NAG AD Library
d03pp (dim1_parab_remesh_fd)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a configuration object that holds information on the differentiation strategy. Details on setting the AD strategy are described in AD handle object in the NAG AD Library Introduction.

2: npde – Integer Input

3: m – Integer Input

4: ts – ADTYPE Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

5: tout – ADTYPE Input

6: pdedef – Callable Input

pdedef needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of pdedef is:

Fortran Interface copy

Subroutine pdedef ( npde, t, x, u, ux, nv, v, vdot, p, q, r, ires, iuser, ruser) Integer, Intent (In) :: npde, nv Integer, Intent (Inout) :: ires, iuser(*) ADTYPE, Intent (In) :: t, x, u(npde), ux(npde), v(nv), vdot(nv) ADTYPE, Intent (Inout) :: ruser(*) ADTYPE, Intent (Out) :: p(npde,npde), q(npde), r(npde) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto pdedef = [&]( const handle_t &ad_handle, const Integer &npde, const ADTYPE &t, const ADTYPE &x, const ADTYPE u[], const ADTYPE ux[], const Integer &nv, const ADTYPE v[], const ADTYPE vdot[], ADTYPE p[], ADTYPE q[], ADTYPE r[], Integer &ires)

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: npde – Integer Input

3: t – ADTYPE Input

4: x – ADTYPE Input

5: u – ADTYPE array Input

6: ux – ADTYPE array Input

7: nv – Integer Input

8: v – ADTYPE array Input

9: vdot – ADTYPE array Input

10: p – ADTYPE array Output

11: q – ADTYPE array Output

12: r – ADTYPE array Output

13: ires – Integer Input/Output

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

7: bndary – Callable Input

bndary needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of bndary is:

Fortran Interface copy

Subroutine bndary ( npde, t, u, ux, nv, v, vdot, ibnd, beta, gamma, ires, iuser, ruser) Integer, Intent (In) :: npde, nv, ibnd Integer, Intent (Inout) :: ires, iuser(*) ADTYPE, Intent (In) :: t, u(npde), ux(npde), v(nv), vdot(nv) ADTYPE, Intent (Inout) :: ruser(*) ADTYPE, Intent (Out) :: beta(npde), gamma(npde) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto bndary = [&]( const handle_t &ad_handle, const Integer &npde, const ADTYPE &t, const ADTYPE u[], const ADTYPE ux[], const Integer &nv, const ADTYPE v[], const ADTYPE vdot[], const Integer &ibnd, ADTYPE beta[], ADTYPE gamma[], Integer &ires)

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: npde – Integer Input

3: t – ADTYPE Input

4: u – ADTYPE array Input

5: ux – ADTYPE array Input

6: nv – Integer Input

7: v – ADTYPE array Input

8: vdot – ADTYPE array Input

9: ibnd – Integer Input

10: beta – ADTYPE array Output

11: gamma – ADTYPE array Output

12: ires – Integer Input/Output

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

8: uvinit – Callable Input

uvinit needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

The specification of uvinit is:

Fortran Interface copy

Subroutine uvinit ( npde, npts, nxi, x, xi, u, nv, v, iuser, ruser) Integer, Intent (In) :: npde, npts, nxi, nv Integer, Intent (Inout) :: iuser(*) ADTYPE, Intent (In) :: x(npts), xi(nxi) ADTYPE, Intent (Inout) :: ruser(*) ADTYPE, Intent (Out) :: u(npde,npts), v(nv) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto uvinit = [&]( const handle_t &ad_handle, const Integer &npde, const Integer &npts, const Integer &nxi, const ADTYPE x[], const ADTYPE xi[], ADTYPE u[], const Integer &nv, ADTYPE v[])

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: npde – Integer Input

3: npts – Integer Input

4: nxi – Integer Input

5: x – ADTYPE array Input

6: xi – ADTYPE array Input

7: u – ADTYPE array Output

8: nv – Integer Input

9: v – ADTYPE array Output

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

9: u(neqn) – ADTYPE array Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

10: npts – Integer Input

11: x(npts) – ADTYPE array Input/Output

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

12: nv – Integer Input

13: odedef – Callable Input

odedef needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

If a null pointer is used as the argument, then a NAG supplied routine will be used as the argument for this parameter (C++ only).

For the Fortran interface, the NAG supplied routine d03pc_AD_k may be used as the actual argument for this parameter.

