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treecode3d_pb.f
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MODULE treecode3d_procedures
C r8 is 8-byte (double precision) real
INTEGER,PARAMETER :: r8=SELECTED_REAL_KIND(12)
C global variables for taylor expansions
INTEGER :: torder,torderlim,torder2
REAL(KIND=r8),ALLOCATABLE,DIMENSION(:) :: cf
REAL(KIND=r8),ALLOCATABLE,DIMENSION(:) :: cf1,cf2,cf3
REAL(KIND=r8),ALLOCATABLE,DIMENSION(:,:,:) :: a,b
C global variables to track tree levels
INTEGER :: minlevel,maxlevel
C global variables used when computing potential/force
INTEGER :: orderoffset
REAL(KIND=r8),DIMENSION(3) :: tarpos,tarq
C ######################################
REAL(KIND=r8) :: tarchr,peng_old(2)
C ######################################
C global variables for position and charge storage
C NOTE: arrays ARE NOT COPIED in this version!! orderarr is still valid
INTEGER,ALLOCATABLE,DIMENSION(:) :: orderarr
REAL(KIND=r8),ALLOCATABLE,DIMENSION(:) :: xcopy,ycopy,zcopy,qcopy
C node pointer and node type declarations
TYPE tnode_pointer
TYPE(tnode), POINTER :: p_to_tnode
END TYPE tnode_pointer
TYPE tnode
INTEGER :: numpar,ibeg,iend
REAL(KIND=r8) :: x_min,y_min,z_min
REAL(KIND=r8) :: x_max,y_max,z_max
REAL(KIND=r8) :: x_mid,y_mid,z_mid
REAL(KIND=r8) :: radius,aspect
INTEGER :: level,num_children,exist_ms
REAL(KIND=r8),DIMENSION(:,:,:,:),POINTER :: ms
TYPE(tnode_pointer), DIMENSION(8) :: child
END TYPE tnode
C#######################################
TYPE(tnode), POINTER::troot
C#######################################
CONTAINS
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE SETUP(x,y,z,q,numpars,order,iflag,xyzminmax)
IMPLICIT NONE
C
C SETUP allocates and initializes arrays needed for the Taylor expansion.
C Also, global variables are set and the Cartesian coordinates of
C the smallest box containing the particles is determined. The particle
C postions and charges are copied so that they can be restored upon exit.
C
INTEGER,INTENT(IN) :: numpars,order,iflag
REAL(KIND=r8),DIMENSION(numpars),INTENT(IN) :: x,y,z,q
REAL(KIND=r8),INTENT(INOUT),DIMENSION(6) :: xyzminmax
C local variables
INTEGER :: err,i,j,k
REAL(KIND=r8) :: t1
C global integers and reals: TORDER, TORDERLIM and THETASQ
C############################################################
torder = order+2
torder2=order
C############################################################
IF (iflag .EQ. 1) THEN
orderoffset=0
ELSE
orderoffset = 1
END IF
torderlim = torder+orderoffset
C allocate global Taylor expansion variables
ALLOCATE(cf(0:torder), STAT=err)
IF (err .NE. 0) THEN
WRITE(6,*) 'Error allocationg Taylor variables! '
STOP
END IF
ALLOCATE(cf1(torderlim),cf2(torderlim),cf3(torderlim),STAT=err)
IF (err .NE. 0) THEN
WRITE(6,*) 'Error allocating Taylor variables! '
STOP
END IF
ALLOCATE(a(-2:torderlim,-2:torderlim,-2:torderlim),
& b(-2:torderlim,-2:torderlim,-2:torderlim),STAT=err)
IF (err .NE. 0) THEN
WRITE(6,*) 'Error allocating Taylor variables! '
STOP
END IF
a=0.0_r8
b=0.0_r8
DO i=0,torder
cf(i) = REAL(i,KIND=r8)+1.0_r8
END DO
DO i=1,torderlim
t1=1.0_r8/REAL(i,KIND=r8)
cf1(i)=t1
cf2(i)=1.0_r8-0.5_r8*t1
cf3(i)=1.0_r8-t1
END DO
C find bounds of Cartesian box enclosing the particles
xyzminmax(1)=MINVAL(x(1:numpars))
xyzminmax(2)=MAXVAL(x(1:numpars))
xyzminmax(3)=MINVAL(y(1:numpars))
xyzminmax(4)=MAXVAL(y(1:numpars))
xyzminmax(5)=MINVAL(z(1:numpars))
xyzminmax(6)=MAXVAL(z(1:numpars))
C#########################################################
ALLOCATE(orderarr(numpars),STAT=err)
IF (err .NE. 0) THEN
WRITE(6,*) 'Error allocating copy variables! '
STOP
END IF
DO i=1,numpars
orderarr(i)=i
END DO
RETURN
END SUBROUTINE SETUP
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
RECURSIVE SUBROUTINE CREATE_TREE(p,ibeg,iend,x,y,z,q,maxparnode,
& xyzmm,level,numpars)
IMPLICIT NONE
C
C CREATE_TREE recursively create the tree structure. Node P is
C input, which contains particles indexed from IBEG to IEND. After
C the node parameters are set subdivision occurs if IEND-IBEG+1 > MAXPARNODE.
C Real array XYZMM contains the min and max values of the coordinates
C of the particle in P, thus defining the box.
