sll_m_time_propagator_pic_vm_1d2v_momentum Module Reference

Description

Particle pusher based on Hamiltonian splitting for 1d2v Vlasov-Maxwell in the momentum conserving, non-geometric form (see the reference)

Author

Katharina Kormann, IPP

MPI parallelization by domain cloning. Periodic boundaries. Spline DoFs numerated by the point the spline starts. Reference: Campos Pinto, Kormann, Sonnendrücker: Variational Framework for Structure-Preserving Electromagnetic Particle-In-Cell Methods, arXiv 2101.09247, 2021. Control variate: Note the we do not account for the analytic j at the moment (TODO: control_variate for current)

Derived types and interfaces
type	sll_t_time_propagator_pic_vm_1d2v_momentum
	Hamiltonian splitting type for Vlasov-Maxwell 1d2v. More...

Functions/Subroutines
subroutine	reinit_fields (self)
	Finalization. More...
subroutine	strang_splitting_pic_vm_1d2v (self, dt, number_steps)
	Strang splitting. More...
subroutine	lie_splitting_pic_vm_1d2v (self, dt, number_steps)
	Lie splitting. More...
subroutine	lie_splitting_back_pic_vm_1d2v (self, dt, number_steps)
	Lie splitting (oposite ordering) More...
subroutine	operatorhp1_pic_vm_1d2v (self, dt)
	Push Hp1: Equations to solve are \partial_t f + v_1 \partial_{x_1} f = 0 -> X_new = X_old + dt V_1 V_new,2 = V_old,2 + \int_0 h V_old,1 B_old \partial_t E_1 = - \int v_1 f(t,x_1, v) dv -> E_{1,new} = E_{1,old} - \int \int v_1 f(t,x_1+s v_1,v) dv ds \partial_t E_2 = 0 -> E_{2,new} = E_{2,old} \partial_t B = 0 => B_new = B_old. More...
subroutine	operatorhp2_pic_vm_1d2v (self, dt)
	Push Hp2: Equations to solve are X_new = X_old V_new,1 = V_old,1 + \int_0 h V_old,2 B_old \partial_t E_1 = 0 -> E_{1,new} = E_{1,old} \partial_t E_2 = - \int v_2 f(t,x_1, v) dv -> E_{2,new} = E_{2,old} - \int \int v_2 f(t,x_1+s v_1,v) dv ds \partial_t B = 0 => B_new = B_old. More...
subroutine	operatorhe_pic_vm_1d2v (self, dt)
	Push H_E: Equations to be solved \partial_t f + E_1 \partial_{v_1} f + E_2 \partial_{v_2} f = 0 -> V_new = V_old + dt * E \partial_t E_1 = 0 -> E_{1,new} = E_{1,old} \partial_t E_2 = 0 -> E_{2,new} = E_{2,old} \partial_t B + \partial_{x_1} E_2 = 0 => B_new = B_old - dt \partial_{x_1} E_2. More...
subroutine	operatorhb_pic_vm_1d2v (self, dt)
	Push H_B: Equations to be solved V_new = V_old \partial_t E_1 = 0 -> E_{1,new} = E_{1,old} \partial_t E_2 = - \partial_{x_1} B -> E_{2,new} = E_{2,old}-dt*\partial_{x_1} B \partial_t B = 0 -> B_new = B_old. More...
subroutine	initialize_pic_vm_1d2v (self, maxwell_solver, kernel_smoother_0, kernel_smoother_1, particle_group, efield_dofs, bfield_dofs, x_min, Lx, filter, jmean, control_variate, i_weight)
	Constructor. More...
subroutine	delete_pic_vm_1d2v (self)
	Destructor. More...
subroutine, public	sll_s_new_time_propagator_pic_vm_1d2v_momentum (splitting, maxwell_solver, kernel_smoother_0, kernel_smoother_1, particle_group, efield_dofs, bfield_dofs, x_min, Lx, filter, jmean, control_variate, i_weight)
	Constructor for allocatable abstract type. More...
subroutine, public	sll_s_new_time_propagator_pic_vm_1d2v_momentum_ptr (splitting, maxwell_solver, kernel_smoother_0, kernel_smoother_1, particle_group, efield_dofs, bfield_dofs, x_min, Lx, filter, jmean)
	Constructor for pointer abstract type. More...

