poisson.F90 File Reference

#include "petsc_version_defs.h"
#include <petsc/finclude/petsc.h>

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Data Types
module	f90moduleinterfaces
	Explicit interfaces to somve PETSc function used by the FSA solver. More...
interface	f90moduleinterfaces::pcsetapplicationcontext
interface	f90moduleinterfaces::pcgetapplicationcontext

Macros
#define	DPOT(inode, iphi)   psn%dpot(inode,1)
#define	IDEN(inode, iphi)   psn%idensity0(inode)
#define	EDEN(inode, iphi)   psn%edensity0(inode)

Functions/Subroutines
subroutine	init_poisson (grid, psn, iflag_dummy)
subroutine	psn_init_poisson_private (psn, grid, solver_data, nrhs)
subroutine	pcshermanmorrisonapply (pc, xin, yout, ierr)
	Applies a Sherman-Morrison preconditioner. More...
subroutine	create_2field_solver (grid, bd, solver, solver_data)
	Sets up a 2x2 block solver for the Poisson equation. The first row is the Poisson equation, the second row is a constraint equation for the flux-surface averaged potential. More...
subroutine	make_12mat (grid, Bmat, BIdentMat, FSAMass_Te, solver, bd, scale, xgc_petsc)
subroutine	make_21mat (grid, Cmat, Cio, Bmat, CConstBCVec, bd, xgc_petsc, petsc_xgc_bd)
subroutine	solve_poisson (grid, psn, n0_only, iflag)
	High level Poisson solver routine, offers choice of outer iterative solver, two-step solver, and FSA solver. More...
subroutine	set_rhs_poisson (grid, psn, iflag)
	Routine to set and process the rhs arrays for both axisymmetric and turbulent poisson solvers. Also sets boundary data for XGCA. More...
subroutine	zero_out_wall (var)
subroutine	solve_axisymmetric_poisson_iter (grid, psn, iflag)
	Poisson solver that uses an iterative method to solve for the axisymmetric electrostatic potential: The Poisson equation for the axisymmetric mode is \[ -\nabla_\perp \cdot \xi \nabla_\perp \overline{\phi}_{k+1} + \frac{e n_0/T_{e,0}} \overline{\phi}_{k+1} = e \left( \langle \overline{\delta n_i} \rangle_g - \overline{\delta n_{e,NA}} \right) + \frac{e n_0/T_{e,0}} \langle \phi_{k} \rangle_{fs} \] where \(k\) is the iteration index, \(xi\) is the electric susceptibility, \(e\) is the elementary charge, \(n_0\) and \(T_0\) are the background density and temperature, \(\langle \overline{\delta n_i} \rangle_g\) is the gyroaveraged ion (gyrocenter) charge density, \(\overline{\delta n_{e,NA}}\) is the non-adiabatic electron charge density, and \(\langle\dots\rangle\) is the the flux-surface average. \(\overline{\dots}\) is the toroidal average. More...
subroutine	post_process_axisymmetric_poisson (grid, psn, n0_only)
	Routine to post process the solution from the axisymmetric poisson solver. More...
subroutine	solve_turb_poisson (grid, psn)
	Routine to solve the non-axisymmetric Poisson equation: \[ -\nabla_\perp \cdot \xi \nabla_\perp \delta\phi + \frac{e n_0/T_{e,0}} \delta\phi = e \left( \langle \delta n_i \rangle_g - \overline{\delta n_{e,NA}} \right) \] . More...
subroutine	post_process_turb_poisson (grid, psn)
	Routine to post process the solution from the non-axisymmetric Poisson equation. More...
subroutine	solve_poisson_private (grid, psn, iflag)
subroutine	update_poisson_solver (grid, psn, solver_data)
	Updates the LHS matrix of the Poisson equation (density and electron temperature) More...
subroutine	ptb_3db_da_solver_init (grid)
	We solve perturbed Ampere's law in the following form: dB = - grad(phi).grad(dA_phi) = grad(phi).grad(dpsi) –> grad(phi).curl(dB) = - grad(phi).curl(grad(phi).grad(dA_phi)) = div.(grad(phi) x (grad(phi) x grad(dA_phi)) = -div.[g^{phi,phi} * (grad(dA_phi) - d(dA_phi)/dphi grad(phi))] = -(1/R) * [d_R((1/R)*d_R(dA_phi)) + d_Z((1/R)*d_Z(dA_phi))] = mu_0 j.grad(phi) –> [d_R((1/R)*d_R(dA_phi)) + d_Z((1/R)*d_Z(dA_phi))] = -mu_0 R j^phi = -mu_0 (B_phi/B) j_parallel –> We need to set up one Helmholtz solver with alpha=1/R and beta=0 –> The RHS is -mu_0*(B_phi/B)*j_parallel –> j_parallel = psnijpar + psnejpar. More...
subroutine	ptb_3db_div_clean_init (grid)
	Initializes a solver for divergence cleaning of the perturbed magnetic field This equation is being solved: div.(R*phi_b) - (ntor^2/R)*phi_b = R*div.delta_B. More...
subroutine	ptb_3db_create_1field_solver (grid, solver, prefix)
	create 1 field solver with A00 built (Amat), just setoperator & setup like 2 field More...

