sll_m_time_propagator_pic_vm_1d2v_trafo_helper Module Reference

Description

Particle pusher based on antisymmetric splitting with AVF for 1d2v Vlasov-Poisson with coordinate transformation.

Author

Benedikt Perse, IPP

MPI parallelization by domain cloning. Periodic boundaries. Spline DoFs numerated by the point the spline starts.

Derived types and interfaces
type	sll_t_time_propagator_pic_vm_1d2v_trafo_helper
	Hamiltonian splitting type for Vlasov-Maxwell 1d2v. More...

Functions/Subroutines
subroutine	advect_x_pic_vm_1d2v_trafo (self, dt)
	Finalization. More...
subroutine	compute_particle_boundary (self, xold, xnew, vi)
	Helper function for advect_x. More...
subroutine	advect_vb_pic_vm_1d2v_trafo (self, dt)
	advect_vb: Equations to be solved $V^{n+1}= (\cos(DF/J_F B)&\sin(DF/J_F B) \ -\sin(DF/J_F B) &\cos(DF/J_F B) ) V^n More...
subroutine	advect_eb_pic_vm_1d2v_trafo (self, dt)
	advect_eb: Equations to be solved Solution with Schur complement: $ S=M_1+\frac{\Delta t^2}{4} D^\top M_2 D $ $ e_2^{n+1}=S^{-1}( (M_1-\frac{\Delta t^2}{4} D^\top M_2 D)e_2^n+\Delta t D^\top M_2 b_3^n) $ $ b_3^{n+1}=b_3^n-\frac{\Delta t}{2} C(e_2^n+e_2^{n+1}) $ More...
subroutine	advect_e_pic_vm_1d2v_trafo (self, dt)
	advect_e: Equations to be solved Solution with Schur complement: $ S_{+}=M_1+\frac{\Delta t^2 q^2}{4 m} (\mathbb{\Lambda}^1)^T DF^{-1} DF^{-T} \mathbb{\Lambda}^1 $ $e^{n+1}=S_{+}^{-1}\left(S_{-}e^n-\Delta t (\mathbb{\Lambda}^1)^\top DF^{-1}\mathbb{W}_q V^n \right)$ $V^{n+1}=V^n+\frac{\Delta t}{2} \mathbb{W}_{\frac{q}{m}} DF^{-\top} \mathbb{\Lambda}^1(e^{n+1}+e^n)$ More...
subroutine	advect_ex_pic_vm_1d2v_trafo (self, dt)
	advect_ex: Equations to be solved $\frac{\Xi^{n+1}-\Xi^n}{\Delta t}=\frac{DF^{-1}(\Xi^{n+1})+DF^{-1}(\Xi^n)}{2} \frac{V^{n+1}+V^n}{2}$ $\frac{V^{n+1}-V^n}{\Delta t}=\mathbb{W}_{\frac{q}{m}} \frac{DF^{-\top}(\Xi^{n+1})+DF^{-\top}(\Xi^n)}{2} \frac{1}{\Delta t}\int_{t^n}^{t^{n+1}} \mathbb{\Lambda}^1(\Xi(\tau)) d\tau \frac{e^{n+1}+e^n}{2}$ $\frac{M_1 e^{n+1}-M_1 e^n}{\Delta t} = - \frac{1}{\Delta t} \int_{t^n}^{t^{n+1}} \mathbb{\Lambda}^1(\Xi(\tau))^\top d\tau \frac{DF^{-1}(\Xi^{n+1})+DF^{-1}(\Xi^n)}{2} \mathbb{W}_q\frac{V^{n+1}+V^n}{2}$ More...
subroutine	compute_particle_boundary_current_evaluate (self, xi, xnew, vi, vbar, wi, qoverm, dt)
	Helper function for advect_ex. More...
subroutine	initialize_pic_vm_1d2v_trafo (self, maxwell_solver, kernel_smoother_0, kernel_smoother_1, particle_group, efield_dofs, bfield_dofs, x_min, Lx, map, boundary_particles, solver_tolerance, iter_tolerance, max_iter, force_sign, rhob, jmean)
	Constructor. More...
subroutine	initialize_file_pic_vm_1d2v_trafo (self, maxwell_solver, kernel_smoother_0, kernel_smoother_1, particle_group, efield_dofs, bfield_dofs, x_min, Lx, map, filename, boundary_particles, force_sign, rhob, jmean)
	Constructor. More...
subroutine	delete_pic_vm_1d2v_trafo (self)
	Destructor. More...