Function/Subroutine Documentation

delete_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::delete_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self )

private

Destructor.

Parameters

[in,out]

self

time splitting object

Definition at line 502 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

initialize_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::initialize_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(out)  self, class(sll_c_maxwell_1d_base), intent(in), target  maxwell_solver, class(sll_c_particle_mesh_coupling_1d), intent(in), target  kernel_smoother_0, class(sll_c_particle_mesh_coupling_1d), intent(in), target  kernel_smoother_1, class(sll_t_particle_array), intent(in), target  particle_group, real(kind=f64), dimension(:,:), intent(in), target  efield_dofs, real(kind=f64), dimension(:), intent(in), target  bfield_dofs, real(kind=f64), intent(in)  x_min, real(kind=f64), intent(in)  Lx, type( sll_t_binomial_filter ), intent(in), target  filter, logical, intent(in), optional  jmean, class(sll_t_control_variates), intent(in), optional, target  control_variate, integer(kind=i32), intent(in), optional  i_weight  )

private

Constructor.

Parameters

[out]	self	time splitting object
[in]	maxwell_solver	Maxwell solver
[in]	kernel_smoother_0	Kernel smoother
[in]	kernel_smoother_1	Kernel smoother
[in]	efield_dofs	array for the coefficients of the efields
[in]	bfield_dofs	array for the coefficients of the bfield
[in]	x_min	Lower bound of x domain
[in]	lx	Length of the domain in x direction.
[in]	control_variate	Control variate (if delta f)
[in]	i_weight	Index of weight to be used by propagator

Definition at line 412 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

lie_splitting_back_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::lie_splitting_back_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt, integer(kind=i32), intent(in)  number_steps  )

private

Lie splitting (oposite ordering)

Parameters

[in,out]	self	time splitting object
[in]	dt	time step
[in]	number_steps	number of time steps

Definition at line 155 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

lie_splitting_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::lie_splitting_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt, integer(kind=i32), intent(in)  number_steps  )

private

Lie splitting.

Parameters

[in,out]	self	time splitting object
[in]	dt	time step
[in]	number_steps	number of time steps

Definition at line 137 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

operatorhb_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::operatorhb_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

Push H_B: Equations to be solved V_new = V_old \partial_t E_1 = 0 -> E_{1,new} = E_{1,old} \partial_t E_2 = - \partial_{x_1} B -> E_{2,new} = E_{2,old}-dt*\partial_{x_1} B \partial_t B = 0 -> B_new = B_old.

Parameters

[in,out]	self	time splitting object
[in]	dt	time step

Definition at line 397 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

operatorhe_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::operatorhe_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

Push H_E: Equations to be solved \partial_t f + E_1 \partial_{v_1} f + E_2 \partial_{v_2} f = 0 -> V_new = V_old + dt * E \partial_t E_1 = 0 -> E_{1,new} = E_{1,old} \partial_t E_2 = 0 -> E_{2,new} = E_{2,old} \partial_t B + \partial_{x_1} E_2 = 0 => B_new = B_old - dt \partial_{x_1} E_2.

Parameters

[in,out]	self	time splitting object
[in]	dt	time step

Definition at line 344 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

operatorhp1_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::operatorhp1_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

Push Hp1: Equations to solve are \partial_t f + v_1 \partial_{x_1} f = 0 -> X_new = X_old + dt V_1 V_new,2 = V_old,2 + \int_0 h V_old,1 B_old \partial_t E_1 = - \int v_1 f(t,x_1, v) dv -> E_{1,new} = E_{1,old} - \int \int v_1 f(t,x_1+s v_1,v) dv ds \partial_t E_2 = 0 -> E_{2,new} = E_{2,old} \partial_t B = 0 => B_new = B_old.

