! D03PP_T1W_F Example Program Text
! Mark 28.5 Release. NAG Copyright 2022.
Module d03pp_t1w_fe_mod
! D03PP_T1W_F Example Program Module:
! Parameters and User-defined Routines
! .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: exp, nagad_t1w_w_rtype, Operator (/), &
Operator (<), Assignment (=), Operator (-), &
Operator (>), Operator (>=), Operator (+), &
Operator (*)
Use nag_library, Only: nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: bndary, monitf, pdedef, uvinit
! .. Parameters ..
Real (Kind=nag_wp), Parameter :: four = 4.0_nag_wp
Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp
Real (Kind=nag_wp), Parameter :: ptone = 0.1_nag_wp
Real (Kind=nag_wp), Parameter, Public :: half = 0.5_nag_wp
Real (Kind=nag_wp), Parameter, Public :: two = 2.0_nag_wp
Real (Kind=nag_wp), Parameter, Public :: zero = 0.0_nag_wp
Integer, Parameter, Public :: itrace = 0, m = 0, nin = 5, &
nout = 6, npde = 1, nv = 0, &
nxfix = 0, nxi = 0
Contains
Subroutine uvinit(ad_handle,npde,npts,nxi,x,xi,u,nv,v,iuser,ruser)
! .. Scalar Arguments ..
Type (c_ptr), Intent (Inout) :: ad_handle
Integer, Intent (In) :: npde, npts, nv, nxi
! .. Array Arguments ..
Type (nagad_t1w_w_rtype), Intent (Inout) :: ruser(*)
Type (nagad_t1w_w_rtype), Intent (Out) :: u(npde,npts), v(nv)
Type (nagad_t1w_w_rtype), Intent (In) :: x(npts), xi(nxi)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Type (nagad_t1w_w_rtype) :: a, b, c, e, t
Integer :: i
! .. Executable Statements ..
e = ruser(1)
t = zero
Do i = 1, npts
a = (x(i)-0.25_nag_wp-0.75_nag_wp*t)/(four*e)
b = (0.9_nag_wp*x(i)-0.325_nag_wp-0.495_nag_wp*t)/(two*e)
If (a>zero .And. a>b) Then
a = exp(-a)
c = (0.8_nag_wp*x(i)-0.4_nag_wp-0.24_nag_wp*t)/(four*e)
c = exp(c)
u(1,i) = (half+ptone*c+a)/(one+c+a)
Else If (b>zero .And. b>=a) Then
b = exp(-b)
c = (-0.8_nag_wp*x(i)+0.4_nag_wp+0.24_nag_wp*t)/(four*e)
c = exp(c)
u(1,i) = (ptone+half*c+b)/(one+c+b)
Else
a = exp(a)
b = exp(b)
u(1,i) = (one+half*a+ptone*b)/(one+a+b)
End If
End Do
! There are no coupled ODEs in this problem (nv = 0):
v(:) = 0._nag_wp
Return
End Subroutine uvinit
Subroutine pdedef(ad_handle,npde,t,x,u,ux,nv,v,vdot,p,q,r,ires,iuser, &
ruser)
! .. Scalar Arguments ..
Type (c_ptr), Intent (Inout) :: ad_handle
Type (nagad_t1w_w_rtype), Intent (In) :: t, x
Integer, Intent (Inout) :: ires
Integer, Intent (In) :: npde, nv
! .. Array Arguments ..
Type (nagad_t1w_w_rtype), Intent (Out) :: p(npde,npde), q(npde), &
r(npde)
Type (nagad_t1w_w_rtype), Intent (Inout) :: ruser(*)
Type (nagad_t1w_w_rtype), Intent (In) :: u(npde), ux(npde), v(nv), &
vdot(nv)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Type (nagad_t1w_w_rtype) :: e
! .. Executable Statements ..
e = ruser(1)
p(1,1) = one
r(1) = e*ux(1)
q(1) = u(1)*ux(1)
Return
End Subroutine pdedef
Subroutine bndary(ad_handle,npde,t,u,ux,nv,v,vdot,ibnd,beta,gamma,ires, &
iuser,ruser)
! .. Scalar Arguments ..
Type (c_ptr), Intent (Inout) :: ad_handle
Type (nagad_t1w_w_rtype), Intent (In) :: t
Integer, Intent (In) :: ibnd, npde, nv
Integer, Intent (Inout) :: ires
! .. Array Arguments ..