C
TYPE(tnode),POINTER :: p
INTEGER,INTENT(IN) :: ibeg,iend,level,maxparnode,numpars
REAL(KIND=r8),DIMENSION(numpars),INTENT(INOUT) :: x,y,z,q
REAL(KIND=r8),DIMENSION(6),INTENT(IN) :: xyzmm
C local variables
REAL(KIND=r8) :: x_mid,y_mid,z_mid,xl,yl,zl,lmax,t1,t2,t3
INTEGER, DIMENSION(8,2) :: ind
REAL(KIND=r8), DIMENSION(6,8) :: xyzmms
INTEGER :: i,j,limin,limax,err,loclev,numposchild
REAL(KIND=r8), DIMENSION(6) :: lxyzmm
C allocate pointer
ALLOCATE(p,STAT=err)
IF (err .NE. 0) THEN
WRITE(6,*) 'Error allocating pointer! '
STOP
END IF
C set node fields: number of particles, exist_ms
C and xyz bounds
p%numpar=iend-ibeg+1
p%exist_ms=0
p%x_min=xyzmm(1)
p%x_max=xyzmm(2)
p%y_min=xyzmm(3)
p%y_max=xyzmm(4)
p%z_min=xyzmm(5)
p%z_max=xyzmm(6)
C compute aspect ratio
xl=p%x_max-p%x_min
yl=p%y_max-p%y_min
zl=p%z_max-p%z_min
lmax=MAX(xl,yl,zl)
t1=lmax
t2=MIN(xl,yl,zl)
IF (t2 .NE. 0.0_r8) THEN
p%aspect=t1/t2
ELSE
p%aspect=0.0_r8
END IF
C midpoint coordinates , RADIUS and SQRADIUS
p%x_mid=(p%x_max+p%x_min)/2.0_r8
p%y_mid=(p%y_max+p%y_min)/2.0_r8
p%z_mid=(p%z_max+p%z_min)/2.0_r8
t1=p%x_max-p%x_mid
t2=p%y_max-p%y_mid
t3=p%z_max-p%z_mid
p%radius=SQRT(t1*t1+t2*t2+t3*t3)
C set particle limits, tree level of node, and nullify children pointers
p%ibeg=ibeg
p%iend=iend
p%level=level
IF (maxlevel .LT. level) THEN
maxlevel=level
END IF
p%num_children=0
DO i=1,8
NULLIFY(p%child(i)%p_to_tnode)
END DO
IF (p%numpar .GT. maxparnode) THEN
C
C set IND array to 0 and then call PARTITION routine. IND array holds indices
C of the eight new subregions. Also, setup XYZMMS array in case SHRINK=1
C
xyzmms(1,1)=p%x_min
xyzmms(2,1)=p%x_max
xyzmms(3,1)=p%y_min
xyzmms(4,1)=p%y_max
xyzmms(5,1)=p%z_min
xyzmms(6,1)=p%z_max
ind=0 !Weihua
ind(1,1)=ibeg
ind(1,2)=iend
x_mid=p%x_mid
y_mid=p%y_mid
z_mid=p%z_mid
CALL PARTITION_8(x,y,z,q,xyzmms,xl,yl,zl,lmax,numposchild,
& x_mid,y_mid,z_mid,ind,numpars)
C########################################################
C Shrink the box
C if (1==2) then
do i=1,8
if (ind(i,1) < ind(i,2)) then
xyzmms(1,i)=minval(x(ind(i,1):ind(i,2)))
xyzmms(2,i)=maxval(x(ind(i,1):ind(i,2)))
xyzmms(3,i)=minval(y(ind(i,1):ind(i,2)))
xyzmms(4,i)=maxval(y(ind(i,1):ind(i,2)))
xyzmms(5,i)=minval(z(ind(i,1):ind(i,2)))
xyzmms(6,i)=maxval(z(ind(i,1):ind(i,2)))
endif
end do
C endif
C########################################################
C
C create children if indicated and store info in parent
C
loclev=level+1
DO i=1,numposchild
IF (ind(i,1) .LE. ind(i,2)) THEN
p%num_children=p%num_children+1
lxyzmm=xyzmms(:,i)
CALL CREATE_TREE(p%child(p%num_children)%p_to_tnode,
& ind(i,1),ind(i,2),x,y,z,q,
& maxparnode,lxyzmm,loclev,numpars)
END IF
END DO
ELSE
IF (level .LT. minlevel) THEN
minlevel=level
END IF
END IF
END SUBROUTINE CREATE_TREE
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE PARTITION_8(x,y,z,q,xyzmms,xl,yl,zl,lmax,numposchild,
& x_mid,y_mid,z_mid,ind,numpars)
IMPLICIT NONE
C
C PARTITION_8 determines the particle indices of the eight sub boxes
C containing the particles after the box defined by particles I_BEG
C to I_END is divided by its midpoints in each coordinate direction.
C The determination of the indices is accomplished by the subroutine
C PARTITION. A box is divided in a coordinate direction as long as the
C resulting aspect ratio is not too large. This avoids the creation of
C "narrow" boxes in which Talyor expansions may become inefficient.
C On exit the INTEGER array IND (dimension 8 x 2) contains
C the indice limits of each new box (node) and NUMPOSCHILD the number
C of possible children. If IND(J,1) > IND(J,2) for a given J this indicates
C that box J is empty.
