adam_prism_pic_object

ADAM, PRISM Particle-in-Cell class definition, CPU backend.

Source: src/app/prism/common/adam_prism_pic_object.F90

Dependencies

Contents

• prism_pic_object
• particle_weighting_interface
• current_weighting_interface
• field_weighting_interface
• totorica_kernels
• check_esirkepov_q_order
• matched_kernels
• set_coherent_gather
• initialize
• set_particle_number
• resize_neighbour_list
• set_plasma_region
• load_from_file
• particle_cartesian_grid_index
• distribute_particles
• exchange_particles
• migrate_particles
• set_gaussian_support_cells
• NGP_charge_weighting
• CIC_charge_weighting
• TSC_charge_weighting
• cubic_charge_weighting
• quartic_charge_weighting
• quintic_charge_weighting
• sextic_charge_weighting
• bspline_charge_weighting
• bspline_closed_weights
• Gaussian_charge_weighting
• NGP_current_weighting
• CIC_current_weighting
• TSC_current_weighting
• cubic_current_weighting
• quartic_current_weighting
• quintic_current_weighting
• sextic_current_weighting
• bspline_current_weighting
• Gaussian_current_weighting
• zeroD_field_weighting
• oneD_field_weighting
• twoD_field_weighting
• threeD_field_weighting
• fourD_field_weighting
• fiveD_field_weighting
• sixD_field_weighting
• Gaussian_field_weighting
• bspline_field_weighting
• shape_field_weighting
• coherent_field_weighting
• transposed_filter_axis
• set_bspline_stencil
• compaction_moves
• conserving_solver_name
• matched_current
• coherent_gather
• matched_gather
• description
• halo_margin_cells
• stencil_radius_cells
• effective_bspline_weight
• gaussian_weight
• effective_gaussian_weight
• bspline_weight

Variables

Name	Type	Attributes	Description
INI_SECTION_NAME	character(len=3)	parameter	INI file section name for PIC configuration.
PLASMA_TYPE_PROBLEM	character(len=6)	parameter	Analyzing physical problem involving the presence of
COHERENT_INITIALIZATION	character(len=8)	parameter	Field initialization through elliptic solver with
ELLIPTIC_CLOSURE_GROUNDED	character(len=8)	parameter	t0 solves: the mean fields of the PEC
ELLIPTIC_CLOSURE_ISOLATED	character(len=8)	parameter	t0 solves: the mean fields of the PEC
SINGLE_PARTICLE_TYPE_PROBLEM	character(len=15)	parameter	Analyzing physical problem involving the
NGP_WEIGHTING_MODEL	character(len=3)	parameter	NGP weighting model.
CIC_WEIGHTING_MODEL	character(len=3)	parameter	CIC weighting model.
TSC_WEIGHTING_MODEL	character(len=3)	parameter	TSC weighting model.
CUBIC_WEIGHTING_MODEL	character(len=5)	parameter	cubic order weighting model.
QUARTIC_WEIGHTING_MODEL	character(len=7)	parameter	quartic order weighting model.
QUINTIC_WEIGHTING_MODEL	character(len=7)	parameter	quintic order weighting model.
SEXTIC_WEIGHTING_MODEL	character(len=6)	parameter	Sextic B-spline weighting.
GAUSSIAN_WEIGHTING_MODEL	character(len=8)	parameter	Gaussian weighting model.
ZEROD_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	0D field weighting.
ONED_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	1D field weighting.
TWOD_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	2D field weighting.
THREED_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	3D field weighting.
FOURD_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	4D field weighting.
FIVED_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	5D field weighting.
SIXD_FIELDS_WEIGHTING_MODEL	character(len=2)	parameter	Sextic field weighting.
NUM_SCHEME_TIME_PIC_LEAPFROG	character(len=8)	parameter	Leapfrog numerical scheme for time operator.
NUM_SCHEME_TIME_PIC_RUNGE_KUTTA	character(len=11)	parameter	Runge-Kutta numerical scheme for time operator.
UNIFORM_DOMAIN	character(len=14)	parameter
UNIFORM_CILINDER	character(len=16)	parameter
UNIFORM_CELL	character(len=12)	parameter
UNIFORM_SLAB	character(len=12)	parameter	Slab spanning the transverse domain.
UNIFORM_BOX	character(len=11)	parameter	Box inside the domain.
CONSERVING_CURRENT_WEIGHTING_MODEL	character(len=10)	parameter	Charge-conserving current model.
LONDRILLO_CURRENT_CONSERVING_SOLVER	character(len=9)	parameter	Esirkepov face flux + inverse
TOTORICA_CURRENT_CONSERVING_SOLVER	character(len=8)	parameter	Matched local current with L = m,
ESIRKEPOV_MODIFIED_CURRENT_CONSERVING_SOLVER	character(len=11)	parameter	Matched local current family

