sll_m_time_propagator_pic_vm_1d2v_cef Module Reference

Description

Particle pusher based on Hamiltonian splitting proposed by Crouseilles, Einkemmer, Faou for 1d2v Vlasov-Maxwell.

Author

Katharina Kormann, IPP

MPI parallelization by domain cloning. Periodic boundaries. Spline DoFs numerated by the point the spline starts. Reference: Kraus, Kormann, Sonnendrücker, Morrison: GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods

Derived types and interfaces
type	sll_t_time_propagator_pic_vm_1d2v_cef
	Hamiltonian splitting type for Vlasov-Maxwell 1d2v. More...

Functions/Subroutines
subroutine	strang_splitting_pic_vm_1d2v (self, dt, number_steps)
	Finalization. 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	operatorhp_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	compute_particle_boundary_current (self, xold, xnew, vi, wi, dt)
	Helper function for operatorHp. 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, boundary_particles, electrostatic, rhob)
	Constructor. More...
subroutine	delete_pic_vm_1d2v (self)
	Destructor. More...

Function/Subroutine Documentation

compute_particle_boundary_current()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::compute_particle_boundary_current ( class(sll_t_time_propagator_pic_vm_1d2v_cef), intent(inout)  self, real(kind=f64), dimension(1), intent(in)  xold, real(kind=f64), dimension(1), intent(inout)  xnew, real(kind=f64), dimension(2), intent(inout)  vi, real(kind=f64), dimension(1), intent(in)  wi, real(kind=f64), intent(in)  dt  )

private

Helper function for operatorHp.

Parameters

[in,out]

self

time splitting object

Definition at line 193 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

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delete_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::delete_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), intent(inout)  self )

private

Destructor.

Parameters

[in,out]

self

time splitting object

Definition at line 410 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

initialize_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::initialize_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), 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, integer(kind=i32), intent(in), optional  boundary_particles, logical, intent(in), optional  electrostatic, real(kind=f64), dimension(:), intent(in), optional, target  rhob  )

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]	particle_group	Particle group
[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]	boundary_particles	particle boundary conditions
[in]	electrostatic	true for electrostatic simulation
[in]	rhob	charge at the boundary

Definition at line 341 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

lie_splitting_back_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::lie_splitting_back_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), 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 128 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

lie_splitting_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::lie_splitting_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), 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 111 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

operatorhb_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::operatorhb_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), 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 300 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

operatorhe_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::operatorhe_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), 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 258 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

operatorhp_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::operatorhp_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), 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 151 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.

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strang_splitting_pic_vm_1d2v()

subroutine sll_m_time_propagator_pic_vm_1d2v_cef::strang_splitting_pic_vm_1d2v ( class(sll_t_time_propagator_pic_vm_1d2v_cef), intent(inout)  self, real(kind=f64), intent(in)  dt, integer(kind=i32), intent(in)  number_steps  )

private

Finalization.

Strang splitting

Parameters

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

Definition at line 91 of file sll_m_time_propagator_pic_vm_1d2v_cef.F90.