Macro Definition Documentation

#define DPOT	(		inode,
			iphi
	)		psn%dpot(inode,1)

#define EDEN	(		inode,
			iphi
	)		psn%edensity0(inode)

#define IDEN	(		inode,
			iphi
	)		psn%idensity0(inode)

Function/Subroutine Documentation

subroutine create_2field_solver	(	type(grid_type)	grid,
		type(boundary2_type)	bd,
		type(xgc_solver)	solver,
		type(solver_init_data), intent(in)	solver_data
	)

Sets up a 2x2 block solver for the Poisson equation. The first row is the Poisson equation, the second row is a constraint equation for the flux-surface averaged potential.

Parameters

[in]	grid	XGC grid object, type(grid_type)
[in]	bd	Object containing the indices of the solver boundary vertices in the XGC mesh.
[in,out]	solver	XGC solver object into which to put the new solver, type(xgc_solver)
[in]	solver_data	Data needed for settug up the ssolver, type(solver_init_data)

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subroutine init_poisson	(	type(grid_type)	grid,
		type(psn_type)	psn,
		integer	iflag_dummy
	)

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subroutine make_12mat	(	type(grid_type)	grid,
		intent(inout)	Bmat,
			BIdentMat,
		intent(in)	FSAMass_Te,
		type(xgc_solver)	solver,
		type(boundary2_type), intent(in)	bd,
		real (8), intent(in)	scale,
		dimension(grid%nnode), intent(in)	xgc_petsc
	)

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subroutine make_21mat	(	type(grid_type)	grid,
			Cmat,
			Cio,
		intent(in)	Bmat,
			CConstBCVec,
		type(boundary2_type), intent(in)	bd,
		dimension(grid%nnode), intent(in)	xgc_petsc,
		dimension(grid%nnode), intent(in)	petsc_xgc_bd
	)

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subroutine pcshermanmorrisonapply	(		pc,
			xin,
			yout,
			ierr
	)

Applies a Sherman-Morrison preconditioner.

Parameters

[in,out]	pc	PETCs PC object (manages preconditioners)
	xin	???, Vec
	yout	???, Vec
[out]	ierr	PETc error code

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subroutine post_process_axisymmetric_poisson	(	type(grid_type)	grid,
		type(psn_type)	psn,
		logical, intent(in)	n0_only
	)

Routine to post process the solution from the axisymmetric poisson solver.

Parameters

[in]	grid	XGC grid data object
[in,out]	psn	XGC field data object
[in]	n0_only	Flag for solving only n=0 mode and then exit (no function in XGCa), logical

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subroutine post_process_turb_poisson	(	type(grid_type), intent(in)	grid,
		type(psn_type), intent(inout)	psn
	)

Routine to post process the solution from the non-axisymmetric Poisson equation.

Parameters

[in]	grid	XGC grid data object
[in,out]	psn	XGC field data object

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subroutine psn_init_poisson_private	(	type(psn_type)	psn,
		type(grid_type)	grid,
		type(solver_init_data), intent(in)	solver_data,
		integer	nrhs
	)

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subroutine ptb_3db_create_1field_solver	(	type(grid_type), intent(in)	grid,
		type(xgc_solver), intent(inout)	solver,
		character(*), intent(in)	prefix
	)

create 1 field solver with A00 built (Amat), just setoperator & setup like 2 field

Parameters

grid	(in) type(grid_type), grid info
solver	(inout) type(xgc_solver_type), XGC data structure for the solver
prefix	(in) char(*), prefix for the solver

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subroutine ptb_3db_da_solver_init

(

type(grid_type), intent(in)

grid

)

We solve perturbed Ampere's law in the following form: dB = - grad(phi).grad(dA_phi) = grad(phi).grad(dpsi) –> grad(phi).curl(dB) = - grad(phi).curl(grad(phi).grad(dA_phi)) = div.(grad(phi) x (grad(phi) x grad(dA_phi)) = -div.[g^{phi,phi} * (grad(dA_phi) - d(dA_phi)/dphi grad(phi))] = -(1/R) * [d_R((1/R)*d_R(dA_phi)) + d_Z((1/R)*d_Z(dA_phi))] = mu_0 j.grad(phi) –> [d_R((1/R)*d_R(dA_phi)) + d_Z((1/R)*d_Z(dA_phi))] = -mu_0 R j^phi = -mu_0 (B_phi/B) j_parallel –> We need to set up one Helmholtz solver with alpha=1/R and beta=0 –> The RHS is -mu_0*(B_phi/B)*j_parallel –> j_parallel = psnijpar + psnejpar.