Derived Types

prism_pic_object

Components

Name	Type	Attributes	Description
plasma_density	real(kind=R8P)		Plasma density
neutral_fraction	real(kind=R8P)		Neutral fraction
particle_weight	real(kind=R8P)		Real particles per macroparticle.
cilinder_length	real(kind=R8P)
cilinder_radius	real(kind=R8P)
cilinder_center	real(kind=R8P)
cilinder_axis	character(len=1)
slab_normal	character(len=1)		Slab normal direction (x, y, z).
slab_thickness	real(kind=R8P)		Slab thickness along the normal.
slab_center	real(kind=R8P)		Slab centre coordinate along the normal.
box_length	real(kind=R8P)		Box side lengths along x, y, z.
box_center	real(kind=R8P)		Box centre.
plasma_region_min	real(kind=R8P)		Slab/box region at t0, minimum corner.
plasma_region_max	real(kind=R8P)		Slab/box region at t0, maximum corner.
sigma	real(kind=R8P)		Standard deviation for a gaussian weighting
cutoff_sigma	real(kind=R8P)		Gaussian cutoff.
gaussian_support_cells	integer(kind=I4P)		Gaussian support radius; negative selects automatic.
particle_number	integer(kind=I4P)		Number of particles owned by this rank.
particle_number_global	integer(kind=I4P)		Total number of particles (all ranks).
particle_capacity	integer(kind=I4P)		Particle arrays capacity of every rank (issue #112).
particle_capacity_factor	real(kind=R8P)		Capacity in units of global/ranks; 0: global.
omega_dt_max	real(kind=R8P)		Accuracy threshold on omega_max dt (plasma frequencies).
charge_conservation_save	integer(kind=I4P)		Charge-conservation history every N steps; 0: none.
n_ions	integer(kind=I4P)		Total ions number
n_electrons	integer(kind=I4P)		Total electrons number
n_neutrals	integer(kind=I4P)		Total neutrals number
neighbour_list	integer(kind=I4P)	allocatable	Particle grid positions array.
bc	type(prism_pic_bc_object)		Particle closures at the domain faces.
problem_type	character(len=99)		Type of problem analyzed
plasma_domain	character(len=99)		Domain of plasma at t0
initialization	character(len=99)		Field initialization solver.
electric_field_elliptic_initialization	logical		Solve for phi (div D = rho) at t0.
magnetic_field_elliptic_initialization	logical		Solve for A (curl B = mu J) at t0.
elliptic_initialization_closure	character(len=99)		Mean fields of the t0 solves.
filter_deposition	logical		Binomial filter for deposition and gather weights.
particle_weighting_model	character(len=99)		Particle weighting model.
current_weighting_model	character(len=99)		Current weighting model.
field_weighting_model	character(len=99)		Field weighting model.
esirkepov_tail_cleanup	logical		Remove small current leakage outside each particle's support.
current_conserving_solver	character(len=99)		Conserving current solver.
esirkepov_q	integer(kind=I4P)		Q filter coefficients of esirkepov_Q (5,6,8,10), 0 otherwise.
gather_q	integer(kind=I4P)		Coherent gather esirkepov_Q: N (5,6,8,10), 0 otherwise.
gather_p	real(kind=R8P)		Coherent matched gather: P kernel of the charge deposit.
gather_radius	integer(kind=I4P)		Coherent matched gather: taps of P.
gather_dual	logical		Coherent gather of an odd esirkepov_Q: base shape on the
scheme_time	character(len=99)		Numerical scheme for time operator [runge_kutta, leapfrog,...].
particle_weighting	procedure(particle_weighting_interface)	pass(self), pointer	Particle weighting.
current_weighting	procedure(current_weighting_interface)	pass(self), pointer	Current weighting.
field_weighting	procedure(field_weighting_interface)	pass(self), pointer	field weighting.

