k+1,:) = ( coord_avgOrder(1,i+1,j+1,k+1,:) *negative(1)*negative(2)*negative(3)&
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+ coord_avgOrder(2,i+1,j+1,k+1,:) *positive(1)*negative(2)*negative(3)&
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+ coord_avgOrder(3,i+1,j+1,k+1,:) *positive(1)*positive(2)*negative(3)&
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+ coord_avgOrder(4,i+1,j+1,k+1,:) *negative(1)*positive(2)*negative(3)&
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+ coord_avgOrder(5,i+1,j+1,k+1,:) *positive(1)*positive(2)*positive(3)&
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+ coord_avgOrder(6,i+1,j+1,k+1,:) *negative(1)*positive(2)*positive(3)&
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+ coord_avgOrder(7,i+1,j+1,k+1,:) *negative(1)*negative(2)*positive(3)&
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+ coord_avgOrder(8,i+1,j+1,k+1,:) *positive(1)*negative(2)*positive(3))*0.125
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enddo; enddo; enddo
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end subroutine deformed
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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|
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subroutine deformed_fft(res_x,res_y,res_z,geomdim,defgrad,defgrad_av,scaling,coords)
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! Routine to calculate coordinates in current configuration for given defgrad
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! using integration in Fourier space (more accurate than deformed(...))
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!
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implicit none
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integer res_x, res_y, res_z
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real*8 geomdim(3)
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real*8 defgrad(res_x,res_y,res_z,3,3)
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real*8 defgrad_av(3,3)
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real*8 scaling
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real*8 coords(res_x,res_y,res_z,3)
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complex*16 coords_fft(res_x/2+1,res_y,res_z,3)
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complex*16 defgrad_fft(res_x,res_y,res_z,3,3)
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|
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integer i, j, k
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integer k_s(3)
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real*8 step(3)
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real*8 offset_coords(3)
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real*8, parameter :: pi = 3.14159265358979323846264338327950288419716939937510
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integer*8 :: plan_fft(2)
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include 'fftw3.f' !header file for fftw3 (declaring variables). Library files are also needed
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print*, 'Restore geometry using FFT-based integration'
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print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim
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print '(a,/,i5,i5,i5)', ' Resolution:', res_x,res_y,res_z
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call dfftw_plan_many_dft(plan_fft(1),3,(/res_x,res_y,res_z/),9,&
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|
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defgrad_fft,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,&
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defgrad_fft,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,FFTW_FORWARD,FFTW_PATIENT)
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call dfftw_plan_many_dft_c2r(plan_fft(2),3,(/res_x,res_y,res_z/),3,&
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coords_fft,(/res_x/2+1,res_y,res_z/),1,(res_x/2+1)*res_y*res_z,&
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coords, (/res_x, res_y,res_z/),1, res_x* res_y*res_z,FFTW_PATIENT)
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coords_fft = 0.0
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defgrad_fft = defgrad
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step(1) = geomdim(1)/real(res_x)
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step(2) = geomdim(2)/real(res_y)