C
INTEGER, INTENT(IN) :: numpars
REAL(KIND=r8),DIMENSION(numpars),INTENT(INOUT) :: x,y,z,q
INTEGER, DIMENSION(8,2),INTENT(INOUT) :: ind
REAL(KIND=r8),DIMENSION(6,8),INTENT(INOUT) :: xyzmms
REAL(KIND=r8), INTENT(IN) :: x_mid,y_mid,z_mid,xl,yl,zl,lmax
INTEGER,INTENT(INOUT) :: numposchild
C local variables
INTEGER :: temp_ind,i
REAL(KIND=r8) :: critlen
numposchild=1
critlen=lmax/sqrt(2.0_r8)
IF (xl .GE. critlen) THEN
CALL PARTITION(x,y,z,q,orderarr,ind(1,1),ind(1,2),
& x_mid,temp_ind,numpars)
ind(2,1)=temp_ind+1
ind(2,2)=ind(1,2)
ind(1,2)=temp_ind
xyzmms(:,2)=xyzmms(:,1)
xyzmms(2,1)=x_mid
xyzmms(1,2)=x_mid
numposchild=2*numposchild
END IF
IF (yl .GE. critlen) THEN
DO i=1,numposchild
CALL PARTITION(y,x,z,q,orderarr,ind(i,1),ind(i,2),
& y_mid,temp_ind,numpars)
ind(numposchild+i,1)=temp_ind+1
ind(numposchild+i,2)=ind(i,2)
ind(i,2)=temp_ind
xyzmms(:,numposchild+i)=xyzmms(:,i)
xyzmms(4,i)=y_mid
xyzmms(3,numposchild+i)=y_mid
END DO
numposchild=2*numposchild
END IF
IF (zl .GE. critlen) THEN
DO i=1,numposchild
CALL PARTITION(z,x,y,q,orderarr,ind(i,1),ind(i,2),
& z_mid,temp_ind,numpars)
ind(numposchild+i,1)=temp_ind+1
ind(numposchild+i,2)=ind(i,2)
ind(i,2)=temp_ind
xyzmms(:,numposchild+i)=xyzmms(:,i)
xyzmms(6,i)=z_mid
xyzmms(5,numposchild+i)=z_mid
END DO
numposchild=2*numposchild
END IF
RETURN
END SUBROUTINE PARTITION_8
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
RECURSIVE SUBROUTINE COMPP_TREE(p,peng,x,y,z,q,tpoten,kappa,theta,
& numpars,kk,eps,tempq,der_cof)
IMPLICIT NONE
INTEGER,INTENT(IN) :: numpars,kk(3,16)
TYPE(tnode),POINTER :: p
REAL(KIND=r8),INTENT(INOUT) :: peng(2)
REAL(KIND=r8),DIMENSION(numpars),INTENT(IN) :: x,y,z
REAL(KIND=r8),DIMENSION(numpars,16,2),INTENT(IN) :: q
REAL(KIND=r8),DIMENSION(2*numpars),INTENT(IN) :: tpoten
REAL(KIND=r8),INTENT(IN):: kappa,theta,eps,tempq(16,2)
REAL(KIND=r8),INTENT(IN)::
& der_cof(0:torder2,0:torder2,0:torder2,16)
C local variables
REAL(KIND=r8) :: tx,ty,tz,dist,penglocal(2),kapa(2)
real(kind=r8) :: SL(4),pt_comp(16,2)
INTEGER :: i,j,k,ijk(3),ikp,indx,err
C determine DISTSQ for MAC test
tx=p%x_mid-tarpos(1)
ty=p%y_mid-tarpos(2)
tz=p%z_mid-tarpos(3)
dist=SQRT(tx*tx+ty*ty+tz*tz)
C intialize potential energy and force
peng=0.0_r8
C If MAC is accepted and there is more than 1 particle in the
C box use the expansion for the approximation.
!print *,p%radius,dist*theta,p%numpar
!pause
IF ((p%radius .LT. dist*theta) .AND.
& (p%numpar .GT. 40)) THEN
C@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
IF (p%exist_ms .EQ. 0) THEN
ALLOCATE(p%ms(16,0:torder,0:torder,0:torder),STAT=err)
C ALLOCATE(p%ms(0:torder,0:torder,0:torder,16),STAT=err)
IF (err .NE. 0) THEN
WRITE(6,*) 'Error allocating node moments! '
STOP
END IF
C#####################################################################
C Generate the moments if not allocated yet
CALL COMP_MS(p,x,y,z,q(:,:,1),numpars)
C#####################################################################
p%exist_ms=1
END IF
CALL COMPP_TREE_PB(kk,p,peng,kappa,theta,eps,tempq,der_cof)
C CALL COMPP_DIRECT_PB(penglocal,p%ibeg,p%iend,
C & x,y,z,tpoten,kappa,numpars,eps)
C write(*,*) peng(1),penglocal(1),(peng(1)-penglocal(1))/peng(1)
C write(*,*) peng(2),penglocal(2),(peng(2)-penglocal(2))/peng(2)
C pause
C peng=penglocal
ELSE
C If MAC fails check to see if there are children. If not, perform direct
C calculation. If there are children, call routine recursively for each.
