From 98513a4e0ddef310e3e839fa1c9b094307cb66a9 Mon Sep 17 00:00:00 2001 From: Martin Diehl Date: Mon, 7 Nov 2011 18:27:33 +0000 Subject: [PATCH] --- processing/post/postprocessingMath.f90 | 1000 ++++++++++++++++++++++++ 1 file changed, 1000 insertions(+) create mode 100644 processing/post/postprocessingMath.f90 diff --git a/processing/post/postprocessingMath.f90 b/processing/post/postprocessingMath.f90 new file mode 100644 index 000000000..77ad4086f --- /dev/null +++ b/processing/post/postprocessingMath.f90 @@ -0,0 +1,1000 @@ +!$Id: postprocessingMath.f90 1054 2011-11-03 13:21:11Z MPIE\p.eisenlohr $ +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +!all function below are taken from math.f90 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +module math + +real*8, parameter :: pi = 3.14159265358979323846264338327950288419716939937510 + +! *** 3x3 Identity *** + real*8, dimension(3,3), parameter :: math_I3 = & + reshape( (/ & + 1.0,0.0,0.0, & + 0.0,1.0,0.0, & + 0.0,0.0,1.0 /),(/3,3/)) + +contains +!************************************************************************** +! matrix multiplication 33x33 = 3x3 +!************************************************************************** +pure function math_mul33x33(A,B) + + implicit none + + integer i,j + real*8, dimension(3,3), intent(in) :: A,B + real*8, dimension(3,3) :: math_mul33x33 + + forall (i=1:3,j=1:3) math_mul33x33(i,j) = & + A(i,1)*B(1,j) + A(i,2)*B(2,j) + A(i,3)*B(3,j) + return + +end function math_mul33x33 + +!************************************************************************** +! Cramer inversion of 3x3 matrix (subroutine) +!************************************************************************** + PURE SUBROUTINE math_invert3x3(A, InvA, DetA, error) + +! Bestimmung der Determinanten und Inversen einer 3x3-Matrix +! A = Matrix A +! InvA = Inverse of A +! DetA = Determinant of A +! error = logical + + implicit none + + logical, intent(out) :: error + + real*8,dimension(3,3),intent(in) :: A + real*8,dimension(3,3),intent(out) :: InvA + real*8, intent(out) :: DetA + + DetA = A(1,1) * ( A(2,2) * A(3,3) - A(2,3) * A(3,2) )& + - A(1,2) * ( A(2,1) * A(3,3) - A(2,3) * A(3,1) )& + + A(1,3) * ( A(2,1) * A(3,2) - A(2,2) * A(3,1) ) + + if (DetA <= tiny(DetA)) then + error = .true. + else + InvA(1,1) = ( A(2,2) * A(3,3) - A(2,3) * A(3,2) ) / DetA + InvA(2,1) = ( -A(2,1) * A(3,3) + A(2,3) * A(3,1) ) / DetA + InvA(3,1) = ( A(2,1) * A(3,2) - A(2,2) * A(3,1) ) / DetA + + InvA(1,2) = ( -A(1,2) * A(3,3) + A(1,3) * A(3,2) ) / DetA + InvA(2,2) = ( A(1,1) * A(3,3) - A(1,3) * A(3,1) ) / DetA + InvA(3,2) = ( -A(1,1) * A(3,2) + A(1,2) * A(3,1) ) / DetA + + InvA(1,3) = ( A(1,2) * A(2,3) - A(1,3) * A(2,2) ) / DetA + InvA(2,3) = ( -A(1,1) * A(2,3) + A(1,3) * A(2,1) ) / DetA + InvA(3,3) = ( A(1,1) * A(2,2) - A(1,2) * A(2,1) ) / DetA + + error = .false. + endif + return + + END SUBROUTINE math_invert3x3 + +!