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step(3) = geomdim(3)/real(res_z)
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call dfftw_execute_dft(plan_fft(1), defgrad_fft, defgrad_fft)
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do k = 1, res_z
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k_s(3) = k-1
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if(k > res_z/2+1) k_s(3) = k_s(3)-res_z
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do j = 1, res_y
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|
k_s(2) = j-1
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if(j > res_y/2+1) k_s(2) = k_s(2)-res_y
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|
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do i = 1, res_x/2+1
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|
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k_s(1) = i-1
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|
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if(i/=1) coords_fft(i,j,k,:) = coords_fft(i,j,k,:)&
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|
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+ defgrad_fft(i,j,k,:,1)*geomdim(1)/(real(k_s(1))*cmplx(0.0,1.0)*pi*2.0)
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|
if(j/=1) coords_fft(i,j,k,:) = coords_fft(i,j,k,:)&
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+ defgrad_fft(i,j,k,:,2)*geomdim(2)/(real(k_s(2))*cmplx(0.0,1.0)*pi*2.0)
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if(k/=1) coords_fft(i,j,k,:) = coords_fft(i,j,k,:)&
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+ defgrad_fft(i,j,k,:,3)*geomdim(3)/(real(k_s(3))*cmplx(0.0,1.0)*pi*2.0)
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enddo; enddo; enddo
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call dfftw_execute_dft_c2r(plan_fft(2), coords_fft, coords)
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|
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coords = coords/real(res_x*res_y*res_z)
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offset_coords = matmul(defgrad(1,1,1,:,:),step/2.0) - scaling*coords(1,1,1,:)
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do k = 1, res_z; do j = 1, res_y; do i = 1, res_x
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coords(i,j,k,:) = scaling*coords(i,j,k,:) + offset_coords + matmul(defgrad_av,&
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(/step(1)*real(i-1),&
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step(2)*real(j-1),&
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step(3)*real(k-1)/))
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enddo; enddo; enddo
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end subroutine deformed_fft
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|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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|
|
subroutine volume_compare(res_x,res_y,res_z,geomdim,nodes,defgrad,volume_mismatch)
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|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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|
|
! Routine to calculate the mismatch between volume of reconstructed (compatible)
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|
|
! cube and determinant of defgrad at the FP
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|
|
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|
use math
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|
|
implicit none
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|
|
|
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|
|
|
real*8 geomdim(3)
|
|
|
|
integer res_x, res_y, res_z
|
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|
|
real*8 nodes(res_x+1,res_y+1,res_z+1,3)
|
|
|
|
real*8 defgrad(res_x ,res_y ,res_z ,3,3)
|
|
|
|
real*8 volume_mismatch(res_x ,res_y ,res_z )
|
|
|
|
real*8 coords(8,3)
|
|
|
|
integer i,j,k
|
|
|
|
real*8, dimension(3,3) :: defgrad_av
|
|
|
|
real*8 vol_initial
|
|
|
|
|
|
|
|
print*, 'Calculating volume mismatch'
|
|
|
|
vol_initial = geomdim(1)*geomdim(2)*geomdim(3)/real(res_x)/real(res_y)/real(res_z)
|
|
|
|
do k = 1,res_z
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|
|
|
do j = 1,res_y
|
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|
|
do i = 1,res_x
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|
|
|
coords(1,:) = nodes(i ,j ,k ,:)