The specification of odedef is:

Fortran Interface copy

Subroutine odedef ( npde, t, nv, v, vdot, nxi, xi, ucp, ucpx, rcp, ucpt, ucptx, f, ires, iuser, ruser) Integer, Intent (In) :: npde, nv, nxi Integer, Intent (Inout) :: ires, iuser(*) ADTYPE, Intent (In) :: t, v(nv), vdot(nv), xi(nxi), ucp(npde,nxi), ucpx(npde,nxi), rcp(npde,nxi), ucpt(npde,nxi), ucptx(npde,nxi) ADTYPE, Intent (Inout) :: ruser(*) ADTYPE, Intent (Out) :: f(nv) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto odedef = [&]( const handle_t &ad_handle, const Integer &npde, const ADTYPE &t, const Integer &nv, const ADTYPE v[], const ADTYPE vdot[], const Integer &nxi, const ADTYPE xi[], const ADTYPE ucp[], const ADTYPE ucpx[], const ADTYPE rcp[], const ADTYPE ucpt[], const ADTYPE ucptx[], ADTYPE f[], Integer &ires)

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: npde – Integer Input

3: t – ADTYPE Input

4: nv – Integer Input

5: v – ADTYPE array Input

6: vdot – ADTYPE array Input

7: nxi – Integer Input

8: xi – ADTYPE array Input

9: ucp – ADTYPE array Input

10: ucpx – ADTYPE array Input

11: rcp – ADTYPE array Input

12: ucpt – ADTYPE array Input

13: ucptx – ADTYPE array Input

14: f – ADTYPE array Output

15: ires – Integer Input/Output

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

14: nxi – Integer Input

15: xi(nxi) – ADTYPE array Input

16: neqn – Integer Input

17: rtol($*$) – ADTYPE array Input

18: atol($*$) – ADTYPE array Input

19: itol – Integer Input

20: norm – character Input

21: laopt – character Input

22: algopt($30$) – ADTYPE array Input

23: remesh – logical Input

24: nxfix – Integer Input

25: xfix(nxfix) – ADTYPE array Input

26: nrmesh – Integer Input

27: dxmesh – ADTYPE Input

28: trmesh – ADTYPE Input

29: ipminf – Integer Input

30: xratio – ADTYPE Input

31: con – ADTYPE Input

32: monitf – Callable Input

monitf needs to be callable with the specification listed below. This can be a C++ lambda, a functor or a (static member) function pointer. If using a lambda, parameters can be captured safely by reference. No copies of the callable are made internally.

If a null pointer is used as the argument, then a NAG supplied routine will be used as the argument for this parameter (C++ only).

For the Fortran interface, the NAG supplied routine d03pc_AD_l may be used as the actual argument for this parameter.

The specification of monitf is:

Fortran Interface copy

Subroutine monitf ( t, npts, npde, x, u, r, fmon, iuser, ruser) Integer, Intent (In) :: npts, npde Integer, Intent (Inout) :: iuser(*) ADTYPE, Intent (In) :: t, x(npts), u(npde,npts), r(npde,npts) ADTYPE, Intent (Inout) :: ruser(*) ADTYPE, Intent (Out) :: fmon(npts) Type (c_ptr), Intent (Inout) :: ad_handle

C++ Interface copy

auto monitf = [&]( const handle_t &ad_handle, const ADTYPE &t, const Integer &npts, const Integer &npde, const ADTYPE x[], const ADTYPE u[], const ADTYPE r[], ADTYPE fmon[])

1: ad_handle – nag::ad::handle_t Input/Output

On entry: a handle to the AD handle object.

2: t – ADTYPE Input

3: npts – Integer Input

4: npde – Integer Input

5: x – ADTYPE array Input

6: u – ADTYPE array Input

7: r – ADTYPE array Input

8: fmon – ADTYPE array Output

*: iuser($*$) – Integer array User Workspace

*: ruser($*$) – ADTYPE array User Workspace

33: rsave(lrsave) – ADTYPE array Communication Array

Please consult Overwriting of Inputs in the NAG AD Library Introduction.

34: lrsave – Integer Input

35: isave(lisave) – Integer array Communication Array

36: lisave – Integer Input

37: itask – Integer Input

38: itrace – Integer Input

39: ind – Integer Input/Output

*: iuser($*$) – Integer array User Workspace

User workspace.

*: ruser($*$) – ADTYPE array User Workspace

User workspace.

40: cwsav($10$) – character array Communication Array

If $\mathbf{ind}=0$, cwsav, lwsav, iwsav and rwsav need not be set on entry.

41: lwsav($100$) – logical array Communication Array

If $\mathbf{ind}=0$, cwsav, lwsav, iwsav and rwsav need not be set on entry.

42: iwsav($505$) – Integer array Communication Array

If $\mathbf{ind}=0$, cwsav, lwsav, iwsav and rwsav need not be set on entry.

43: rwsav($1100$) – ADTYPE array Communication Array

If $\mathbf{ind}=0$, cwsav, lwsav, iwsav and rwsav need not be set on entry.

44: ifail – Integer Input/Output

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Adjoint modes

10.2 Tangent modes

10.3 Passive mode