******************************************************************** +! determinant of a 3x3 matrix +!******************************************************************** + pure function math_det3x3(m) + + implicit none + + real*8, dimension(3,3), intent(in) :: m + real*8 math_det3x3 + + math_det3x3 = m(1,1)*(m(2,2)*m(3,3)-m(2,3)*m(3,2)) & + -m(1,2)*(m(2,1)*m(3,3)-m(2,3)*m(3,1)) & + +m(1,3)*(m(2,1)*m(3,2)-m(2,2)*m(3,1)) + return + + end function math_det3x3 + +!**************************************************************** + pure subroutine math_pDecomposition(FE,U,R,error) +!-----FE = R.U +!**************************************************************** + implicit none + + real*8, intent(in) :: FE(3,3) + real*8, intent(out) :: R(3,3), U(3,3) + logical, intent(out) :: error + real*8 CE(3,3),EW1,EW2,EW3,EB1(3,3),EB2(3,3),EB3(3,3),UI(3,3),det + + error = .false. + ce = math_mul33x33(transpose(FE),FE) + + CALL math_spectral1(CE,EW1,EW2,EW3,EB1,EB2,EB3) + U=DSQRT(EW1)*EB1+DSQRT(EW2)*EB2+DSQRT(EW3)*EB3 + call math_invert3x3(U,UI,det,error) + if (.not. error) R = math_mul33x33(FE,UI) + + return + + end subroutine math_pDecomposition + +!************************************************************************** +! Cramer inversion of 3x3 matrix (function) +!************************************************************************** + pure function math_inv3x3(A) + +! direct Cramer inversion of matrix A. +! returns all zeroes if not possible, i.e. if det close to zero + + implicit none + + real*8,dimension(3,3),intent(in) :: A + real*8 DetA + + real*8,dimension(3,3) :: math_inv3x3 + + math_inv3x3 = 0.0 + + DetA = A(1,1) * ( A(2,2) * A(3,3) - A(2,3) * A(3,2) )& + - A(1,2) * ( A(2,1) * A(3,3) - A(2,3) * A(3,1) )& + + A(1,3) * ( A(2,1) * A(3,2) - A(2,2) * A(3,1) ) + + if (DetA > tiny(DetA)) then + math_inv3x3(1,1) = ( A(2,2) * A(3,3) - A(2,3) * A(3,2) ) / DetA + math_inv3x3(2,1) = ( -A(2,1) * A(3,3) + A(2,3) * A(3,1) ) / DetA + math_inv3x3(3,1) = ( A(2,1) * A(3,2) - A(2,2) * A(3,1) ) / DetA + + math_inv3x3(1,2) = ( -A(1,2) * A(3,3) + A(1,3) * A(3,2) ) / DetA + math_inv3x3(2,2) = ( A(1,1) * A(3,3) - A(1,3) * A(3,1) ) / DetA + math_inv3x3(3,2) = ( -A(1,1) * A(3,2) + A(1,2) * A(3,1) ) / DetA + + math_inv3x3(1,3) = ( A(1,2) * A(2,3) - A(1,3) * A(2,2) ) / DetA + math_inv3x3(2,3) = ( -A(1,1) * A(2,3) + A(1,3) * A(2,1) ) / DetA + math_inv3x3(3,3) = ( A(1,1) * A(2,2) - A(1,2) * A(2,1) ) / DetA + endif + return + + end function math_inv3x3 + +!********************************************************************** +! HAUPTINVARIANTEN HI1M, HI2M, HI3M DER 3X3 MATRIX M +!********************************************************************** + + PURE SUBROUTINE math_hi(M,HI1M,HI2M,HI3M) + implicit none + + real*8, intent(in) :: M(3,3) + real*8, intent(out) :: HI1M, HI2M, HI3M + + HI1M=M(1,1)+M(2,2)+M(3,3) + 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) + HI3M=math_det3x3(M) +! QUESTION: is 3rd equiv det(M) ?? if yes, use function math_det !agreed on YES + return + + END SUBROUTINE math_hi + +!