Parameters

grid	(in) type(grid_type), grid information

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subroutine ptb_3db_div_clean_init

(

type(grid_type), intent(in)

grid

)

Initializes a solver for divergence cleaning of the perturbed magnetic field This equation is being solved: div.(R*phi_b) - (ntor^2/R)*phi_b = R*div.delta_B.

Parameters

grid	(in) type(grid_type), grid information
ntor	(in) integer, toroidal mode number

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subroutine set_rhs_poisson	(	type(grid_type)	grid,
		type(psn_type)	psn,
		integer, intent(in)	iflag
	)

Routine to set and process the rhs arrays for both axisymmetric and turbulent poisson solvers. Also sets boundary data for XGCA.

Parameters

[in]	grid	XGC grid data object
[in,out]	psn	XGC field data object
[in]	iflag	Flag to indicate whether adiabatic elec or full eq. is solved, integer

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subroutine solve_axisymmetric_poisson_iter	(	type(grid_type), intent(in)	grid,
		type(psn_type), intent(inout)	psn,
		integer, intent(in)	iflag
	)

Poisson solver that uses an iterative method to solve for the axisymmetric electrostatic potential: The Poisson equation for the axisymmetric mode is

\[ -\nabla_\perp \cdot \xi \nabla_\perp \overline{\phi}_{k+1} + \frac{e n_0/T_{e,0}} \overline{\phi}_{k+1} = e \left( \langle \overline{\delta n_i} \rangle_g - \overline{\delta n_{e,NA}} \right) + \frac{e n_0/T_{e,0}} \langle \phi_{k} \rangle_{fs} \]

where \(k\) is the iteration index, \(xi\) is the electric susceptibility, \(e\) is the elementary charge, \(n_0\) and \(T_0\) are the background density and temperature, \(\langle \overline{\delta n_i} \rangle_g\) is the gyroaveraged ion (gyrocenter) charge density, \(\overline{\delta n_{e,NA}}\) is the non-adiabatic electron charge density, and \(\langle\dots\rangle\) is the the flux-surface average. \(\overline{\dots}\) is the toroidal average.

The RHS and LHS of the axisymmetric equation can be Fourier-filtered (poloidal modes). The LHS of the non-axisymmetric equation can be Fourier-filtered in the toroidal and poloidal direction. The solver in both cases is a linear finite-element solver on an unstructured triangular grid.

Parameters

[in]	grid	Solver grid data, type(grid_type)
[in,out]	psn	Field data; the potential is stored there, type(psn_type)
[in]	iflag	Flag to indicate whether adiabatic elec or full eq. is solved, integer

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subroutine solve_poisson	(	type(grid_type), intent(in)	grid,
		type(psn_type), intent(inout)	psn,
		logical, intent(in)	n0_only,
		integer, intent(in)	iflag
	)

High level Poisson solver routine, offers choice of outer iterative solver, two-step solver, and FSA solver.

Parameters

[in]	grid	XGC grid data object
[in,out]	psn	XGC field data object
[in]	n0_only	Flag for solving only n=0 mode and then exit (no function in XGCa), logical
[in]	iflag	Flag to indicate whether adiabatic elec or full eq. is solved, integer

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subroutine solve_poisson_private	(	type(grid_type)	grid,
		type(psn_type)	psn,
		integer, intent(in)	iflag
	)

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subroutine solve_turb_poisson	(	type(grid_type), intent(in)	grid,
		type(psn_type), intent(inout)	psn
	)

Routine to solve the non-axisymmetric Poisson equation:

\[ -\nabla_\perp \cdot \xi \nabla_\perp \delta\phi + \frac{e n_0/T_{e,0}} \delta\phi = e \left( \langle \delta n_i \rangle_g - \overline{\delta n_{e,NA}} \right) \]

.

Parameters

[in]	grid	XGC grid data object
[in,out]	psn	XGC field data object

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subroutine update_poisson_solver	(	type(grid_type), intent(in)	grid,
		type(psn_type), intent(inout)	psn,
		type(solver_init_data), intent(in)	solver_data
	)

Updates the LHS matrix of the Poisson equation (density and electron temperature)

Parameters

[in]	grid	XGC grid data object, type(grid_type)
[in,out]	psn	XGC field data object, type(psn_type)
[in]	solver_data	Object with profile and magnetic data for solvers

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subroutine zero_out_wall

(

real (8), dimension(grid%nnode), intent(inout)

var

)

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