pchelms Module Reference

This file solves the helmholtz equation to set inital fields that match vmec and vacuum currents from the vector potential. Initial vector potential on the edge is supplied by the BMW code. More...

Functions/Subroutines
subroutine	run_pchelms
	Run the pchelms code to solve for inital jbsup values.
subroutine	curla_pchelms (Asubsmnf, Asubumnf, Asubvmnf,
	Compute real-space components of contravariant jac*B^i on half radial grid from curl(A). More...
subroutine	curlb_pchelms (ksupsmnf, ksupumnf, ksupvmnf, asubsmnf,
	Compute real-space components of contravariant jac*J^i on full radial grid from curl(B). More...
subroutine	cyl2vmec_a (A_r, A_p, A_z, cA_s, cA_u, cA_v)
	Convert cylindical vector potential to contravariant components. More...
subroutine	get_e_s (rij_h, zij_h, rs, zs, parity)
	Get the e_s basis vector. More...
subroutine	init_a (cA_s, cA_u, cA_v, A_s, A_u, A_v, parity)
	Initialize vector potential. More...
subroutine	init_f (Fsupsmn, Fsupumn, Fsupvmn, jcurrumn, jcurrvmn, p
	Initialize expected currents. More...
subroutine	compare_current (Fsupsmn, Fsupumn, Fsupvmn, jcurrumn, jc
	Compare Curl(Curl(A)) with the expected VMEC and vacuum currents. More...
subroutine	dump_b (js, iunit)
	Write out magnetic field to file. More...
subroutine	getfsq_pchelms
	The the current residual.
subroutine	cleanup
	Deallocate arrays.
subroutine	check_current
	Check that the line integral of Bsubuij equals the integrated toroidal current.
subroutine	compute_forces_lin
	Compute linear forces.
subroutine	backslv
	Update solution.
subroutine	init_pchelms
	Initialize helmholtz solver.
subroutine	compute_forces (lNLinear)
	Compute Fourier components of Curl(Curl(A)) - mu0J operator on full radial grid. More...
subroutine	boundaryconditions (Fsupsmn, Fsupumn, Fsupvmn, iparity)
	Apply boundary conditions. More...
subroutine	gmres_pchelms
	Setup and run GMRES solver for the helmholtz problem. More...
subroutine	matvec_pchelms (p, Ap, ndim)
	Serial callback function for MatVec GMRES routine. More...
subroutine	matvec_par_pchelms (ploc, Ap, nloc)
	Parallel callback function for MatVec GMRES routine. More...
subroutine	getnlforce_pchelms (xcstate, fsq_nl, bnorm)
	Non linear force callback. More...

Detailed Description

This file solves the helmholtz equation to set inital fields that match vmec and vacuum currents from the vector potential. Initial vector potential on the edge is supplied by the BMW code.

Function/Subroutine Documentation

boundaryconditions()

subroutine pchelms::boundaryconditions	(		Fsupsmn,
			Fsupumn,
			Fsupvmn,
			iparity
	)

Apply boundary conditions.

Parameters

[in,out]	Fsupsmn	Contravariant current in the s direction.
[in,out]	Fsupumn	Contravariant current in the u direction.
[in,out]	Fsupvmn	Contravariant current in the v direction.
[in]	iparity	Fourier parity of the residuals.

compare_current()

subroutine pchelms::compare_current	(	real (dp), dimension(:,:,:), intent(in)	Fsupsmn,
		real (dp), dimension(:,:,:), intent(in)	Fsupumn,
		real (dp), dimension(:,:,:), intent(in)	Fsupvmn,
		real (dp), dimension(:,:,:), intent(in)	jcurrumn,
			jc
	)

Compare Curl(Curl(A)) with the expected VMEC and vacuum currents.