Type (nagad_t1w_w_rtype), Intent (Out) :: beta(npde), gamma(npde)
Type (nagad_t1w_w_rtype), Intent (Inout) :: ruser(*)
Type (nagad_t1w_w_rtype), Intent (In) :: u(npde), ux(npde), v(nv), &
vdot(nv)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Type (nagad_t1w_w_rtype) :: a, b, c, e, ue, x
! .. Executable Statements ..
e = ruser(1)
beta(1) = zero
If (ibnd==0) Then
x = zero
a = (x-0.25_nag_wp-0.75_nag_wp*t)/(four*e)
b = (0.9_nag_wp*x-0.325_nag_wp-0.495_nag_wp*t)/(two*e)
If (a>zero .And. a>b) Then
a = exp(-a)
c = (0.8_nag_wp*x-0.4_nag_wp-0.24_nag_wp*t)/(four*e)
c = exp(c)
ue = (half+ptone*c+a)/(one+c+a)
Else If (b>zero .And. b>=a) Then
b = exp(-b)
c = (-0.8_nag_wp*x+0.4_nag_wp+0.24_nag_wp*t)/(four*e)
c = exp(c)
ue = (ptone+half*c+b)/(one+c+b)
Else
a = exp(a)
b = exp(b)
ue = (one+half*a+ptone*b)/(one+a+b)
End If
Else
x = one
a = (x-0.25_nag_wp-0.75_nag_wp*t)/(four*e)
b = (0.9_nag_wp*x-0.325_nag_wp-0.495_nag_wp*t)/(two*e)
If (a>zero .And. a>b) Then
a = exp(-a)
c = (0.8_nag_wp*x-0.4_nag_wp-0.24_nag_wp*t)/(four*e)
c = exp(c)
ue = (half+ptone*c+a)/(one+c+a)
Else If (b>zero .And. b>=a) Then
b = exp(-b)
c = (-0.8_nag_wp*x+0.4_nag_wp+0.24_nag_wp*t)/(four*e)
c = exp(c)
ue = (ptone+half*c+b)/(one+c+b)
Else
a = exp(a)
b = exp(b)
ue = (one+half*a+ptone*b)/(one+a+b)
End If
End If
gamma(1) = u(1) - ue
Return
End Subroutine bndary
Subroutine monitf(ad_handle,t,npts,npde,x,u,r,fmon,iuser,ruser)
! .. Scalar Arguments ..
Type (c_ptr), Intent (Inout) :: ad_handle
Type (nagad_t1w_w_rtype), Intent (In) :: t
Integer, Intent (In) :: npde, npts
! .. Array Arguments ..
Type (nagad_t1w_w_rtype), Intent (Out) :: fmon(npts)
Type (nagad_t1w_w_rtype), Intent (In) :: r(npde,npts), u(npde,npts), &
x(npts)
Type (nagad_t1w_w_rtype), Intent (Inout) :: ruser(*)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Type (nagad_t1w_w_rtype) :: drdx, h
Integer :: i, k, l
! .. Intrinsic Procedures ..
Intrinsic :: max, min
! .. Executable Statements ..
Do i = 1, npts - 1
k = max(1,i-1)
l = min(npts,i+1)
h = (x(l)-x(k))*half
! Second derivative ..
drdx = (r(1,i+1)-r(1,i))/h
If (drdx<0.0_nag_wp) Then
drdx = -drdx
End If
fmon(i) = drdx
End Do
fmon(npts) = fmon(npts-1)
Return
End Subroutine monitf
End Module d03pp_t1w_fe_mod
Program d03pp_t1w_fe
! D03PP_T1W_F Example Main Program
! .. Use Statements ..
Use d03pp_t1w_fe_mod, Only: bndary, half, itrace, m, monitf, nin, nout, &
npde, nv, nxfix, nxi, pdedef, two, uvinit, &
zero
Use iso_c_binding, Only: c_ptr
Use nagad_library, Only: d03pp_t1w_f, d03pz_t1w_f, d53pc_t1w_k, min, &
nagad_t1w_set_derivative, nagad_t1w_w_rtype, &
x10aa_t1w_f, x10ab_t1w_f, Assignment (=), &
Operator (>)
Use nag_library, Only: nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Type (c_ptr) :: ad_handle
Type (nagad_t1w_w_rtype) :: con, dxmesh, tout, trmesh, ts, &
xratio
Real (Kind=nag_wp) :: dx, e, x0, xmid
Integer :: i, ifail, ind, intpts, ipminf, it, &
itask, itol, itype, lenode, neqn, &
niw, npts, nrmesh, nw, nwkres
Logical :: remesh, theta
Character (1) :: laopt, norm
! .. Local Arrays ..