C
IF (p%num_children .EQ. 0) THEN
CALL COMPP_DIRECT_PB(penglocal,p%ibeg,p%iend,
& x,y,z,tpoten,kappa,numpars,eps)
peng=penglocal
ELSE
DO i=1,p%num_children
CALL COMPP_TREE(p%child(i)%p_to_tnode,penglocal,x,y,z,q,
& tpoten,kappa,theta,numpars,kk,eps,tempq,der_cof)
peng=peng+penglocal
END DO
END IF
END IF
RETURN
END SUBROUTINE COMPP_TREE
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE COMPP_TREE_PB(kk,p,peng,kappa,theta,eps,tempq,der_cof)
IMPLICIT NONE
INTEGER,INTENT(IN) :: kk(3,16)
TYPE(tnode),POINTER :: p
REAL(KIND=r8),INTENT(INOUT) :: peng(2)
C REAL(KIND=r8),DIMENSION(numpars),INTENT(IN) :: x,y,z
C REAL(KIND=r8),DIMENSION(numpars,16,2),INTENT(IN) :: q
C REAL(KIND=r8),DIMENSION(2*numpars),INTENT(IN) :: tpoten
REAL(KIND=r8),INTENT(IN):: kappa,theta,eps,tempq(16,2),
& der_cof(0:torder2,0:torder2,0:torder2,16)
C local variables
REAL(KIND=r8) :: kapa(2)
real(kind=r8) :: SL(4),pt_comp(16,2)
INTEGER :: i,j,k,ikp,indx,kk1,kk2,kk3
kapa=(/0.d0,kappa/)
do ikp=1,2
C Get the fundermental solution of Poisson equation and PB equation
CALL COMP_TCOEFF(p,kapa(ikp))
do indx=1,16
!kk1=kk(1,indx)
!kk2=kk(2,indx)
!kk3=kk(3,indx)
peng=0.0d0
DO k=0,torder2
DO j=0,torder2-k
DO i=0,torder2-k-j
peng(ikp)=peng(ikp)+der_cof(i,j,k,indx)
& *a(i+kk(1,indx),j+kk(2,indx),k+kk(3,indx))
& *p%ms(indx,i,j,k)
END DO
END DO
END DO
pt_comp(indx,ikp)=tempq(indx,ikp)*peng(ikp)
enddo
enddo
sL(1)=pt_comp(1,1)-pt_comp(1,2)
sL(2)=eps*(sum(pt_comp(2:4,2)))-sum(pt_comp(2:4,1))
sL(3)=-(sum(pt_comp(5:7,1))-1/eps*sum(pt_comp(5:7,2)))
sL(4)=sum(pt_comp(8:16,2))-sum(pt_comp(8:16,1))
peng(1)=sL(1)+sL(2)
peng(2)=sL(3)+sL(4)
END SUBROUTINE COMPP_TREE_PB
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE COMP_TCOEFF_NEW(p,kappa)
IMPLICIT NONE
C
C COMP_TCOEFF computes the Taylor coefficients of the potential
C using a recurrence formula. The center of the expansion is the
C midpoint of the node P. TARPOS and TORDERLIM are globally defined.
C
TYPE(tnode),POINTER :: p
REAL(KIND=r8),INTENT(IN) :: kappa
C local varaibles
REAL(KIND=r8) :: dx,dy,dz,ddx,ddy,ddz,dist,fac,cf1_new(torderlim)
REAL(KIND=r8) :: kappax,kappay,kappaz
INTEGER :: i,j,k
C################################
C Temp variables for saving time
real*8:: a0,b0,ab0,cft1,cft2,cft3
C################################
C setup variables
cf1_new=cf1*kappa
dx=tarpos(1)-p%x_mid
dy=tarpos(2)-p%y_mid
dz=tarpos(3)-p%z_mid
ddx=2.0_r8*dx
ddy=2.0_r8*dy
ddz=2.0_r8*dz
kappax=kappa*dx
kappay=kappa*dy
kappaz=kappa*dz
dist=dx*dx+dy*dy+dz*dz
fac=1.0_r8/dist
dist=SQRT(dist)
C 0th coeff or function val
b(0,0,0)=EXP(-kappa*dist)
a(0,0,0)=b(0,0,0)/dist
C 2 indices are 0
C##############################
a0=a(0,0,0)
b0=b(0,0,0)
ab0=fac*(a0+kappa*b0)
C#############################
b(1,0,0)=kappax*a0
b(0,1,0)=kappay*a0
b(0,0,1)=kappaz*a0
a(1,0,0)=dx*(ab0)
a(0,1,0)=dy*(ab0)
a(0,0,1)=dz*(ab0)
DO i=2,torderlim
C#############################
cft1=cf1_new(i)
cft2=cf2(i)
cft3=cf3(i)
C#############################
b(i,0,0)=cft1*(dx*a(i-1,0,0)-a(i-2,0,0))
b(0,i,0)=cft1*(dy*a(0,i-1,0)-a(0,i-2,0))
b(0,0,i)=cft1*(dz*a(0,0,i-1)-a(0,0,i-2))
a(i,0,0)=fac*(ddx*cft2*a(i-1,0,0)-cft3*a(i-2,0,0)+
& cft1*(dx*b(i-1,0,0)-b(i-2,0,0)))
a(0,i,0)=fac*(ddy*cft2*a(0,i-1,0)-cft3*a(0,i-2,0)+
& cft1*(dy*b(0,i-1,0)-b(0,i-2,0)))