********************************************************************** + pure subroutine math_spectral1(M,EW1,EW2,EW3,EB1,EB2,EB3) +!**** EIGENWERTE UND EIGENWERTBASIS DER SYMMETRISCHEN 3X3 MATRIX M + + implicit none + + real*8, intent(in) :: M(3,3) + real*8, intent(out) :: EB1(3,3),EB2(3,3),EB3(3,3),EW1,EW2,EW3 + real*8 HI1M,HI2M,HI3M,TOL,R,S,T,P,Q,RHO,PHI,Y1,Y2,Y3,D1,D2,D3 + real*8 C1,C2,C3,M1(3,3),M2(3,3),M3(3,3),arg + TOL=1.e-14 + CALL math_hi(M,HI1M,HI2M,HI3M) + R=-HI1M + S= HI2M + T=-HI3M + P=S-R**2.0/3.0 + Q=2.0/27.0*R**3.0-R*S/3.0+T + EB1=0.0 + EB2=0.0 + EB3=0.0 + IF((ABS(P).LT.TOL).AND.(ABS(Q).LT.TOL))THEN +! DREI GLEICHE EIGENWERTE + EW1=HI1M/3.0 + EW2=EW1 + EW3=EW1 +! this is not really correct, but this way U is calculated +! correctly in PDECOMPOSITION (correct is EB?=I) + EB1(1,1)=1.0 + EB2(2,2)=1.0 + EB3(3,3)=1.0 + ELSE + RHO=DSQRT(-3.0*P**3.0)/9.0 + arg=-Q/RHO/2.0 + if(arg.GT.1) arg=1 + if(arg.LT.-1) arg=-1 + PHI=DACOS(arg) + Y1=2*RHO**(1.0/3.0)*DCOS(PHI/3.0) + Y2=2*RHO**(1.0/3.0)*DCOS(PHI/3.0+2.0/3.0*PI) + Y3=2*RHO**(1.0/3.0)*DCOS(PHI/3.0+4.0/3.0*PI) + EW1=Y1-R/3.0 + EW2=Y2-R/3.0 + EW3=Y3-R/3.0 + C1=ABS(EW1-EW2) + C2=ABS(EW2-EW3) + C3=ABS(EW3-EW1) + + IF(C1.LT.TOL) THEN +! EW1 is equal to EW2 + D3=1.0/(EW3-EW1)/(EW3-EW2) + M1=M-EW1*math_I3 + M2=M-EW2*math_I3 + EB3=math_mul33x33(M1,M2)*D3 + + EB1=math_I3-EB3 +! both EB2 and EW2 are set to zero so that they do not +! contribute to U in PDECOMPOSITION + EW2=0.0 + ELSE IF(C2.LT.TOL) THEN +! EW2 is equal to EW3 + D1=1.0/(EW1-EW2)/(EW1-EW3) + M2=M-math_I3*EW2 + M3=M-math_I3*EW3 + EB1=math_mul33x33(M2,M3)*D1 + EB2=math_I3-EB1 +! both EB3 and EW3 are set to zero so that they do not +! contribute to U in PDECOMPOSITION + EW3=0.0 + ELSE IF(C3.LT.TOL) THEN +! EW1 is equal to EW3 + D2=1.0/(EW2-EW1)/(EW2-EW3) + M1=M-math_I3*EW1 + M3=M-math_I3*EW3 + EB2=math_mul33x33(M1,M3)*D2 + EB1=math_I3-EB2 +! both EB3 and EW3 are set to zero so that they do not +! contribute to U in PDECOMPOSITION + EW3=0.0 + ELSE +! all three eigenvectors are different + D1=1.0/(EW1-EW2)/(EW1-EW3) + D2=1.0/(EW2-EW1)/(EW2-EW3) + D3=1.0/(EW3-EW1)/(EW3-EW2) + M1=M-EW1*math_I3 + M2=M-EW2*math_I3 + M3=M-EW3*math_I3 + EB1=math_mul33x33(M2,M3)*D1 + EB2=math_mul33x33(M1,M3)*D2 + EB3=math_mul33x33(M1,M2)*D3 + + END IF + END IF + RETURN + END SUBROUTINE math_spectral1 + +!************************************************************************** +! volume of tetrahedron given by four vertices +!