Type-Bound Procedures

Name	Attributes	Description
description	pass(self)	Return pretty-printed object description.
conserving_solver_name	pass(self)	Input name of the conserving current solver.
matched_current	pass(self)	True for the local matched currents (totorica, esirkepov_Q).
check_esirkepov_q_order	pass(self)	Check the esirkepov_Q filter against the FD order.
coherent_gather	pass(self)	True for the gathers named after a conserving solver.
matched_gather	pass(self)	True for the coherent gathers of totorica and esirkepov_Q.
set_coherent_gather	pass(self)	Set the coherent gather kernels, warn on a deposit mismatch.
initialize	pass(self)	Initialize IC.
load_from_file	pass(self)	Load config from file.
set_particle_number	pass(self)	Scale the plasma inputs, set the particle number at t0.
resize_neighbour_list	pass(self)	Reallocate the neighbour list, keeping its first columns.
set_plasma_region	pass(self)	Set and check the slab/box region of the plasma at t0.
particle_cartesian_grid_index	pass(self)	Compute the grid index corresponding to a particle position.
halo_margin_cells	pass(self)	Cells a particle may lie outside its block interior.
distribute_particles	pass(self)	Keep the injected particles owned by this rank.
exchange_particles	pass(self)	Hand departing particles to their owner ranks.
migrate_particles	pass(self)	Migrate particles between ranks (host arrays).
set_gaussian_support_cells	pass(self)	Automatic Gaussian support radius on the final grid.
stencil_radius_cells	pass(self)	Max cells reached by deposit/gather stencils beyond the particle cell.
CIC_charge_weighting	pass(self)	Cloud-in-Cell weighting of particle quantities to the grid.
NGP_charge_weighting	pass(self)	Nearest Grid Point weighting of particle quantities to the grid.
TSC_charge_weighting	pass(self)	Triangular Shaped Cloud weighting of particle quantities to the grid.
cubic_charge_weighting	pass(self)	3rd order weighting of particle quantities to the grid.
quartic_charge_weighting	pass(self)	4th order weighting of particle quantities to the grid.
sextic_charge_weighting	pass(self)
sextic_current_weighting	pass(self)
quintic_charge_weighting	pass(self)	5th order weighting of particle quantities to the grid.
Gaussian_charge_weighting	pass(self)	Gaussian Shaped Cloud weighting of particle quantities to the grid.
CIC_current_weighting	pass(self)	Cloud-in-Cell weighting of particle quantities to the grid.
NGP_current_weighting	pass(self)	Nearest Grid Point weighting of particle quantities to the grid.
TSC_current_weighting	pass(self)	Triangular Shaped Cloud weighting of particle quantities to the grid.
Gaussian_current_weighting	pass(self)	Gaussian Shaped Cloud weighting of particle quantities to the grid.
zeroD_field_weighting	pass(self)
oneD_field_weighting	pass(self)
twoD_field_weighting	pass(self)
threeD_field_weighting	pass(self)
fourD_field_weighting	pass(self)
sixD_field_weighting	pass(self)
fiveD_field_weighting	pass(self)
Gaussian_field_weighting	pass(self)
bspline_field_weighting	pass(self)
shape_field_weighting	pass(self)	Gather with the particle shape (charge deposit of the model).
coherent_field_weighting	pass(self)	Gather with the transpose of the conserving charge operator.