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|
|
|
coords(2,:) = nodes(i+1,j ,k ,:)
|
|
|
|
coords(3,:) = nodes(i+1,j+1,k ,:)
|
|
|
|
coords(4,:) = nodes(i ,j+1,k ,:)
|
|
|
|
coords(5,:) = nodes(i ,j, k+1,:)
|
|
|
|
coords(6,:) = nodes(i+1,j ,k+1,:)
|
|
|
|
coords(7,:) = nodes(i+1,j+1,k+1,:)
|
|
|
|
coords(8,:) = nodes(i ,j+1,k+1,:)
|
|
|
|
volume_mismatch(i,j,k) = abs(math_volTetrahedron(coords(7,:),coords(1,:),coords(8,:),coords(4,:))) &
|
|
|
|
+ abs(math_volTetrahedron(coords(7,:),coords(1,:),coords(8,:),coords(5,:))) &
|
|
|
|
+ abs(math_volTetrahedron(coords(7,:),coords(1,:),coords(3,:),coords(4,:))) &
|
|
|
|
+ abs(math_volTetrahedron(coords(7,:),coords(1,:),coords(3,:),coords(2,:))) &
|
|
|
|
+ abs(math_volTetrahedron(coords(7,:),coords(5,:),coords(2,:),coords(6,:))) &
|
|
|
|
+ abs(math_volTetrahedron(coords(7,:),coords(5,:),coords(2,:),coords(1,:)))
|
|
|
|
volume_mismatch(i,j,k) = volume_mismatch(i,j,k)/math_det3x3(defgrad(i,j,k,:,:))
|
|
|
|
enddo; enddo; enddo
|
|
|
|
volume_mismatch = volume_mismatch/vol_initial
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|
|
|
end subroutine volume_compare
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine shape_compare(res_x,res_y,res_z,geomdim,nodes,centroids,defgrad,shape_mismatch)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
! Routine to calculate the mismatch between the vectors from the central point to
|
|
|
|
! the corners of reconstructed (combatible) volume element and the vectors calculated by deforming
|
|
|
|
! the initial volume element with the current deformation gradient
|
|
|
|
implicit none
|
|
|
|
|
|
|
|
real*8 geomdim(3)
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
real*8 nodes(res_x+1,res_y+1,res_z+1,3)
|
|
|
|
real*8 centroids(res_x ,res_y ,res_z ,3)
|
|
|
|
real*8 defgrad(res_x ,res_y ,res_z ,3,3)
|
|
|
|
real*8 shape_mismatch(res_x ,res_y ,res_z)
|
|
|
|
real*8 coords(8,3)
|
|
|
|
real*8 coords_initial(8,3)
|
|
|
|
integer i,j,k,n
|
|
|
|
|
|
|
|
print*, 'Calculating shape mismatch'
|
|
|
|
coords_initial(1,:) = (/-geomdim(1)/2.0/real(res_x),-geomdim(2)/2.0/real(res_y),-geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(2,:) = (/+geomdim(1)/2.0/real(res_x),-geomdim(2)/2.0/real(res_y),-geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(3,:) = (/+geomdim(1)/2.0/real(res_x),+geomdim(2)/2.0/real(res_y),-geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(4,:) = (/-geomdim(1)/2.0/real(res_x),+geomdim(2)/2.0/real(res_y),-geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(5,:) = (/-geomdim(1)/2.0/real(res_x),-geomdim(2)/2.0/real(res_y),+geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(6,:) = (/+geomdim(1)/2.0/real(res_x),-geomdim(2)/2.0/real(res_y),+geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(7,:) = (/+geomdim(1)/2.0/real(res_x),+geomdim(2)/2.0/real(res_y),+geomdim(3)/2.0/real(res_z)/)
|
|
|
|
coords_initial(8,:) = (/-geomdim(1)/2.0/real(res_x),+geomdim(2)/2.0/real(res_y),+geomdim(3)/2.0/real(res_z)/)
|
|
|
|
do i=1,8
|
|
|
|
enddo
|
|
|
|
do k = 1,res_z
|
|
|
|
do j = 1,res_y
|
|
|
|
do i = 1,res_x
|
|
|
|
shape_mismatch(i,j,k) = sqrt(sum((nodes(i ,j ,k ,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(1,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i+1,j ,k ,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(2,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i+1,j+1,k ,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(3,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i ,j+1,k ,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(4,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i ,j, k+1,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(5,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i+1,j ,k+1,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(6,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i+1,j+1,k+1,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(7,:)))**2.0))&
|
|
|
|
+ sqrt(sum((nodes(i ,j+1,k+1,:) - centroids(i,j,k,:) - matmul(defgrad(i,j,k,:,:), coords_initial(8,:)))**2.0))
|
|
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine shape_compare
|
|
|
|
|
|
|
|
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine inverse_reconstruction(res_x,res_y,res_z,reference_configuration,current_configuration,defgrad)
|
|
|
|
!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
! Routine to calculate deformation gradient from reference and current configuration
|
|
|
|
! NOT WORKING BY NOW!!!!!!!!!!!!!
|
|
|
|
!