************************************************************************** + pure function math_volTetrahedron(v1,v2,v3,v4) + + implicit none + + real*8 math_volTetrahedron + real*8, dimension (3), intent(in) :: v1,v2,v3,v4 + real*8, dimension (3,3) :: m + + m(:,1) = v1-v2 + m(:,2) = v2-v3 + m(:,3) = v3-v4 + + math_volTetrahedron = math_det3x3(m)/6.0 + + end function math_volTetrahedron + +!subroutines below are for postprocessing with python + +!two small helper functions for indexing +! CAREFULL, index and location runs from 0 to N-1 (python style) + + function mesh_location(idx,resolution) + integer, intent(in) :: idx + integer, intent(in) :: resolution(3) + integer :: mesh_location(3) + mesh_location = (/modulo(idx/ resolution(3) / resolution(2),resolution(1)), & + modulo(idx/ resolution(3), resolution(2)), & + modulo(idx, resolution(3))/) + end function mesh_location + + function mesh_index(location,resolution) + integer, intent(in) :: location(3) + integer, intent(in) :: resolution(3) + integer :: mesh_index + + mesh_index = modulo(location(3), resolution(3)) +& + (modulo(location(2), resolution(2)))*resolution(3) +& + (modulo(location(1), resolution(1)))*resolution(3)*resolution(2) + end function mesh_index + + end module math + + + + +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +subroutine mesh(res_x,res_y,res_z,geomdim,defgrad_av,centroids,nodes) +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +! Routine to build a regular mesh of cubes for given coordinates (= center of the cubes) +! + implicit none + + real*8 geomdim(3) + integer res_x, res_y, res_z + real*8 wrappedCentroids(res_x+2,res_y+2,res_z+2,3) + real*8 nodes(res_x+1,res_y+1,res_z+1,3) + real*8 centroids(res_x ,res_y ,res_z ,3) + + integer, dimension(3,8) :: neighbor = reshape((/ & + 0, 0, 0, & + 1, 0, 0, & + 1, 1, 0, & + 0, 1, 0, & + 0, 0, 1, & + 1, 0, 1, & + 1, 1, 1, & + 0, 1, 1 & + /), & + (/3,8/)) + + integer i,j,k,n + real*8, dimension(3,3) :: defgrad_av + integer, dimension(3) :: diag, shift, lookup, me, res + + nodes = 0.0 + diag = 1 + shift = 0 + lookup = 0 + + res = (/res_x,res_y,res_z/) + + wrappedCentroids = 0.0 + wrappedCentroids(2:res_x+1,2:res_y+1,2:res_z+1,:) = centroids + + do k = 0,res_z+1 + do j = 0,res_y+1 + do i = 0,res_x+1 + if (k==0 .or. k==res_z+1 .or. & ! z skin + j==0 .or. j==res_y+1 .or. & ! y skin + i==0 .or. i==res_x+1 ) then ! x skin + me = (/i,j,k/) ! me on skin + shift = sign(abs(res+diag-2*me)/(res+diag),res+diag-2*me) + lookup = me-diag+shift*res + wrappedCentroids(i+1,j+1,k+1,:) = centroids(lookup(1)+1,lookup(2)+1,lookup(3)+1,:) - & + matmul(defgrad_av, shift*geomdim) + endif + enddo; enddo; enddo + do k = 0,res_z + do j = 0,res_y + do i = 0,res_x + do n = 1,8 + nodes(i+1,j+1,k+1,:) = nodes(i+1,j+1,k+1,:) + wrappedCentroids(i+1+neighbor(1,n), & + j+1+neighbor(2,n), & + k+1+neighbor(3,n), :) + enddo; enddo; enddo; enddo + nodes = nodes/8.0 + +end subroutine mesh + +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +subroutine deformed(res_x,res_y,res_z,geomdim,defgrad,defgrad_av,coord_avgCorner) +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +! Routine to calculate coordinates in current configuration for given defgrad +! using linear interpolation (blurres out high frequency defomation) +! + implicit none + real*8 geomdim(3) + integer