Parameters

[in]	Fsupsmn	Contravariant current in the s direction on the full grid.
[in]	Fsupumn	Contravariant current in the u direction on the full grid.
[in]	Fsupvmn	Contravariant current in the v direction on the full grid.
[in]	jcurrumn	Contravariant VMEC current in the u direction on the full grid.
[in]	jcurrvmn	Contravariant VMEC current in the v direction on the full grid.
[in]	iparity	Parity flag to indicate stellaratory symmetry.

compute_forces()

subroutine pchelms::compute_forces

(

logical, intent(in)

lNLinear

)

Compute Fourier components of Curl(Curl(A)) - mu0J operator on full radial grid.

Parameters

[in]

lNLinear

Use Non linear equations.

curla_pchelms()

subroutine pchelms::curla_pchelms	(		Asubsmnf,
			Asubumnf,
			Asubvmnf
	)

Compute real-space components of contravariant jac*B^i on half radial grid from curl(A).

Parameters

[in]	Asubsmnf	Covariant vector potential in the s direction.
[in]	Asubumnf	Covariant vector potential in the u direction.
[in]	Asubvmnf	Covariant vector potential in the v direction.
[in,out]	jbsupsmnh	Contravariant B field and jacobian in the s direction.
[in,out]	jbsupumnh	Contravariant B field and jacobian in the u direction.
[in,out]	jbsupvmnh	Contravariant B field and jacobian in the v direction.
[in]	parity	Parity flag to indicate stellaratory symmetry.

curlb_pchelms()

subroutine pchelms::curlb_pchelms	(	real(dp), dimension(:,:,:), pointer	ksupsmnf,
		real(dp), dimension(:,:,:), pointer	ksupumnf,
		real(dp), dimension(:,:,:), pointer	ksupvmnf,
		real(dp), dimension(:,:,:), pointer	asubsmnf
	)

Compute real-space components of contravariant jac*J^i on full radial grid from curl(B).

Parameters

[in,out]	ksupsmnf	Contravariant current and jacobian in the s direction on the full grid.
[in,out]	ksupumnf	Contravariant current and jacobian in the u direction on the full grid.
[in,out]	ksupvmnf	Contravariant current and jacobian in the v direction on the full grid.
[in,out]	asubsmnf	Covariant vector potential in the s direction on the full grid.
[in]	bsupsmnh	Contravariant current and jacobian in the v direction on the half grid.
[in]	iparity	Parity flag to indicate stellaratory symmetry.
[in,out]	curtor	Current enclosed at the boundary.

cyl2vmec_a()

subroutine pchelms::cyl2vmec_a	(	real (dp), dimension(:,:,:), intent(inout)	A_r,
		real (dp), dimension(:,:,:), intent(inout)	A_p,
		real (dp), dimension(:,:,:), intent(inout)	A_z,
		real (dp), dimension(:,:,:), intent(out)	cA_s,
		real (dp), dimension(:,:,:), intent(out)	cA_u,
		real (dp), dimension(:,:,:), intent(out)	cA_v
	)

Convert cylindical vector potential to contravariant components.

Parameters

[in]	A_r	Cylindical r component of the vector potential at the last surface.
[in]	A_p	Cylindical p component of the vector potential at the last surface.
[in]	A_z	Cylindical z component of the vector potential at the last surface.
[out]	cA_s	Contravariant vector potential in the s direction on the last surface grid.
[out]	cA_u	Contravariant vector potential in the u direction on the last surface grid.
[out]	cA_v	Contravariant vector potential in the v direction on the last surface grid.

dump_b()

subroutine pchelms::dump_b	(	integer, intent(in)	js,
		integer, intent(in)	iunit
	)

Write out magnetic field to file.

Parameters

[in]	js	Radial index.
[in]	iunit	File unit to write to.

get_e_s()

subroutine pchelms::get_e_s	(	real (dp), dimension(:,:,:), intent(in)	rij_h,
		real (dp), dimension(:,:,:), intent(in)	zij_h,
		real (dp), dimension(:,:,:), intent(inout)	rs,
		real (dp), dimension(:,:,:), intent(inout)	zs,
		integer, intent(in)	parity
	)

Get the e_s basis vector.