Interfaces

particle_weighting_interface

current_weighting_interface

field_weighting_interface

Subroutines

totorica_kernels

Totorica's matched current (Totorica 2025, eq. 53-54, S^JO = I) for the centered FD of half stencil hs. The derivative factors as D = delta A, A the face reconstruction FV1_CC(:,hs) (A = m C, m = [1,1]/2); then L = Q = m and P = A m: center i <- faces i-1/2, i+1/2 (weight 1/2 each) <- centers i+1-m, i+m and i-m, i-1+m (weight a_m). FD2 gives P = [1,2,1]/4, the former esirkepov_Q2; from FD4 on P has negative lobes (those of C).

Attributes: pure

subroutine totorica_kernels(hs, p, qw, radius, qfirst, nq)

Arguments

Name	Type	Intent	Attributes	Description
hs	integer(kind=I4P)	in		FD half stencil.
p	real(kind=R8P)	out		P kernel on cell centers.
qw	real(kind=R8P)	out		Q kernel from the faces to the centers.
radius	integer(kind=I4P)	out		Taps of P.
qfirst	integer(kind=I4P)	out		Offset of the first Q face (flux index = center + qfirst).
nq	integer(kind=I4P)	out		Taps of Q.

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check_esirkepov_q_order

The esirkepov_Q<N> filters are built on D = delta A with P = A Q for FD6 (A6 = [1,-8,37,37,-8,1]/60): Q5, Q6, Q8 and Q10 require fdv_order = 6. No-op for the other solvers (totorica adapts to any centered FD order).

subroutine check_esirkepov_q_order(self, fdv_order)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.
fdv_order	integer(kind=I4P)	in		FD order.

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matched_kernels

P = A Q maps the base-shape nodes to centers, Q maps the face prefix sums to centers (A2 = [1,1]/2 for FD2, A6 = [1,-8,37,37,-8,1]/60 for FD6, so that D J = P H). Even Q: base on centers, P odd and centered, Q from faces. Odd Q: base on the dual nodes (node m at x_m+dx/2), P even with taps m=i-N/2-2..i+N/2+2, Q centered on the prefix sums at centers (flux index f = center-1). radius bounds the taps of P (plus one if odd). totorica: totorica_kernels.

subroutine matched_kernels(solver, q, hs, p, qw, radius, qfirst, nq)

Arguments

Name	Type	Intent	Attributes	Description
solver	character(len=*)	in		Matched solver (totorica or esirkepov_Q).
q	integer(kind=I4P)	in		esirkepov_Q filter N.
hs	integer(kind=I4P)	in		FD half stencil (totorica).
p	real(kind=R8P)	out		P kernel on cell centers.
qw	real(kind=R8P)	out		Q kernel from the faces to the centers.
radius	integer(kind=I4P)	out		Taps of P.
qfirst	integer(kind=I4P)	out		Offset of the first Q face (flux index = center + qfirst).
nq	integer(kind=I4P)	out		Taps of Q.

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set_coherent_gather

Set the P kernel of the coherent matched gathers (totorica needs the FD half stencil) and warn when the gather is not the coherent one of the deposit in use: it is then not the adjoint of the charge deposit and self-forces are not cancelled. A conserving solver is coherent with the gather of its name (londrillo also with the gather of the particle shape, S^rho = S); a non-conserving deposit with the gather of its particle shape.

subroutine set_coherent_gather(self, hs)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
hs	integer(kind=I4P)	in		FD half stencil.

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initialize

Initialize PIC.

subroutine initialize(self, field, grid, file_parameters, physics)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		Pic object.
field	type(field_object)	in		Field (sibling realm component, threaded in).
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
file_parameters	type(file_ini)	in		Simulation parameters ini file handler.
physics	type(prism_physics_object)	in

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set_particle_number

Scale the plasma inputs of a non-dimensional model and set the particle number from the plasma volume at t0.