a(0,0,i)=fac*(ddz*cft2*a(0,0,i-1)-cft3*a(0,0,i-2)+
& cft1*(dz*b(0,0,i-1)-b(0,0,i-2)))
END DO
C 1 index 0, 1 index 1, other >=1
b(1,1,0)=kappax*a(0,1,0)
b(1,0,1)=kappax*a(0,0,1)
b(0,1,1)=kappay*a(0,0,1)
a(1,1,0)=fac*(dx*a(0,1,0)+ddy*a(1,0,0)+kappax*b(0,1,0))
a(1,0,1)=fac*(dx*a(0,0,1)+ddz*a(1,0,0)+kappax*b(0,0,1))
a(0,1,1)=fac*(dy*a(0,0,1)+ddz*a(0,1,0)+kappay*b(0,0,1))
DO i=2,torderlim-1
b(1,0,i)=kappax*a(0,0,i)
b(0,1,i)=kappay*a(0,0,i)
b(0,i,1)=kappaz*a(0,i,0)
b(1,i,0)=kappax*a(0,i,0)
b(i,1,0)=kappay*a(i,0,0)
b(i,0,1)=kappaz*a(i,0,0)
a(1,0,i)=fac*(dx*a(0,0,i)+ddz*a(1,0,i-1)-a(1,0,i-2)+
& kappax*b(0,0,i))
a(0,1,i)=fac*(dy*a(0,0,i)+ddz*a(0,1,i-1)-a(0,1,i-2)+
& kappay*b(0,0,i))
a(0,i,1)=fac*(dz*a(0,i,0)+ddy*a(0,i-1,1)-a(0,i-2,1)+
& kappaz*b(0,i,0))
a(1,i,0)=fac*(dx*a(0,i,0)+ddy*a(1,i-1,0)-a(1,i-2,0)+
& kappax*b(0,i,0))
a(i,1,0)=fac*(dy*a(i,0,0)+ddx*a(i-1,1,0)-a(i-2,1,0)+
& kappay*b(i,0,0))
a(i,0,1)=fac*(dz*a(i,0,0)+ddx*a(i-1,0,1)-a(i-2,0,1)+
& kappaz*b(i,0,0))
END DO
C 1 index 0, others >= 2
DO i=2,torderlim-2
C#############################
cft1=cf1_new(i)
cft2=cf2(i)
cft3=cf3(i)
C#############################
DO j=2,torderlim-i
b(i,j,0)=cft1*(dx*a(i-1,j,0)-a(i-2,j,0))
b(i,0,j)=cft1*(dx*a(i-1,0,j)-a(i-2,0,j))
b(0,i,j)=cft1*(dy*a(0,i-1,j)-a(0,i-2,j))
a(i,j,0)=fac*(ddx*cft2*a(i-1,j,0)+ddy*a(i,j-1,0)
& -cft3*a(i-2,j,0)-a(i,j-2,0)+
& cft1*(dx*b(i-1,j,0)-b(i-2,j,0)))
a(i,0,j)=fac*(ddx*cft2*a(i-1,0,j)+ddz*a(i,0,j-1)
& -cft3*a(i-2,0,j)-a(i,0,j-2)+
& cft1*(dx*b(i-1,0,j)-b(i-2,0,j)))
a(0,i,j)=fac*(ddy*cft2*a(0,i-1,j)+ddz*a(0,i,j-1)
& -cft3*a(0,i-2,j)-a(0,i,j-2)+
& cft1*(dy*b(0,i-1,j)-b(0,i-2,j)))
END DO
END DO
C 2 indices 1, other >= 1
C b(1,1,1) is correct, but a little tricky!
C b(1,1,1)=5.0*dz*fac*b(1,1,0)
b(1,1,1)=kappax*a(0,1,1)
a(1,1,1)=fac*(dx*a(0,1,1)+ddy*a(1,0,1)+ddz*a(1,1,0)+
& kappax*b(0,1,1))
DO i=2,torderlim-2
b(1,1,i)=kappax*a(0,1,i)
b(1,i,1)=kappax*a(0,i,1)
b(i,1,1)=kappay*a(i,0,1)
a(1,1,i)=fac*(dx*a(0,1,i)+ddy*a(1,0,i)+ddz*a(1,1,i-1)
& -a(1,1,i-2)+kappax*b(0,1,i))
a(1,i,1)=fac*(dx*a(0,i,1)+ddy*a(1,i-1,1)+ddz*a(1,i,0)
& -a(1,i-2,1)+kappax*b(0,i,1))
a(i,1,1)=fac*(dy*a(i,0,1)+ddx*a(i-1,1,1)+ddz*a(i,1,0)
& -a(i-2,1,1)+kappay*b(i,0,1))
END DO
C 1 index 1, others >=2
DO i=2,torderlim-3
DO j=2,torderlim-i
b(1,i,j)=kappax*a(0,i,j)
b(i,1,j)=kappay*a(i,0,j)
b(i,j,1)=kappaz*a(i,j,0)
a(1,i,j)=fac*(dx*a(0,i,j)+ddy*a(1,i-1,j)+ddz*a(1,i,j-1)
& -a(1,i-2,j)-a(1,i,j-2)+kappax*b(0,i,j))
a(i,1,j)=fac*(dy*a(i,0,j)+ddx*a(i-1,1,j)+ddz*a(i,1,j-1)
& -a(i-2,1,j)-a(i,1,j-2)+kappay*b(i,0,j))
a(i,j,1)=fac*(dz*a(i,j,0)+ddx*a(i-1,j,1)+ddy*a(i,j-1,1)
& -a(i-2,j,1)-a(i,j-2,1)+kappaz*b(i,j,0))
END DO
END DO
C all indices >=2
DO k=2,torderlim-4
DO j=2,torderlim-2-k
DO i=2,torderlim-k-j
b(i,j,k)=cf1_new(i)*(dx*a(i-1,j,k)-a(i-2,j,k))
a(i,j,k)=fac*(ddx*cf2(i)*a(i-1,j,k)+ddy*a(i,j-1,k)
& +ddz*a(i,j,k-1)-cf3(i)*a(i-2,j,k)
& -a(i,j-2,k)-a(i,j,k-2)+
& cf1_new(i)*(dx*b(i-1,j,k)-b(i-2,j,k)))
END DO
END DO
END DO
RETURN
END SUBROUTINE COMP_TCOEFF_NEW
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE COMP_TCOEFF(p,kappa)
IMPLICIT NONE
C
C COMP_TCOEFF computes the Taylor coefficients of the potential
C using a recurrence formula. The center of the expansion is the
C midpoint of the node P. TARPOS and TORDERLIM are globally defined.