Parameters

[in]	rij_h	Real space R on the half grid.
[in]	zij_h	Real space Z on the half grid.
[in,out]	rs	R' on the full grid.
[in,out]	zs	Z' on the full grid.
[in]	parity	Fourier parity.

getnlforce_pchelms()

subroutine pchelms::getnlforce_pchelms	(	real (dp), dimension(neqs), intent(in)	xcstate,
		real (dp), intent(out)	fsq_nl,
		real (dp), intent(in)	bnorm
	)

Non linear force callback.

Parameters

[in]	xcstate	Displacement parameters.
[out]	fsq_nl	|F^2| non-linear residual.
[in]	bnorm	Internal GMRES normalization

gmres_pchelms()

subroutine pchelms::gmres_pchelms

Setup and run GMRES solver for the helmholtz problem.

GMRES solves r == b + Ax = 0

init_a()

subroutine pchelms::init_a	(	real (dp), dimension(:,:,:), intent(inout)	cA_s,
		real (dp), dimension(:,:,:), intent(inout)	cA_u,
		real (dp), dimension(:,:,:), intent(inout)	cA_v,
		real (dp), dimension(0:mpol,-ntor:ntor,ns), intent(out)	A_s,
		real (dp), dimension(0:mpol,-ntor:ntor,ns), intent(out)	A_u,
		real (dp), dimension(0:mpol,-ntor:ntor,ns), intent(out)	A_v,
		integer, intent(in)	parity
	)

Initialize vector potential.

This subroutine is only called once so no need to parallelize. Linearly extrapolat to the center or match surface.

Parameters

[in,out]	cA_s	Contravariant vector potential in the s direction on the full grid.
[in,out]	cA_u	Contravariant vector potential in the u direction on the full grid.
[in,out]	cA_v	Contravariant vector potential in the v direction on the full grid.
[out]	A_s	Contravariant fourier vector potential in the s direction on the full grid.
[out]	A_u	Contravariant fourier vector potential in the u direction on the full grid.
[out]	A_v	Contravariant fourier vector potential in the v direction on the full grid.
[in]	parity	Parity flag to indicate stellaratory symmetry.

init_f()

subroutine pchelms::init_f	(	real (dp), dimension(0:mpol,-ntor:ntor,ns), intent(out)	Fsupsmn,
		real (dp), dimension(0:mpol,-ntor:ntor,ns), intent(out)	Fsupumn,
		real (dp), dimension(0:mpol,-ntor:ntor,ns), intent(out)	Fsupvmn,
			jcurrumn,
			jcurrvmn,
			p
	)

Initialize expected currents.

Up to the vmec last closed flux surface, initialize with the VMEC currents. outside, initalize to zero.

Parameters

[out]	Fsupsmn	Contravariant current in the s direction on the full grid.
[out]	Fsupumn	Contravariant current in the u direction on the full grid.
[out]	Fsupvmn	Contravariant current in the v direction on the full grid.
[in]	jcurrumn	Contravariant VMEC current in the u direction on the full grid.
[in]	jcurrvmn	Contravariant VMEC current in the v direction on the full grid.
[in]	parity	Fourier parity of the residuals.

matvec_par_pchelms()

subroutine pchelms::matvec_par_pchelms	(	real(dp), dimension(nloc), intent(in)	ploc,
		real(dp), dimension(nloc), intent(out)	Ap,
		integer, intent(in)	nloc
	)

Parallel callback function for MatVec GMRES routine.

Parameters

[in]	ploc	Local displacement parameters.
[out]	Ap	Local Matrix element.
[in]	nloc	Local number of dimensiona.

matvec_pchelms()

subroutine pchelms::matvec_pchelms	(	real(dp), dimension(ndim), intent(in)	p,
		real(dp), dimension(ndim), intent(out)	Ap,
		integer, intent(in)	ndim
	)

Serial callback function for MatVec GMRES routine.

Parameters

[in]	p	Displacement parameters.
[out]	Ap	Matrix element.
[in]	ndim	Number of dimensiona.