|
|
|
|
use math
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
real*8 reference_configuration(res_x+1,res_y+1,res_z+1,3)
|
|
|
|
real*8 current_configuration(res_x+1,res_y+1,res_z+1,3)
|
|
|
|
real*8 defgrad(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 delta, tolerance, res, res_center
|
|
|
|
real*8 reference(8,3)
|
|
|
|
real*8 current(8,3)
|
|
|
|
real*8 defgrad_temp(3,3)
|
|
|
|
real*8 dres_dF(3,3)
|
|
|
|
real*8 identity(3,3)
|
|
|
|
real*8 ref_bar(3)
|
|
|
|
real*8 current_bar(3)
|
|
|
|
real*8 r(8)
|
|
|
|
real*8 differentiate(9,3,3)
|
|
|
|
integer i, j, k, m, l, x, y, o
|
|
|
|
|
|
|
|
identity = 0.0
|
|
|
|
identity(1,1) = 1.0
|
|
|
|
identity(2,2) = 1.0
|
|
|
|
identity(3,3) = 1.0
|
|
|
|
|
|
|
|
differentiate = 0.0
|
|
|
|
|
|
|
|
tolerance = 1e-10
|
|
|
|
delta = 1e-9
|
|
|
|
|
|
|
|
k = 0
|
|
|
|
do j = 1, 3; do i = 1, 3
|
|
|
|
k = k+1
|
|
|
|
differentiate(k,i,j) = 1.0
|
|
|
|
enddo; enddo
|
|
|
|
|
|
|
|
do k = 1, res_z
|
|
|
|
do j = 1, res_y
|
|
|
|
do i = 1, res_x
|
|
|
|
reference(1,:) = reference_configuration(i ,j ,k ,:)
|
|
|
|
reference(2,:) = reference_configuration(i+1,j ,k ,:)
|
|
|
|
reference(3,:) = reference_configuration(i+1,j+1,k ,:)
|
|
|
|
reference(4,:) = reference_configuration(i ,j+1,k ,:)
|
|
|
|
reference(5,:) = reference_configuration(i ,j ,k+1,:)
|
|
|
|
reference(6,:) = reference_configuration(i+1,j ,k+1,:)
|
|
|
|
reference(7,:) = reference_configuration(i+1,j+1,k+1,:)
|
|
|
|
reference(8,:) = reference_configuration(i ,j+1,k+1,:)
|
|
|
|
current(1,:) = current_configuration(i ,j ,k ,:)
|
|
|
|
current(2,:) = current_configuration(i+1,j ,k ,:)
|
|
|
|
current(3,:) = current_configuration(i+1,j+1,k ,:)
|
|
|
|
current(4,:) = current_configuration(i ,j+1,k ,:)
|
|
|
|
current(5,:) = current_configuration(i ,j ,k+1,:)
|
|
|
|
current(6,:) = current_configuration(i+1,j ,k+1,:)
|
|
|
|
current(7,:) = current_configuration(i+1,j+1,k+1,:)
|
|
|
|
current(8,:) = current_configuration(i ,j+1,k+1,:)
|
|
|
|
|
|
|
|
do o=1,3
|
|
|
|
ref_bar(o) = sum(reference(:,o))/8.0
|
|
|
|
current_bar(o) = sum(current(:,o))/8.0
|
|
|
|
enddo
|
|
|
|
|
|
|
|
do o=1,8
|
|
|
|
reference(o,:) = reference(o,:) -ref_bar
|
|
|
|
current(o,:) = current(o,:) -current_bar
|
|
|
|
enddo
|
|
|
|
|
|
|
|
defgrad_temp = identity
|
|
|
|
res_center = 2.0*tolerance
|
|
|
|
o=0
|
|
|
|
do while(res_center >= tolerance)
|
|
|
|
o = o + 1
|
|
|
|
do l = 1,8 ! loop over corners
|
|
|
|
r(l) = sqrt(sum((current(l,:)-matmul(defgrad_temp,reference(l,:)))**2)) ! corner distance
|
|
|
|
enddo
|
|
|
|
res_center = sum(r*r) ! current residuum
|
|
|
|
print*, 'res_center', res_center
|
|
|
|
m=0
|
|
|
|
do y=1,3; do x=1,3 ! numerical differentiation
|
|
|
|
m = m+1
|
|
|
|
do l = 1,8
|
|
|
|
r(l) = sqrt(sum((current(l,:)-matmul((defgrad_temp+differentiate(m,:,:)*delta),reference(l,:)))**2)) ! corner distance
|
|
|
|
enddo
|
|
|
|
res = sum(r*r)
|
|
|
|
print*,'res step', m, res
|
|
|
|
dres_dF(x,y) = (res-res_center)/delta
|
|
|
|
enddo; enddo
|
|
|
|
print*, 'dres_dF', dres_dF
|
|
|
|
print*, 'deltadef', math_inv3x3(dres_dF)*res_center
|
|
|
|
defgrad_temp = defgrad_temp - math_inv3x3(dres_dF)*res_center ! Newton--Raphson
|
|
|
|
print*, o, res_center
|
|
|
|
pause
|
|
|
|
enddo
|
|
|
|
defgrad(i,j,k,:,:) = defgrad_temp
|
|
|
|
enddo; enddo; enddo
|
|
|
|
|
|
|
|
end subroutine inverse_reconstruction
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine tensor_avg(res_x,res_y,res_z,tensor,avg)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
!calculate average of tensor field
|
|
|
|
!