Needs only the input (load_from_file) and the domain corners, so it also serves the memory estimate made before the grid exists (issue #112). Every rank holds the whole set until distribute_particles keeps its own ones.

subroutine set_particle_number(self, emin, emax, physics)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
emin	real(kind=R8P)	in		Domain minimum corner.
emax	real(kind=R8P)	in		Domain maximum corner.
physics	type(prism_physics_object)	in		Physics.

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resize_neighbour_list

Reallocate the neighbour list to n particles, keeping its first min(n, old) columns (issue #112): the injection and the distribution index the whole injected set, the run the capacity of the rank.

subroutine resize_neighbour_list(self, n)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
n	integer(kind=I4P)	in		New number of particles.

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set_plasma_region

Set the slab/box region of the plasma at t0, stop if it leaves the domain.

The slab spans the whole domain across its normal; a face of the region may touch a domain face.

subroutine set_plasma_region(self, emin, emax)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
emin	real(kind=R8P)	in		Domain minimum corner.
emax	real(kind=R8P)	in		Domain maximum corner.

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load_from_file

Load PIC configuration from file. The removed key, if present.

subroutine load_from_file(self, file_parameters, go_on_fail)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
file_parameters	type(file_ini)	in		File handler.
go_on_fail	logical	in	optional	Go on if load fails.

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particle_cartesian_grid_index

Compute the grid index corresponding to a particle position. Good for cartesian grids only.

A particle is first searched in the interior cells of the local blocks (ownership). With several ranks a particle may leave the blocks of its rank within a time step (RK stages, end-of-step deposit before the migration): it is then located in the ghost cells of a local block, at most halo_margin_cells() cells outside the interior, so that its stencil stays within the ghosts (deposits are folded back by reduce_ghost_local/mpi, gathers read exchanged ghosts). With owned_only the halo search is skipped and a non-owned particle gets a zero row, without errors (injection, migration). A particle beyond a periodic face is located the same way, in the ghost halo of the block on that face (the periodic ghosts are images of the opposite interior), until its position is wrapped at the end of the step. A particle outside the domain across a face without particle closure, or beyond the halo of every local block, stops the run.

subroutine particle_cartesian_grid_index(self, field, grid, q_pic, owned_only)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	in		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in)
q_pic	real(kind=R8P)	in		PIC variables.
owned_only	logical	in	optional	Locate owned particles only, no halo search.

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distribute_particles

Keep only the particles owned by the local blocks: the injection fills the whole set on every rank (same sequence), each rank keeps its own ones, in injection order, and the local count becomes particle_number. Every particle must be owned by exactly one rank (checked globally). With one rank nothing moves.

subroutine distribute_particles(self, field, grid, q_pic)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	in		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in)
q_pic	real(kind=R8P)	inout		PIC variables.

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exchange_particles

Hand the departing particles (no longer owned by this rank) to the ranks that own them: every rank receives all the departing particles (MPI_Allgatherv) and keeps the ones owned by its local blocks, in rank order. Every departing particle must be claimed by exactly one rank (checked globally; particles do not leave the domain yet).

subroutine exchange_particles(self, field, grid, departing, arrived, n_arrived)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	in		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in)
departing	real(kind=R8P)	in		Departing particles [variable, particle].
arrived	real(kind=R8P)	inout	allocatable	Arrived particles owned by this rank [variable, particle].
n_arrived	integer(kind=I4P)	out		Number of arrived particles.

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migrate_particles

Hand the particles that left the local blocks to the owner ranks (end of a time step, host arrays). The departed slots are filled by the last particles (stable for the particles that stay before the first hole), the arrived ones are appended, then the particles are located again. Collective; with one rank it is a no-op.

subroutine migrate_particles(self, field, grid, q_pic)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	in		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in)
q_pic	real(kind=R8P)	inout		PIC variables.

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set_gaussian_support_cells

Automatic Gaussian support radius (gaussian_support_cells < 0 in input): ceiling(cutoff_sigma*sigma/dx_min) + 1 over all blocks of all ranks. To be called once the grid is final (after the uniform refinement): on the root blocks the support would be underestimated by 2**iu_ref_levels.

subroutine set_gaussian_support_cells(self, field)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	in		Field (sibling realm component, threaded in).