C
TYPE(tnode),POINTER :: p
REAL(KIND=r8),INTENT(IN) :: kappa
C local varaibles
REAL(KIND=r8) :: dx,dy,dz,ddx,ddy,ddz,dist,fac,cf1_new(torderlim)
REAL(KIND=r8) :: kappax,kappay,kappaz
INTEGER :: i,j,k
C setup variables
cf1_new=cf1*kappa
dx=tarpos(1)-p%x_mid
dy=tarpos(2)-p%y_mid
dz=tarpos(3)-p%z_mid
ddx=2.0_r8*dx
ddy=2.0_r8*dy
ddz=2.0_r8*dz
kappax=kappa*dx
kappay=kappa*dy
kappaz=kappa*dz
dist=dx*dx+dy*dy+dz*dz
fac=1.0_r8/dist
dist=SQRT(dist)
C 0th coeff or function val
b(0,0,0)=EXP(-kappa*dist)
a(0,0,0)=b(0,0,0)/dist
C 2 indices are 0
b(1,0,0)=kappax*a(0,0,0)
b(0,1,0)=kappay*a(0,0,0)
b(0,0,1)=kappaz*a(0,0,0)
a(1,0,0)=fac*dx*(a(0,0,0)+kappa*b(0,0,0))
a(0,1,0)=fac*dy*(a(0,0,0)+kappa*b(0,0,0))
a(0,0,1)=fac*dz*(a(0,0,0)+kappa*b(0,0,0))
DO i=2,torderlim
b(i,0,0)=cf1_new(i)*(dx*a(i-1,0,0)-a(i-2,0,0))
b(0,i,0)=cf1_new(i)*(dy*a(0,i-1,0)-a(0,i-2,0))
b(0,0,i)=cf1_new(i)*(dz*a(0,0,i-1)-a(0,0,i-2))
a(i,0,0)=fac*(ddx*cf2(i)*a(i-1,0,0)-cf3(i)*a(i-2,0,0)+
& cf1_new(i)*(dx*b(i-1,0,0)-b(i-2,0,0)))
a(0,i,0)=fac*(ddy*cf2(i)*a(0,i-1,0)-cf3(i)*a(0,i-2,0)+
& cf1_new(i)*(dy*b(0,i-1,0)-b(0,i-2,0)))
a(0,0,i)=fac*(ddz*cf2(i)*a(0,0,i-1)-cf3(i)*a(0,0,i-2)+
& cf1_new(i)*(dz*b(0,0,i-1)-b(0,0,i-2)))
END DO
C 1 index 0, 1 index 1, other >=1
b(1,1,0)=kappax*a(0,1,0)
b(1,0,1)=kappax*a(0,0,1)
b(0,1,1)=kappay*a(0,0,1)
a(1,1,0)=fac*(dx*a(0,1,0)+ddy*a(1,0,0)+kappax*b(0,1,0))
a(1,0,1)=fac*(dx*a(0,0,1)+ddz*a(1,0,0)+kappax*b(0,0,1))
a(0,1,1)=fac*(dy*a(0,0,1)+ddz*a(0,1,0)+kappay*b(0,0,1))
DO i=2,torderlim-1
b(1,0,i)=kappax*a(0,0,i)
b(0,1,i)=kappay*a(0,0,i)
b(0,i,1)=kappaz*a(0,i,0)
b(1,i,0)=kappax*a(0,i,0)
b(i,1,0)=kappay*a(i,0,0)
b(i,0,1)=kappaz*a(i,0,0)
a(1,0,i)=fac*(dx*a(0,0,i)+ddz*a(1,0,i-1)-a(1,0,i-2)+
& kappax*b(0,0,i))
a(0,1,i)=fac*(dy*a(0,0,i)+ddz*a(0,1,i-1)-a(0,1,i-2)+
& kappay*b(0,0,i))
a(0,i,1)=fac*(dz*a(0,i,0)+ddy*a(0,i-1,1)-a(0,i-2,1)+
& kappaz*b(0,i,0))
a(1,i,0)=fac*(dx*a(0,i,0)+ddy*a(1,i-1,0)-a(1,i-2,0)+
& kappax*b(0,i,0))
a(i,1,0)=fac*(dy*a(i,0,0)+ddx*a(i-1,1,0)-a(i-2,1,0)+
& kappay*b(i,0,0))
a(i,0,1)=fac*(dz*a(i,0,0)+ddx*a(i-1,0,1)-a(i-2,0,1)+
& kappaz*b(i,0,0))
END DO
C 1 index 0, others >= 2
DO i=2,torderlim-2
DO j=2,torderlim-i
b(i,j,0)=cf1_new(i)*(dx*a(i-1,j,0)-a(i-2,j,0))
b(i,0,j)=cf1_new(i)*(dx*a(i-1,0,j)-a(i-2,0,j))
b(0,i,j)=cf1_new(i)*(dy*a(0,i-1,j)-a(0,i-2,j))
a(i,j,0)=fac*(ddx*cf2(i)*a(i-1,j,0)+ddy*a(i,j-1,0)
& -cf3(i)*a(i-2,j,0)-a(i,j-2,0)+
& cf1_new(i)*(dx*b(i-1,j,0)-b(i-2,j,0)))
a(i,0,j)=fac*(ddx*cf2(i)*a(i-1,0,j)+ddz*a(i,0,j-1)
& -cf3(i)*a(i-2,0,j)-a(i,0,j-2)+
& cf1_new(i)*(dx*b(i-1,0,j)-b(i-2,0,j)))
a(0,i,j)=fac*(ddy*cf2(i)*a(0,i-1,j)+ddz*a(0,i,j-1)
& -cf3(i)*a(0,i-2,j)-a(0,i,j-2)+
& cf1_new(i)*(dy*b(0,i-1,j)-b(0,i-2,j)))