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
real*8 tensor(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 avg(3,3)
|
|
|
|
real*8 wgt
|
|
|
|
integer m,n
|
|
|
|
|
|
|
|
wgt = 1/real(res_x*res_y*res_z)
|
|
|
|
|
|
|
|
do m = 1,3; do n = 1,3
|
|
|
|
avg(m,n) = sum(tensor(:,:,:,m,n)) * wgt
|
|
|
|
enddo; enddo
|
|
|
|
end subroutine tensor_avg
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine logstrain_spat(res_x,res_y,res_z,defgrad,logstrain_field)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
!calculate logarithmic strain in spatial configuration for given defgrad field
|
|
|
|
!
|
|
|
|
use math
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
integer i, j, k
|
|
|
|
real*8 defgrad(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 logstrain_field(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 temp33_Real(3,3), temp33_Real2(3,3)
|
|
|
|
real*8 eigenvectorbasis(3,3,3)
|
|
|
|
real*8 eigenvalue(3)
|
|
|
|
logical errmatinv
|
|
|
|
|
|
|
|
do k = 1, res_z; do j = 1, res_y; do i = 1, res_x
|
|
|
|
call math_pDecomposition(defgrad(i,j,k,:,:),temp33_Real2,temp33_Real,errmatinv) !store R in temp33_Real
|
|
|
|
temp33_Real2 = math_inv3x3(temp33_Real)
|
|
|
|
temp33_Real = math_mul33x33(defgrad(i,j,k,:,:),temp33_Real2) ! v = F o inv(R), store in temp33_Real2
|
|
|
|
call math_spectral1(temp33_Real, eigenvalue(1), eigenvalue(2), eigenvalue(3),&
|
|
|
|
eigenvectorbasis(1,:,:), eigenvectorbasis(2,:,:), eigenvectorbasis(3,:,:))
|
|
|
|
eigenvalue = log(sqrt(eigenvalue))
|
|
|
|
logstrain_field(i,j,k,:,:) = eigenvalue(1)*eigenvectorbasis(1,:,:)+&
|
|
|
|
eigenvalue(2)*eigenvectorbasis(2,:,:)+&
|
|
|
|
eigenvalue(3)*eigenvectorbasis(3,:,:)
|
|
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine logstrain_spat
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine logstrain_mat(res_x,res_y,res_z,defgrad,logstrain_field)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
!calculate logarithmic strain in material configuration for given defgrad field
|
|
|
|
!