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NGP_charge_weighting

subroutine NGP_charge_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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CIC_charge_weighting

Cloud-in-Cell weighting of particle quantities to the grid.

subroutine CIC_charge_weighting(self, field, grid, q, q_PIC, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_PIC	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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TSC_charge_weighting

subroutine TSC_charge_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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cubic_charge_weighting

subroutine cubic_charge_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Charge variable index.

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quartic_charge_weighting

subroutine quartic_charge_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Charge variable index.

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quintic_charge_weighting

subroutine quintic_charge_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Charge variable index.

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sextic_charge_weighting

subroutine sextic_charge_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Charge variable index.

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bspline_charge_weighting

Deposit particle charge density with the fixed (order+1)^3 B-spline support.

subroutine bspline_charge_weighting(self, field, grid, q, q_pic, nv, order)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
q	real(kind=R8P)	inout
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in
order	integer(kind=I4P)	in

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bspline_closed_weights

Close the unfiltered B-spline weights of one stencil to sum to 1 by changing only the largest one. The raw sum misses 1 by the roundoff of the cell-center spacing (x_cell is not exactly equispaced in floating point). That residual depends on the stencil: for a C0 shape (CIC) it jumps when the stencil changes, so the Esirkepov line sums no longer vanish and a spurious current runs to the domain boundary. Closing every stencil removes it.

Attributes: pure

subroutine bspline_closed_weights(order, x_p, x_cell, dx, w, pu_error)

Arguments

Name	Type	Intent	Attributes	Description
order	integer(kind=I4P)	in		B-spline order (0=NGP ... 6=sextic).
x_p	real(kind=R8P)	in		Particle coordinate.
x_cell	real(kind=R8P)	in		Cell centers of the stencil.
dx	real(kind=R8P)	in		Cell size.
w	real(kind=R8P)	out		Closed weights of the stencil.
pu_error	real(kind=R8P)	out	optional	|raw sum - 1| before the closure.

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Gaussian_charge_weighting

Gaussian weighting of particle charge density to the grid.

subroutine Gaussian_charge_weighting(self, field, grid, q, q_PIC, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid object.
q	real(kind=R8P)	inout		Field variables.
q_PIC	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Charge-density variable index.

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NGP_current_weighting

subroutine NGP_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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CIC_current_weighting

Cloud-in-Cell weighting of particle quantities to the grid.

subroutine CIC_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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TSC_current_weighting

Triangular-Shaped-Cloud weighting of particle current density to the grid.

subroutine TSC_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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cubic_current_weighting

Cubic B-spline weighting of particle current density to the grid.

subroutine cubic_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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quartic_current_weighting

Quartic B-spline weighting of particle current density to the grid.

subroutine quartic_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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quintic_current_weighting

Quintic B-spline weighting of particle current density to the grid.

subroutine quintic_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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sextic_current_weighting

Sextic B-spline weighting of particle current density to the grid.

subroutine sextic_current_weighting(self, field, grid, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		External fields.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid (sibling realm component, threaded in).
q	real(kind=R8P)	inout		Field variables.
q_pic	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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bspline_current_weighting

Deposit particle current density with B-spline support and optional binomial filtering.

subroutine bspline_current_weighting(self, field, grid, q, q_pic, nv, order)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
q	real(kind=R8P)	inout
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in
order	integer(kind=I4P)	in

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Gaussian_current_weighting

Gaussian weighting of particle current density to the grid.

subroutine Gaussian_current_weighting(self, field, grid, q, q_PIC, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid object.
q	real(kind=R8P)	inout		Field variables.
q_PIC	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Index following Jx, Jy, Jz.