END DO
END DO
C 2 indices 1, other >= 1
C b(1,1,1) is correct, but a little tricky!
C b(1,1,1)=5.0*dz*fac*b(1,1,0)
b(1,1,1)=kappax*a(0,1,1)
a(1,1,1)=fac*(dx*a(0,1,1)+ddy*a(1,0,1)+ddz*a(1,1,0)+
& kappax*b(0,1,1))
DO i=2,torderlim-2
b(1,1,i)=kappax*a(0,1,i)
b(1,i,1)=kappax*a(0,i,1)
b(i,1,1)=kappay*a(i,0,1)
a(1,1,i)=fac*(dx*a(0,1,i)+ddy*a(1,0,i)+ddz*a(1,1,i-1)
& -a(1,1,i-2)+kappax*b(0,1,i))
a(1,i,1)=fac*(dx*a(0,i,1)+ddy*a(1,i-1,1)+ddz*a(1,i,0)
& -a(1,i-2,1)+kappax*b(0,i,1))
a(i,1,1)=fac*(dy*a(i,0,1)+ddx*a(i-1,1,1)+ddz*a(i,1,0)
& -a(i-2,1,1)+kappay*b(i,0,1))
END DO
C 1 index 1, others >=2
DO i=2,torderlim-3
DO j=2,torderlim-i
b(1,i,j)=kappax*a(0,i,j)
b(i,1,j)=kappay*a(i,0,j)
b(i,j,1)=kappaz*a(i,j,0)
a(1,i,j)=fac*(dx*a(0,i,j)+ddy*a(1,i-1,j)+ddz*a(1,i,j-1)
& -a(1,i-2,j)-a(1,i,j-2)+kappax*b(0,i,j))
a(i,1,j)=fac*(dy*a(i,0,j)+ddx*a(i-1,1,j)+ddz*a(i,1,j-1)
& -a(i-2,1,j)-a(i,1,j-2)+kappay*b(i,0,j))
a(i,j,1)=fac*(dz*a(i,j,0)+ddx*a(i-1,j,1)+ddy*a(i,j-1,1)
& -a(i-2,j,1)-a(i,j-2,1)+kappaz*b(i,j,0))
END DO
END DO
C all indices >=2
DO k=2,torderlim-4
DO j=2,torderlim-2-k
DO i=2,torderlim-k-j
b(i,j,k)=cf1_new(i)*(dx*a(i-1,j,k)-a(i-2,j,k))
a(i,j,k)=fac*(ddx*cf2(i)*a(i-1,j,k)+ddy*a(i,j-1,k)
& +ddz*a(i,j,k-1)-cf3(i)*a(i-2,j,k)
& -a(i,j-2,k)-a(i,j,k-2)+
& cf1_new(i)*(dx*b(i-1,j,k)-b(i-2,j,k)))
END DO
END DO
END DO
RETURN
END SUBROUTINE COMP_TCOEFF
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE COMP_MS(p,x,y,z,q,numpars)
IMPLICIT NONE
C
C COMP_MS computes the moments for node P needed in the Taylor approximation
C
INTEGER,INTENT(IN) :: numpars
TYPE(tnode),POINTER :: p
REAL(KIND=r8),DIMENSION(numpars),INTENT(IN) :: x,y,z
C##################################################################
REAL(KIND=r8),DIMENSION(numpars,16),INTENT(IN) ::q
C##################################################################
C local variables
INTEGER :: i,k1,k2,k3,j
REAL(KIND=r8) :: dx,dy,dz,tx,ty,tz,txyz
p%ms=0.0_r8
DO i=p%ibeg,p%iend
dx=x(i)-p%x_mid
dy=y(i)-p%y_mid
dz=z(i)-p%z_mid
tz=1.0_r8
DO k3=0,torder
ty=1.0_r8
DO k2=0,torder-k3
tx=1.0_r8
DO k1=0,torder-k3-k2
C####################################################################
txyz=tx*ty*tz
C p%ms(k1,k2,k3,1:7)=p%ms(k1,k2,k3,1:7)+q(i,1:7)*txyz
C p%ms(k1,k2,k3,8:14:3)=p%ms(k1,k2,k3,8:14:3)+q(i,8:14:3)*txyz
p%ms(1:7,k1,k2,k3)=p%ms(1:7,k1,k2,k3)+q(i,1:7)*txyz
p%ms(8:14:3,k1,k2,k3)=p%ms(8:14:3,k1,k2,k3)+q(i,8:14:3)*txyz
C####################################################################
tx=tx*dx
END DO
ty=ty*dy
END DO
tz=tz*dz
END DO
END DO
C####################################################################
p%ms(9,:,:,:) =p%ms(8,:,:,:)
p%ms(10,:,:,:)=p%ms(8,:,:,:)