|
|
|
|
use math
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
integer i, j, k
|
|
|
|
real*8 defgrad(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 logstrain_field(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 temp33_Real(3,3), temp33_Real2(3,3)
|
|
|
|
real*8 eigenvectorbasis(3,3,3)
|
|
|
|
real*8 eigenvalue(3)
|
|
|
|
logical errmatinv
|
|
|
|
|
|
|
|
do k = 1, res_z; do j = 1, res_y; do i = 1, res_x
|
|
|
|
call math_pDecomposition(defgrad(i,j,k,:,:),temp33_Real,temp33_Real2,errmatinv) !store U in temp33_Real
|
|
|
|
call math_spectral1(temp33_Real, eigenvalue(1), eigenvalue(2), eigenvalue(3),&
|
|
|
|
eigenvectorbasis(1,:,:), eigenvectorbasis(2,:,:), eigenvectorbasis(3,:,:))
|
|
|
|
eigenvalue = log(sqrt(eigenvalue))
|
|
|
|
logstrain_field(i,j,k,:,:) = eigenvalue(1)*eigenvectorbasis(1,:,:)+&
|
|
|
|
eigenvalue(2)*eigenvectorbasis(2,:,:)+&
|
|
|
|
eigenvalue(3)*eigenvectorbasis(3,:,:)
|
|
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine logstrain_mat
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine calculate_cauchy(res_x,res_y,res_z,defgrad,p_stress,c_stress)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
!calculate cauchy stress for given PK1 stress and defgrad field
|
|
|
|
!
|
|
|
|
use math
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
integer i, j, k
|
|
|
|
real*8 defgrad(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 p_stress(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 c_stress(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 jacobi
|
|
|
|
c_stress = 0.0
|
|
|
|
do k = 1, res_z; do j = 1, res_y; do i = 1, res_x
|
|
|
|
jacobi = math_det3x3(defgrad(i,j,k,:,:))
|
|
|
|
c_stress(i,j,k,:,:) = matmul(p_stress(i,j,k,:,:),transpose(defgrad(i,j,k,:,:)))/jacobi
|
|
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine calculate_cauchy
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine calculate_mises(res_x,res_y,res_z,tensor,vm)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
!calculate von Mises equivalent of tensor field
|
|
|
|
!
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z
|
|
|
|
integer i, j, k
|
|
|
|
real*8 tensor(res_x,res_y,res_z,3,3)
|
|
|
|
real*8 vm(res_x,res_y,res_z,1)
|
|
|
|
real*8 deviator(3,3)
|
|
|
|
real*8 delta(3,3)
|
|
|
|
real*8 J_2
|
|
|
|
|
|
|
|
delta =0.0
|
|
|
|
delta(1,1) = 1.0
|
|
|
|
delta(2,2) = 1.0
|
|
|
|
delta(3,3) = 1.0
|
|
|
|
do k = 1, res_z; do j = 1, res_y; do i = 1, res_x
|
|
|
|
deviator = tensor(i,j,k,:,:) - 1.0/3.0*tensor(i,j,k,1,1)*tensor(i,j,k,2,2)*tensor(i,j,k,3,3)*delta
|
|
|
|
J_2 = deviator(1,1)*deviator(2,2)&
|
|
|
|
+ deviator(2,2)*deviator(3,3)&
|
|
|
|
+ deviator(1,1)*deviator(3,3)&
|
|
|
|
- (deviator(1,2))**2&
|
|
|
|
- (deviator(2,3))**2&
|
|
|
|
- (deviator(1,3))**2
|
|
|
|
vm(i,j,k,:) = sqrt(3*J_2)
|
|
|
|
enddo; enddo; enddo
|
|
|
|
end subroutine calculate_mises
|
|
|
|
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
subroutine divergence_fft(res_x,res_y,res_z,vec_tens,geomdim,field,divergence_field)
|
|
|
|
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
|
|
|
|
! calculates divergence field using integration in Fourier space
|
|
|
|
!use vec_tens to decide if tensor (3) or vector (1)
|
|
|
|
|
|
|
|
implicit none
|
|
|
|
integer res_x, res_y, res_z, vec_tens
|
|
|
|
real*8 geomdim(3)
|
|
|
|
real*8 field(res_x,res_y,res_z,vec_tens,3)
|
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real*8 field_copy(res_x,res_y,res_z,vec_tens,3)
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real*8 xi(res_x,res_y,res_z,3)
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real*8 divergence_field(res_x,res_y,res_z,vec_tens)
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complex*16 divergence_field_fft(res_x/2+1,res_y,res_z,vec_tens)
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complex*16 field_fft(res_x,res_y,res_z,vec_tens,3)
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complex*16 img
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integer i, j, k
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integer k_s(3)
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real*8, parameter :: pi = 3.14159265358979323846264338327950288419716939937510
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integer*8 :: plan_fft(2)
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include 'fftw3.f' !header file for fftw3 (declaring variables). Library files are also needed
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img = cmplx(0.0,1.0)
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call dfftw_plan_many_dft_r2c(plan_fft(1),3,(/res_x,res_y,res_z/),vec_tens*3,&