res_x, res_y, res_z + real*8 coord(8,6,res_x,res_y,res_z,3) + real*8 coord_avgOrder(8,res_x,res_y,res_z,3) + real*8 coord_avgCorner(res_x,res_y,res_z,3) + real*8 defgrad(res_x,res_y,res_z,3,3) + integer, dimension(3,8) :: corner = reshape((/ & + 0, 0, 0,& + 1, 0, 0,& + 1, 1, 0,& + 0, 1, 0,& + 1, 1, 1,& + 0, 1, 1,& + 0, 0, 1,& + 1, 0, 1 & + /), & + (/3,8/)) + integer, dimension(3,8) :: step = reshape((/ & + 1, 1, 1,& + -1, 1, 1,& + -1,-1, 1,& + 1,-1, 1,& + -1,-1,-1,& + 1,-1,-1,& + 1, 1,-1,& + -1, 1,-1 & + /), & + (/3,8/)) + integer, dimension(3,6) :: order = reshape((/ & + 1, 2, 3,& + 1, 3, 2,& + 2, 1, 3,& + 2, 3, 1,& + 3, 1, 2,& + 3, 2, 1 & + /), & + (/3,6/)) + + real*8 myStep(3), fones(3), parameter_coords(3) + real*8 defgrad_av(3,3) + real*8 negative(3), positive(3) + integer rear(3), init(3), ones(3), oppo(3), me(3), res(3) + integer i, j, k, s, o + + print*, 'Restore geometry using linear integration' + print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim + print '(a,/,i5,i5,i5)', ' Resolution:', res_x,res_y,res_z + ones = 1 + fones = 1.0 + coord_avgOrder=0.0 + + res = (/res_x,res_y,res_z/) + + do s = 0, 7 ! corners (from 0 to 7) + init = corner(:,s+1)*(res-ones) +ones + oppo = corner(:,mod((s+4),8)+1)*(res-ones) +ones + do o=1,6 ! orders ! from 1 to 6) + do k = init(order(3,o)), oppo(order(3,o)), step(order(3,o),s+1) + rear(order(2,o)) = init(order(2,o)) + do j = init(order(2,o)), oppo(order(2,o)), step(order(2,o),s+1) + rear(order(1,o)) = init(order(1,o)) + do i = init(order(1,o)), oppo(order(1,o)), step(order(1,o),s+1) + me(order(1,o)) = i + me(order(2,o)) = j + me(order(3,o)) = k + if ( (me(1)==init(1)).and.(me(2)==init(2)).and. (me(3)==init(3)) ) then + coord(s+1,o,me(1),me(2),me(3),:) = geomdim * (matmul(defgrad_av,corner(:,s+1)) + & + matmul(defgrad(me(1),me(2),me(3),:,:),0.5*step(:,s+1)/res)) + + else + myStep = (me-rear)*geomdim/res + coord(s+1,o,me(1),me(2),me(3),:) = coord(s+1,o,rear(1),rear(2),rear(3),:) + & + 0.5*matmul(defgrad(me(1),me(2),me(3),:,:) + & + defgrad(rear(1),rear(2),rear(3),:,:),myStep) + endif + rear = me + enddo; enddo; enddo; enddo + do i=1,6 + coord_avgOrder(s+1,:,:,:,:) = coord_avgOrder(s+1,:,:,:,:) + coord(s+1,i,:,:,:,:)/6.0 + enddo + enddo + + do k=0, res_z-1 + do j=0, res_y-1 + do i=0, res_x-1 + parameter_coords = (2.0*(/i+0.0,j+0.0,k+0.0/)-real(res)+fones)/(real(res)-fones) + positive = fones + parameter_coords + negative = fones - parameter_coords + coord_avgCorner(i+1,j+1,k+1,:) = ( coord_avgOrder(1,i+1,j+1,k+1,:) *negative(1)*negative(2)*negative(3)& + + coord_avgOrder(2,i+1,j+1,k+1,:) *positive(1)*negative(2)*negative(3)& + + coord_avgOrder(3,i+1,j+1,k+1,:) *positive(1)*positive(2)*negative(3)& + + coord_avgOrder(4,i+1,j+1,k+1,:) *negative(1)*positive(2)*negative(3)& + + coord_avgOrder(5,i+1,j+1,k+1,:) *positive(1)*positive(2)*positive(3)& + + coord_avgOrder(6,i+1,j+1,k+1,:) *negative(1)*positive(2)*positive(3)& + + coord_avgOrder(7,i+1,j+1,k+1,:) *negative(1)*negative(2)*positive(3)& + + coord_avgOrder(8,i+1,j+1,k+1,:) *positive(1)*negative(2)*positive(3))*0.125 + enddo; enddo; enddo +end subroutine deformed + +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +subroutine deformed_fft(res_x,res_y,res_z,geomdim,defgrad,defgrad_av,scaling,coords) +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +! Routine to calculate coordinates in current configuration for given defgrad +! using integration in Fourier space (more accurate than deformed(...)) +! + implicit none + integer res_x, res_y, res_z + real*8 geomdim(3) + real*8 defgrad(res_x,res_y,res_z,3,3) + real*8 defgrad_av(3,3) + real*8 scaling + real*8 coords(res_x,res_y,res_z,3) + complex*16 coords_fft(res_x/2+1,res_y,res_z,3) + complex*16 defgrad_fft(res_x,res_y,res_z,3,3) + integer i, j, k + integer k_s(3) + real*8 step(3) + real*8 offset_coords(3) + real*8, parameter :: pi = 3.14159265358979323846264338327950288419716939937510 + integer*8 :: plan_fft(2) + + print*, 'Restore geometry using FFT-based integration' + print '(a,/,e12.5,e12.5,e12.5)', ' Dimension:', geomdim + print '(a,/,i5,i5,i5)', ' Resolution:', res_x,res_y,res_z + + call dfftw_plan_many_dft(plan_fft(1),3,(/res_x,res_y,res_z/),9,& + defgrad_fft,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,& + defgrad_fft,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,-1 + 32) ! -1 = FFTW_FORWARD, 32 =FFTW_PATIENT + + call dfftw_plan_many_dft_c2r(plan_fft(2),3,(/res_x,res_y,res_z/),3,& + coords_fft,(/res_x/2+1,res_y,res_z/),1,(res_x/2+1)*res_y*res_z,& + coords, (/res_x, res_y,res_z/),1, res_x* res_y*res_z,32) ! 32 = FFTW_PATIENT + + coords_fft = 0.0 + defgrad_fft = defgrad + + step(1) = geomdim(1)/real(res_x) + step(2) = geomdim(2)/real(res_y) + step(3) = geomdim(3)/real(res_z) + + call dfftw_execute_dft(plan_fft(1), defgrad_fft, defgrad_fft) + + do k = 1, res_z + k_s(3) = k-1 + if(k > res_z/2+1) k_s(3) = k_s(3)-res_z + do j = 1, res_y + k_s(2) = j-1 + if(j > res_y/2+1) k_s(2) = k_s(2)-res_y + do i = 1, res_x/2+1 + k_s(1) = i-1 + if(i/=1) coords_fft(i,j,k,:) = coords_fft(i,j,k,:)& + + defgrad_fft(i,j,k,:,1)*geomdim(1)/(real(k_s(1))*cmplx(0.0,1.0)*pi*2.0) + if(j/=1) coords_fft(i,j,k,:) = coords_fft(i,j,k,:)& + + defgrad_fft(i,j,k,:,2)*geomdim(2)/(real(k_s(2))*cmplx(0.0,1.0)*pi*2.0) + if(k/=1) coords_fft(i,j,k,:) = coords_fft(i,j,k,:)& + + defgrad_fft(i,j,k,:,3)*geomdim(3)/(real(k_s(3))*cmplx(0.0,1.0)*pi*2.0) + enddo; enddo; enddo + + call dfftw_execute_dft_c2r(plan_fft(2), coords_fft, coords) + coords = coords/real(res_x*res_y*res_z) + + offset_coords = matmul(defgrad(1,1,1,:,:),step/2.0) - scaling*coords(1,1,1,:) + do k = 1, res_z; do j = 1, res_y; do i = 1, res_x + coords(i,j,k,:) = scaling*coords(i,j,k,:) + offset_coords + matmul(defgrad_av,& + (/step(1)*real(i-1),& + step(2)*real(j-1),& + step(3)*real(k-1)/)) + + enddo; enddo; enddo +end subroutine deformed_fft + + +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +subroutine volume_compare(res_x,res_y,res_z,geomdim,nodes,defgrad,volume_mismatch) +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +! Routine to calculate the mismatch between volume of reconstructed (compatible) +! cube and determinant of defgrad at the FP + + use math + 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 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 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 + do j = 1,res_y + do i = 1,res_x + coords(1,:) = nodes(i ,j ,k ,:) + 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 +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_initial(8,3) + integer i,j,k + + 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) + real*8 field_copy(res_x,res_y,res_z,vec_tens,3) + real*8 xi(res_x,res_y,res_z,3) + real*8 divergence_field(res_x,res_y,res_z,vec_tens) + complex*16 divergence_field_fft(res_x/2+1,res_y,res_z,vec_tens) + complex*16 field_fft(res_x,res_y,res_z,vec_tens,3) + complex*16 img + integer i, j, k + real*8, parameter :: pi = 3.14159265358979323846264338327950288419716939937510 + integer*8 :: plan_fft(2) + + img = cmplx(0.0,1.0) + + call dfftw_plan_many_dft_r2c(plan_fft(1),3,(/res_x,res_y,res_z/),vec_tens*3,& + field_copy,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,& + field_fft,(/res_x/2+1,res_y,res_z/),1,(res_x/2+1)*res_y*res_z,32) ! 32 =FFTW_PATIENT + + call dfftw_plan_many_dft_c2r(plan_fft(2),3,(/res_x,res_y,res_z/),vec_tens,& + divergence_field_fft,(/res_x/2+1,res_y,res_z/),1,(res_x/2+1)*res_y*res_z,& + divergence_field,(/res_x,res_y,res_z/),1,res_x*res_y*res_z,32) ! 32 = FFTW_PATIENT + +! field_copy is destroyed during plan creation + field_copy = field + + call dfftw_execute_dft_r2c(plan_fft(1), field_copy, field_fft) + + xi = 0.0 +! Alternative calculation of discrete frequencies k_s, ordered as in FFTW (wrap around) +! do k = 0,res_z/2 -1 + ! do j = 0,res_y/2 -1 + ! do i = 0,res_x/2 -1 + ! 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 + ! xi(1+i, 1+mod(res_y-j,res_y),1+mod(res_z-k,res_z),:) = (/ i,-j,-k/)/geomdim + ! xi(1+mod(res_x-i,res_x),1+j, 1+mod(res_z-k,res_z),:) = (/-i, j,-k/)/geomdim + ! xi(1+i, 1+j, 1+mod(res_z-k,res_z),:) = (/ i, j,-k/)/geomdim + ! xi(1+mod(res_x-i,res_x),1+mod(res_y-j,res_y),1+k, :) = (/-i,-j, k/)/geomdim + ! xi(1+i, 1+mod(res_y-j,res_y),1+k, :) = (/ i,-j, k/)/geomdim + ! xi(1+mod(res_x-i,res_x),1+j, 1+k, :) = (/-i, j, k/)/geomdim + ! xi(1+i, 1+j, 1+k, :) = (/ i, j, k/)/geomdim + ! xi(1+i, 1+j, 1+k, :) = (/ i, j, k/)/geomdim + ! xi(1+mod(res_x-i,res_x),1+j, 1+k, :) = (/-i, j, k/)/geomdim + ! xi(1+i, 1+mod(res_y-j,res_y),1+k, :) = (/ i,-j, k/)/geomdim + ! xi(1+mod(res_x-i,res_x),1+mod(res_y-j,res_y),1+k, :) = (/-i,-j, k/)/geomdim + ! xi(1+i, 1+j, 1+mod(res_z-k,res_z),:) = (/ i, j,-k/)/geomdim + ! xi(1+mod(res_x-i,res_x),1+j, 1+mod(res_z-k,res_z),:) = (/-i, j,-k/)/geomdim + ! xi(1+i, 1+mod(res_y-j,res_y),1+mod(res_z-k,res_z),:) = (/ i,-j,-k/)/geomdim + ! 