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zeroD_field_weighting

Zeroth-order spatial interpolation of cell-centered fields to particle locations.

subroutine zeroD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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oneD_field_weighting

First-order spatial interpolation of cell-centered fields to particle locations.

subroutine oneD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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twoD_field_weighting

Second-order spatial interpolation of cell-centered fields to particle locations.

subroutine twoD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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threeD_field_weighting

Third-order spatial interpolation of cell-centered fields to particle locations.

subroutine threeD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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fourD_field_weighting

Fourth-order spatial interpolation of cell-centered fields to particle locations.

subroutine fourD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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fiveD_field_weighting

Fifth-order spatial interpolation of cell-centered fields to particle locations.

subroutine fiveD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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sixD_field_weighting

Sixth-order spatial interpolation of cell-centered fields to particle locations.

subroutine sixD_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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Gaussian_field_weighting

Gaussian interpolation of cell-centered fields to particle locations.

subroutine Gaussian_field_weighting(self, field, grid, pic_fields, q, q_PIC, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout		PIC object.
field	type(field_object)	inout		The field.
grid	type(grid_object)	in		Grid object.
pic_fields	real(kind=R8P)	inout		Fields at particle locations.
q	real(kind=R8P)	in		Field variables.
q_PIC	real(kind=R8P)	in		PIC variables.
nv	integer(kind=I4P)	in		Number of variables.

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bspline_field_weighting

B-spline interpolation of cell-centered fields to particle locations.

subroutine bspline_field_weighting(self, field, grid, pic_fields, q, q_pic, nv, order)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in
order	integer(kind=I4P)	in

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shape_field_weighting

Gather with the particle shape of particle_weighting_model (the transpose of its charge deposit), with or without the binomial filter.

subroutine shape_field_weighting(self, field, grid, pic_fields, q, q_pic, nv, filter)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in
filter	logical	in		Binomial filter of the shape.

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coherent_field_weighting

Gather E and B with the transpose of the charge operator S^rho of the conserving solver the gather is named after, the adjoint of its charge deposit (cancels the electrostatic and magnetostatic self-forces, as the polynomial gathers do for their deposits): londrillo : rho = S rho^P (binomial filter included), gather with the particle shape S; totorica, esirkepov_Q<N>: rho = P S rho^P (no binomial filter), gather P^T on the fields, then the unfiltered base shape, on the dual nodes x_c+dx/2 for the odd esirkepov_Q<N> (the particle seen at x-dx/2). P^T is applied block by block with the zero extension of deposit_pic_modified_charge, circular along a periodic axis (whose filtered ghosts are then the periodic images): single block, single rank (the multi-block conserving path is FNL only).

subroutine coherent_field_weighting(self, field, grid, pic_fields, q, q_pic, nv)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	inout
field	type(field_object)	inout
grid	type(grid_object)	in
pic_fields	real(kind=R8P)	inout
q	real(kind=R8P)	in
q_pic	real(kind=R8P)	in
nv	integer(kind=I4P)	in

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transposed_filter_axis

Transpose of the P filter along one axis of a block interior, zero extension (circular along a periodic axis, single block): output_m = sum_s p(s) input_{m-s} (P^T, equal to P for the symmetric kernels).

Attributes: pure

subroutine transposed_filter_axis(input, output, axis, p, radius, periodic)

Arguments

Name	Type	Intent	Attributes	Description
input	real(kind=R8P)	in		Fields (6, ni, nj, nk).
output	real(kind=R8P)	out		Filtered fields.
axis	integer(kind=I4P)	in		Filter axis.
p	real(kind=R8P)	in		P kernel.
radius	integer(kind=I4P)	in		Taps of P.
periodic	logical	in		Periodic axis.

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set_bspline_stencil

Compute the one-dimensional B-spline stencil.

Attributes: pure

subroutine set_bspline_stencil(order, x_p, x_c, i_p, i_min, i_max)

Arguments

Name	Type	Intent	Attributes	Description
order	integer(kind=I4P)	in
x_p	real(kind=R8P)	in
x_c	real(kind=R8P)	in
i_p	integer(kind=I4P)	in
i_min	integer(kind=I4P)	out
i_max	integer(kind=I4P)	out

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compaction_moves

Moves that compact the particle arrays after the departure of the particles listed (ascending) in departed: the holes within the first particle_number-size(departed) slots are filled, in order, by the particles that stay among the last size(departed) slots. Deterministic, and the particles before the first hole do not move.