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field_copy,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,&
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field_fft,(/res_x/2+1,res_y,res_z/),1,(res_x/2+1)*res_y*res_z,FFTW_PATIENT)
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call dfftw_plan_many_dft_c2r(plan_fft(2),3,(/res_x,res_y,res_z/),vec_tens,&
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divergence_field_fft,(/res_x/2+1,res_y,res_z/),1,(res_x/2+1)*res_y*res_z,&
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divergence_field,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,FFTW_PATIENT)
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! field_copy is destroyed during plan creation
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field_copy = field
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call dfftw_execute_dft_r2c(plan_fft(1), field_copy, field_fft)
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xi = 0.0
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! Alternative calculation of discrete frequencies k_s, ordered as in FFTW (wrap around)
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! do k = 0,res_z/2 -1
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! do j = 0,res_y/2 -1
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! do i = 0,res_x/2 -1
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! xi(1+mod(res_x-i,res_x),1+mod(res_y-j,res_y),1+mod(res_z-k,res_z),:) = (/-i,-j,-k/)/geomdim
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! xi(1+i, 1+mod(res_y-j,res_y),1+mod(res_z-k,res_z),:) = (/ i,-j,-k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+j, 1+mod(res_z-k,res_z),:) = (/-i, j,-k/)/geomdim
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! xi(1+i, 1+j, 1+mod(res_z-k,res_z),:) = (/ i, j,-k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+mod(res_y-j,res_y),1+k, :) = (/-i,-j, k/)/geomdim
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! xi(1+i, 1+mod(res_y-j,res_y),1+k, :) = (/ i,-j, k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+j, 1+k, :) = (/-i, j, k/)/geomdim
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! xi(1+i, 1+j, 1+k, :) = (/ i, j, k/)/geomdim
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! xi(1+i, 1+j, 1+k, :) = (/ i, j, k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+j, 1+k, :) = (/-i, j, k/)/geomdim
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! xi(1+i, 1+mod(res_y-j,res_y),1+k, :) = (/ i,-j, k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+mod(res_y-j,res_y),1+k, :) = (/-i,-j, k/)/geomdim
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! xi(1+i, 1+j, 1+mod(res_z-k,res_z),:) = (/ i, j,-k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+j, 1+mod(res_z-k,res_z),:) = (/-i, j,-k/)/geomdim
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! xi(1+i, 1+mod(res_y-j,res_y),1+mod(res_z-k,res_z),:) = (/ i,-j,-k/)/geomdim
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! xi(1+mod(res_x-i,res_x),1+mod(res_y-j,res_y),1+mod(res_z-k,res_z),:) = (/-i,-j,-k/)/geomdim
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! enddo; enddo; enddo
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do k = 0, res_z-1
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do j = 0, res_y-1
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do i = 0, res_x/2
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xi(i+1,j+1,k+1,:) = (/real(i),real(j),real(k)/)/geomdim
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if(k==res_z/2) xi(i+1,j+1,k+1,3)= 0.0 ! set highest frequencies to zero
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if(j==res_y/2) xi(i+1,j+1,k+1,2)= 0.0
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if(i==res_x/2) xi(i+1,j+1,k+1,1)= 0.0
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enddo; enddo; enddo
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do k = 1, res_z
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do j = 1, res_y
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do i = 1, res_x/2+1
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divergence_field_fft(i,j,k,1) = sum(field_fft(i,j,k,1,:)*xi(i,j,k,:))
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if(vec_tens == 3) then
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divergence_field_fft(i,j,k,2) = sum(field_fft(i,j,k,2,:)*xi(i,j,k,:))
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divergence_field_fft(i,j,k,3) = sum(field_fft(i,j,k,3,:)*xi(i,j,k,:))
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endif
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enddo; enddo; enddo
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divergence_field_fft = divergence_field_fft*img*2.0*pi