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 + ! enddo; enddo; enddo + + do k = 0, res_z-1 + do j = 0, res_y-1 + do i = 0, res_x/2 + xi(i+1,j+1,k+1,:) = (/real(i),real(j),real(k)/)/geomdim + if(k==res_z/2) xi(i+1,j+1,k+1,3)= 0.0 ! set highest frequencies to zero + if(j==res_y/2) xi(i+1,j+1,k+1,2)= 0.0 + if(i==res_x/2) xi(i+1,j+1,k+1,1)= 0.0 + enddo; enddo; enddo + + + do k = 1, res_z + do j = 1, res_y + do i = 1, res_x/2+1 + divergence_field_fft(i,j,k,1) = sum(field_fft(i,j,k,1,:)*xi(i,j,k,:)) + if(vec_tens == 3) then + divergence_field_fft(i,j,k,2) = sum(field_fft(i,j,k,2,:)*xi(i,j,k,:)) + divergence_field_fft(i,j,k,3) = sum(field_fft(i,j,k,3,:)*xi(i,j,k,:)) + endif + enddo; enddo; enddo + divergence_field_fft = divergence_field_fft*img*2.0*pi + + call dfftw_execute_dft_c2r(plan_fft(2), divergence_field_fft, divergence_field) + +end subroutine divergence_fft + +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +subroutine divergence(res_x,res_y,res_z,vec_tens,order,geomdim,field,divergence_field) +!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +! calculates divergence field using FDM with variable accuracy +!use vec_tes to decide if tensor (3) or vector (1) + + use math + implicit none + integer res_x, res_y, res_z, vec_tens, order + integer coordinates(6,3) + real*8 geomdim(3) + real*8 field(res_x,res_y,res_z,vec_tens,3) + real*8 divergence_field(res_x,res_y,res_z,vec_tens) + integer i, j, k, m, l + real*8, dimension(4,4) :: FDcoefficient = reshape((/ & !from http://en.wikipedia.org/wiki/Finite_difference_coefficients + 1.0/2.0, 0.0, 0.0, 0.0,& + 2.0/3.0,-1.0/12.0, 0.0, 0.0,& + 3.0/4.0,-3.0/20.0,1.0/ 60.0, 0.0,& + 4.0/5.0,-1.0/ 5.0,4.0/105.0,-1.0/280.0/),& + (/4,4/)) + divergence_field = 0.0 + order = order + 1 + do k = 0, res_z-1; do j = 0, res_y-1; do i = 0, res_x-1 + do m = 1, order + 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/) + 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/) + 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/) + 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/) + 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/) + 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/) + do l = 1, vec_tens + divergence_field(i+1,j+1,k+1,l) = divergence_field(i+1,j+1,k+1,l) + FDcoefficient(m,order) * & + ((field(coordinates(1,1),coordinates(1,2),coordinates(1,3),l,1)- & + field(coordinates(2,1),coordinates(2,2),coordinates(2,3),l,1))*real(res_x)/geomdim(1) +& + (field(coordinates(3,1),coordinates(3,2),coordinates(3,3),l,2)- & + field(coordinates(4,1),coordinates(4,2),coordinates(4,3),l,2))*real(res_y)/geomdim(2) +& + (field(coordinates(5,1),coordinates(5,2),coordinates(5,3),l,3)- & + field(coordinates(6,1),coordinates(6,2),coordinates(6,3),l,3))*real(res_z)/geomdim(3)) + enddo + enddo + enddo; enddo; enddo +end subroutine divergence + +