Parameters

[in,out]	self	time splitting object
[in]	dt	time step

Definition at line 179 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

operatorhp2_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::operatorhp2_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

Push Hp2: Equations to solve are X_new = X_old V_new,1 = V_old,1 + \int_0 h V_old,2 B_old \partial_t E_1 = 0 -> E_{1,new} = E_{1,old} \partial_t E_2 = - \int v_2 f(t,x_1, v) dv -> E_{2,new} = E_{2,old} - \int \int v_2 f(t,x_1+s v_1,v) dv ds \partial_t B = 0 => B_new = B_old.

Parameters

[in,out]	self	time splitting object
[in]	dt	time step

Definition at line 274 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

reinit_fields()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::reinit_fields ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self )

private

Finalization.

Parameters

[in,out]

self

time splitting object

Definition at line 105 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

sll_s_new_time_propagator_pic_vm_1d2v_momentum()

subroutine, public sll_m_time_propagator_pic_vm_1d2v_momentum::sll_s_new_time_propagator_pic_vm_1d2v_momentum	(	class(sll_c_time_propagator_base), intent(out), allocatable	splitting,
		class(sll_c_maxwell_1d_base), intent(in), target	maxwell_solver,
		class(sll_c_particle_mesh_coupling_1d), intent(in), target	kernel_smoother_0,
		class(sll_c_particle_mesh_coupling_1d), intent(in), target	kernel_smoother_1,
		class(sll_t_particle_array), intent(in), target	particle_group,
		real(kind=f64), dimension(:,:), intent(in), target	efield_dofs,
		real(kind=f64), dimension(:), intent(in), target	bfield_dofs,
		real(kind=f64), intent(in)	x_min,
		real(kind=f64), intent(in)	Lx,
		type( sll_t_binomial_filter ), intent(in), target	filter,
		logical, intent(in), optional	jmean,
		class(sll_t_control_variates), intent(in), optional, target	control_variate,
		intent(in)	i_weight
	)

Constructor for allocatable abstract type.

Parameters

[out]	splitting	time splitting object
[in]	maxwell_solver	Maxwell solver
[in]	kernel_smoother_0	Kernel smoother
[in]	kernel_smoother_1	Kernel smoother
[in]	efield_dofs	array for the coefficients of the efields
[in]	bfield_dofs	array for the coefficients of the bfield
[in]	x_min	Lower bound of x domain
[in]	lx	Length of the domain in x direction.
[in]	jmean	Should jmean be substracted in Ampere's law?
[in]	control_variate	Control variate (if delta f)

Definition at line 519 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

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sll_s_new_time_propagator_pic_vm_1d2v_momentum_ptr()

subroutine, public sll_m_time_propagator_pic_vm_1d2v_momentum::sll_s_new_time_propagator_pic_vm_1d2v_momentum_ptr	(	class(sll_c_time_propagator_base), intent(out), pointer	splitting,
		class(sll_c_maxwell_1d_base), intent(in), target	maxwell_solver,
		class(sll_c_particle_mesh_coupling_1d), intent(in), target	kernel_smoother_0,
		class(sll_c_particle_mesh_coupling_1d), intent(in), target	kernel_smoother_1,
		class(sll_t_particle_array), intent(in), target	particle_group,
		dimension(:,:), intent(in)	efield_dofs,
		dimension(:), intent(in)	bfield_dofs,
		intent(in)	x_min,
		intent(in)	Lx,
		type( sll_t_binomial_filter ), intent(in), target	filter,
		logical, intent(in), optional	jmean
	)

Constructor for pointer abstract type.

Parameters

[out]	splitting	time splitting object
[in]	maxwell_solver	Maxwell solver
[in]	kernel_smoother_0	Kernel smoother
[in]	kernel_smoother_1	Kernel smoother
[in]	jmean	Should jmean be substracted in Ampere's law?

Definition at line 595 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.

strang_splitting_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_momentum::strang_splitting_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_momentum), intent(inout)  self, real(kind=f64), intent(in)  dt, integer(kind=i32), intent(in)  number_steps  )

private

Strang splitting.

Parameters

[in,out]	self	time splitting object
[in]	dt	time step
[in]	number_steps	number of time steps

Definition at line 115 of file sll_m_time_propagator_pic_vm_1d2v_momentum.F90.