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call dfftw_execute_dft_c2r(plan_fft(2), divergence_field_fft, divergence_field)
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end subroutine divergence_fft
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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subroutine divergence(res_x,res_y,res_z,vec_tens,order,geomdim,field,divergence_field)
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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
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! calculates divergence field using FDM with variable accuracy
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!use vec_tes to decide if tensor (3) or vector (1)
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use math
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implicit none
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integer res_x, res_y, res_z, vec_tens, order
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integer coordinates(6,3)
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real*8 geomdim(3)
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real*8 field(res_x,res_y,res_z,vec_tens,3)
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real*8 divergence_field(res_x,res_y,res_z,vec_tens)
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integer i, j, k, m, l, x
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integer k_s(3)
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real*8, dimension(4,4) :: FDcoefficient = reshape((/ & !from http://en.wikipedia.org/wiki/Finite_difference_coefficients
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1.0/2.0, 0.0, 0.0, 0.0,&
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2.0/3.0,-1.0/12.0, 0.0, 0.0,&
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3.0/4.0,-3.0/20.0,1.0/ 60.0, 0.0,&
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4.0/5.0,-1.0/ 5.0,4.0/105.0,-1.0/280.0/),&
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(/4,4/))
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divergence_field = 0.0
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order = order + 1
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do k = 0, res_z-1; do j = 0, res_y-1; do i = 0, res_x-1
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do m = 1, order
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coordinates(1,:) = mesh_location(mesh_index((/i+m,j,k/),(/res_x,res_y,res_z/)),(/res_x,res_y,res_z/)) + (/1,1,1/)
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coordinates(2,:) = mesh_location(mesh_index((/i-m,j,k/),(/res_x,res_y,res_z/)),(/res_x,res_y,res_z/)) + (/1,1,1/)
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coordinates(3,:) = mesh_location(mesh_index((/i,j+m,k/),(/res_x,res_y,res_z/)),(/res_x,res_y,res_z/)) + (/1,1,1/)
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coordinates(4,:) = mesh_location(mesh_index((/i,j-m,k/),(/res_x,res_y,res_z/)),(/res_x,res_y,res_z/)) + (/1,1,1/)
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coordinates(5,:) = mesh_location(mesh_index((/i,j,k+m/),(/res_x,res_y,res_z/)),(/res_x,res_y,res_z/)) + (/1,1,1/)
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coordinates(6,:) = mesh_location(mesh_index((/i,j,k-m/),(/res_x,res_y,res_z/)),(/res_x,res_y,res_z/)) + (/1,1,1/)
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do l = 1, vec_tens
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divergence_field(i+1,j+1,k+1,l) = divergence_field(i+1,j+1,k+1,l) + FDcoefficient(m,order) * &
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((field(coordinates(1,1),coordinates(1,2),coordinates(1,3),l,1)- &
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field(coordinates(2,1),coordinates(2,2),coordinates(2,3),l,1))*real(res_x)/geomdim(1) +&
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(field(coordinates(3,1),coordinates(3,2),coordinates(3,3),l,2)- &
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field(coordinates(4,1),coordinates(4,2),coordinates(4,3),l,2))*real(res_y)/geomdim(2) +&
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(field(coordinates(5,1),coordinates(5,2),coordinates(5,3),l,3)- &
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field(coordinates(6,1),coordinates(6,2),coordinates(6,3),l,3))*real(res_z)/geomdim(3))
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enddo
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enddo
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enddo; enddo; enddo
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end subroutine divergence
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