p%ms(12,:,:,:)=p%ms(11,:,:,:)
p%ms(13,:,:,:)=p%ms(11,:,:,:)
p%ms(15,:,:,:)=p%ms(14,:,:,:)
p%ms(16,:,:,:)=p%ms(14,:,:,:)
C p%ms(:,:,:,9) =p%ms(:,:,:,8)
C p%ms(:,:,:,10)=p%ms(:,:,:,8)
C p%ms(:,:,:,12)=p%ms(:,:,:,11)
C p%ms(:,:,:,13)=p%ms(:,:,:,11)
C p%ms(:,:,:,15)=p%ms(:,:,:,14)
C p%ms(:,:,:,16)=p%ms(:,:,:,14)
C####################################################################
RETURN
END SUBROUTINE COMP_MS
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE COMPP_DIRECT_PB(peng,ibeg,iend,x,y,z,
& tpoten,kappa,numpars,eps)
use treecode, only: tr_area,tr_q
IMPLICIT NONE
real*8, external:: H1,H2,H3,H4
C
C COMPF_DIRECT directly computes the force on the current target
C particle determined by the global variable TARPOS.
C
INTEGER,INTENT(IN) :: ibeg,iend,numpars
REAL*8,DIMENSION(numpars),INTENT(IN) :: x,y,z
REAL*8,DIMENSION(2*numpars),INTENT(IN) :: tpoten
REAL*8,INTENT(IN) :: kappa,eps
REAL*8,INTENT(OUT) :: peng(2)
C local variables
INTEGER :: j
REAL*8 :: dist2,dist,tx,ty,tz,soupos(3),souq(3)
real*8 :: peng_old(2),L1,L2,L3,L4, area,temp_area
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
real*8 :: r(3),s(3),v(3),v0(3),pi,rs,cos_theta,cos_theta0,kappa_rs
real*8 :: G0,Gk,G10,G20,G1,G2,G3,G4,one_over_4pi,exp_kappa_rs
real*8 :: tp1,tp2,tp3
common // pi,one_over_4pi
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
peng=0.0_r8
DO j=ibeg,iend
C###########################################
C The following content has to be precisely fast
C Since it is the part called most
!soupos=(/x(j),y(j),z(j)/)
!souq=tr_q(:,j)
C###########################################
C Temperarily delete the singular part
C if (dist <1.d-10) then
C goto 1022
C endif
C############################################
C L1=H1(souq,soupos,tarpos,eps,kappa)
C L2=H2(soupos,tarpos,kappa)
C L3=H3(tarq,souq,soupos,tarpos,kappa)
C L4=H4(tarq,soupos,tarpos,kappa,eps)
C%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
r=(/x(j),y(j),z(j)/)
v=tr_q(:,j)
s=tarpos
v0=tarq
rs=sqrt(dot_product(r-s,r-s))
! if (rs<1.d-6) goto 1022
G0=one_over_4pi/rs
kappa_rs=kappa*rs
exp_kappa_rs=exp(-kappa_rs)
Gk=exp_kappa_rs*G0
cos_theta=dot_product(v,r-s)/rs
cos_theta0=dot_product(v0,r-s)/rs
tp1=G0/rs
tp2=(1.d0+kappa_rs)*exp_kappa_rs
G10=cos_theta0*tp1
G20=tp2*G10
G1=cos_theta*tp1
G2=tp2*G1
G3=(dot_product(v0,v)-3.d0*cos_theta0*cos_theta)/rs*tp1
G4=tp2*G3-kappa**2*cos_theta0*cos_theta*Gk
L1=G1-eps*G2
L2=G0-Gk
L3=G4-G3
L4=G10-G20/eps
peng_old(1)=tpoten(j)
peng_old(2)=tpoten(j+numpars)
area=tr_area(j)
peng(1)=peng(1)+(L1*peng_old(1)+L2*peng_old(2))*area
peng(2)=peng(2)+(L3*peng_old(1)+L4*peng_old(2))*area
C#############################################
!1022 continue