Type (nagad_t1w_w_rtype) :: algopt(30), atol(1), rtol(1), &
ruser(1), rwsav(1100), xfix(nxfix), &
xi(nxi)
Type (nagad_t1w_w_rtype), Allocatable :: u(:), uout(:,:,:), w(:), x(:), &
xout(:)
Real (Kind=nag_wp), Allocatable :: de(:)
Real (Kind=nag_wp) :: tol(2)
Integer :: iuser(1), iwsav(505)
Integer, Allocatable :: iw(:)
Logical :: lwsav(100)
Character (80) :: cwsav(10)
! .. Intrinsic Procedures ..
Intrinsic :: real
! .. Executable Statements ..
Write (nout,*) 'D03PP_T1W_F Example Program Results'
! Skip heading in data file
Read (nin,*)
Read (nin,*) npts, intpts, itype
neqn = npde*npts + nv
niw = 25 + nxfix
nwkres = npde*(npts+3*npde+21) + 7*npts + nxfix + 3
lenode = 11*neqn + 50
nw = neqn*neqn + neqn + nwkres + lenode
Allocate (u(neqn),uout(npde,intpts,itype),w(nw),x(npts),xout(intpts), &
iw(niw),de(npts))
Read (nin,*) itol
Read (nin,*) tol(1:2)
atol(1) = tol(1)
rtol(1) = tol(2)
Read (nin,*) e
ruser(1) = e
! Create AD configuration data object
ifail = 0
Call x10aa_t1w_f(ad_handle,ifail)
! Initialise mesh
Do i = 1, npts
x(i) = real(i-1,kind=nag_wp)/real(npts-1,kind=nag_wp)
End Do
! Set remesh parameters
remesh = .True.
nrmesh = 3
dxmesh = half
con = two/real(npts-1,kind=nag_wp)
xratio = 1.5_nag_wp
ipminf = 0
norm = 'A'
laopt = 'F'
ind = 0
itask = 1
! Set theta to .TRUE. if the Theta integrator is required
theta = .False.
algopt(1:30) = zero
If (theta) Then
algopt(1) = two
End If
! Register variables to differentiate w.r.t.
Call nagad_t1w_set_derivative(ruser(1),1.0E0_nag_wp)
! Loop over output value of t
ts = zero
tout = zero
Do it = 1, 1
xmid = half + 0.1_nag_wp*real(it-1,kind=nag_wp)
tout = 0.2_nag_wp*real(it,kind=nag_wp)
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call d03pp_t1w_f(ad_handle,npde,m,ts,tout,pdedef,bndary,uvinit,u,npts, &
x,nv,d53pc_t1w_k,nxi,xi,neqn,rtol,atol,itol,norm,laopt,algopt, &
remesh,nxfix,xfix,nrmesh,dxmesh,trmesh,ipminf,xratio,con,monitf,w, &
nw,iw,niw,itask,itrace,ind,cwsav,lwsav,iwsav,rwsav,iuser,ruser, &
ifail)
If (it==1) Then
Write (nout,99997) tol(1), npts
Write (nout,99995) nrmesh
Write (nout,99994) e
Write (nout,*)
End If
! Set output points
dx = 0.1_nag_wp
If (tout>half) Then
dx = 0.05_nag_wp
End If
x0 = xmid - half*real(intpts-1,kind=nag_wp)*dx
Do i = 1, intpts
xout(i) = x0
x0 = x0 + dx
End Do
xout(intpts) = min(xout(intpts),x(npts))
! Interpolate at output points
ifail = 0
Call d03pz_t1w_f(ad_handle,npde,m,u,npts,x,xout,intpts,itype,uout, &
ifail)
End Do
Write (nout,99998) ts%value
Write (nout,99996) iw(1), iw(2), iw(3), iw(5)
Do i = 1, npts
de(i) = u(i)%tangent
End Do
Write (nout,*)
Write (nout,*) ' Derivatives calculated: First order tangents'
Write (nout,*) ' Computational mode : algorithmic'
Write (nout,*) ' Derivatives (final time solution w.r.t. E):'
Write (nout,*) ' x u(t) du(t)/dE'
Do i = 1, npts
Write (nout,99999) x(i)%value, u(i)%value, de(i)
End Do
99999 Format (1X,2(1X,E12.5),1X,E10.2)
! Remove computational data object
ifail = 0
Call x10ab_t1w_f(ad_handle,ifail)
99998 Format (' T = ',F6.3)
99997 Format (/,/,' Accuracy requirement =',E10.3,' Number of points = ',I3, &
/)
99996 Format (' Number of integration steps in time = ',I6,/,' Number o', &
'f function evaluations = ',I6,/,' Number of Jacobian eval', &
'uations =',I6,/,' Number of iterations = ',I6)
99995 Format (2X,'Remeshing every',I3,' time steps',/)
99994 Format (2X,'E =',F8.3)
End Program d03pp_t1w_fe