Attributes: pure

subroutine compaction_moves(particle_number, departed, moves, n_moves)

Arguments

Name	Type	Intent	Attributes	Description
particle_number	integer(kind=I4P)	in		Particles before the departure.
departed	integer(kind=I4P)	in		Departing particles, ascending.
moves	integer(kind=I4P)	out	allocatable	Moves [from/to, move].
n_moves	integer(kind=I4P)	out		Number of moves.

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Functions

conserving_solver_name

Input name of the conserving current solver: esirkepov_Q<N> for the matched-current family, the stored tag otherwise.

Returns: character(len=:)

function conserving_solver_name(self) result(name)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.

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matched_current

True for the local matched currents J_d = L_d P_transverse F_d^E with rho = P rho^P (totorica, esirkepov_Q<N>): they share the deposit of the filtered charge, the P/Q kernels and the per-particle cleanup.

Attributes: pure

Returns: logical

function matched_current(self) result(matched)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.

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coherent_gather

True for the gathers named after a conserving solver (londrillo, totorica, esirkepov_Q<N>): E and B are gathered with the transpose of that solver's charge operator S^rho, the adjoint of its charge deposit.

Attributes: pure

Returns: logical

function coherent_gather(self) result(coherent)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.

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matched_gather

True for the coherent gathers of the matched currents (totorica, esirkepov_Q<N>): P^T on the fields, then the base shape (on the dual nodes for the odd esirkepov_Q<N>).

Attributes: pure

Returns: logical

function matched_gather(self) result(matched)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.

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description

Return a pretty-formatted object description.

Returns: character(len=:)

function description(self) result(desc)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		External fields.

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halo_margin_cells

Cells a particle may lie outside the interior of a local block while its deposit/gather stencil stays within the ghosts.

Returns: integer(kind=I4P)

function halo_margin_cells(self, ngc) result(m)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.
ngc	integer(kind=I4P)	in		Ghost cells number.

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stencil_radius_cells

Max number of cells, beyond the particle cell, reached by the configured charge, current and field stencils. B-spline of order o (NGP=0 ... sextic=6, field nD = order n): (o+1)/2 cells; Gaussian: gaussian_support_cells; binomial filter: one more cell. A conserving current deposits with the particle shape.

Returns: integer(kind=I4P)

function stencil_radius_cells(self) result(radius)

Arguments

Name	Type	Intent	Attributes	Description
self	class(prism_pic_object)	in		PIC object.

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effective_bspline_weight

Return the optionally binomial-filtered one-dimensional B-spline weight.

Attributes: pure

Returns: real(kind=R8P)

function effective_bspline_weight(order, r, filter) result(weight)

Arguments

Name	Type	Intent	Attributes	Description
order	integer(kind=I4P)	in
r	real(kind=R8P)	in
filter	logical	in

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gaussian_weight

Return an unnormalized one-dimensional Gaussian weight with compact cutoff.

Attributes: pure

Returns: real(kind=R8P)

function gaussian_weight(r, cutoff_limit) result(weight)

Arguments

Name	Type	Intent	Attributes	Description
r	real(kind=R8P)	in
cutoff_limit	real(kind=R8P)	in

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effective_gaussian_weight

Return the optionally binomial-filtered one-dimensional Gaussian weight.

Attributes: pure

Returns: real(kind=R8P)

function effective_gaussian_weight(r, shift, cutoff_limit, filter) result(weight)

Arguments

Name	Type	Intent	Attributes	Description
r	real(kind=R8P)	in
shift	real(kind=R8P)	in
cutoff_limit	real(kind=R8P)	in
filter	logical	in

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bspline_weight

Return the centered cardinal B-spline weight.

Attributes: pure

Returns: real(kind=R8P)

function bspline_weight(order, r) result(weight)

Arguments

Name	Type	Intent	Attributes	Description
order	integer(kind=I4P)	in
r	real(kind=R8P)	in

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