Function/Subroutine Documentation

advect_e_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::advect_e_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

advect_e: Equations to be solved Solution with Schur complement: $ S_{+}=M_1+\frac{\Delta t^2 q^2}{4 m} (\mathbb{\Lambda}^1)^T DF^{-1} DF^{-T} \mathbb{\Lambda}^1 $ $e^{n+1}=S_{+}^{-1}\left(S_{-}e^n-\Delta t (\mathbb{\Lambda}^1)^\top DF^{-1}\mathbb{W}_q V^n \right)$ $V^{n+1}=V^n+\frac{\Delta t}{2} \mathbb{W}_{\frac{q}{m}} DF^{-\top} \mathbb{\Lambda}^1(e^{n+1}+e^n)$

Parameters

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

Definition at line 284 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

advect_eb_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::advect_eb_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

advect_eb: Equations to be solved Solution with Schur complement: $ S=M_1+\frac{\Delta t^2}{4} D^\top M_2 D $ $ e_2^{n+1}=S^{-1}( (M_1-\frac{\Delta t^2}{4} D^\top M_2 D)e_2^n+\Delta t D^\top M_2 b_3^n) $ $ b_3^{n+1}=b_3^n-\frac{\Delta t}{2} C(e_2^n+e_2^{n+1}) $

Parameters

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

Definition at line 269 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

advect_ex_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::advect_ex_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

advect_ex: Equations to be solved $\frac{\Xi^{n+1}-\Xi^n}{\Delta t}=\frac{DF^{-1}(\Xi^{n+1})+DF^{-1}(\Xi^n)}{2} \frac{V^{n+1}+V^n}{2}$ $\frac{V^{n+1}-V^n}{\Delta t}=\mathbb{W}_{\frac{q}{m}} \frac{DF^{-\top}(\Xi^{n+1})+DF^{-\top}(\Xi^n)}{2} \frac{1}{\Delta t}\int_{t^n}^{t^{n+1}} \mathbb{\Lambda}^1(\Xi(\tau)) d\tau \frac{e^{n+1}+e^n}{2}$ $\frac{M_1 e^{n+1}-M_1 e^n}{\Delta t} = - \frac{1}{\Delta t} \int_{t^n}^{t^{n+1}} \mathbb{\Lambda}^1(\Xi(\tau))^\top d\tau \frac{DF^{-1}(\Xi^{n+1})+DF^{-1}(\Xi^n)}{2} \mathbb{W}_q\frac{V^{n+1}+V^n}{2}$

Parameters

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

Definition at line 417 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

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advect_vb_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::advect_vb_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

advect_vb: Equations to be solved $V^{n+1}= (\cos(DF/J_F B)&\sin(DF/J_F B) \ -\sin(DF/J_F B) &\cos(DF/J_F B) ) V^n

Parameters

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

Definition at line 231 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

advect_x_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::advect_x_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), intent(in)  dt  )

private

Finalization.

advect_x: Equations to be solved $\Xi^{n+1}=\Xi^n+ \frac{\Delta t}{2} (DF^{-1}(\Xi^{n+1})+DF^{-1}(\Xi^n)) V^n$

Parameters

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

Definition at line 148 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

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compute_particle_boundary()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::compute_particle_boundary ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), intent(inout)  xold, real(kind=f64), intent(inout)  xnew, real(kind=f64), intent(inout)  vi  )

private

Helper function for advect_x.

Definition at line 190 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

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compute_particle_boundary_current_evaluate()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::compute_particle_boundary_current_evaluate ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self, real(kind=f64), dimension(1), intent(in)  xi, real(kind=f64), dimension(1), intent(inout)  xnew, real(kind=f64), dimension(2), intent(inout)  vi, real(kind=f64), dimension(2), intent(inout)  vbar, real(kind=f64), dimension(1), intent(in)  wi, real(kind=f64), intent(in)  qoverm, real(kind=f64), intent(in)  dt  )

private

Helper function for advect_ex.

Parameters

[in,out]

self

time splitting object

Definition at line 629 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

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delete_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::delete_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), intent(inout)  self )

private

Destructor.

Parameters

[in,out]

self

time propagator object

Definition at line 1077 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

initialize_file_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::initialize_file_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), 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_mapping_3d), intent(in), target  map, character(len=*), intent(in)  filename, integer(kind=i32), intent(in), optional  boundary_particles, real(kind=f64), intent(in), optional  force_sign, real(kind=f64), dimension(:), intent(in), optional, target  rhob, logical, intent(in), optional  jmean  )

private

Constructor.

Parameters

[out]	self	time propagator 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]	map	Coordinate transformation
[in]	boundary_particles	particle boundary conditions
[in]	force_sign	sign of particle force
[in]	rhob	charge at the boundary
[in]	jmean	logical for mean value of current

Definition at line 884 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.

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initialize_pic_vm_1d2v_trafo()

subroutine sll_m_time_propagator_pic_vm_1d2v_trafo_helper::initialize_pic_vm_1d2v_trafo ( class(sll_t_time_propagator_pic_vm_1d2v_trafo_helper), 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_mapping_3d), intent(in), target  map, integer(kind=i32), intent(in), optional  boundary_particles, real(kind=f64), intent(in), optional  solver_tolerance, real(kind=f64), intent(in), optional  iter_tolerance, integer(kind=i32), intent(in), optional  max_iter, real(kind=f64), intent(in), optional  force_sign, real(kind=f64), dimension(:), intent(in), optional, target  rhob, logical, intent(in), optional  jmean  )

private

Constructor.

Parameters

[out]	self	time propagator 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]	map	Coordinate transformation
[in]	boundary_particles	particle boundary conditions
[in]	solver_tolerance	solver tolerance
[in]	iter_tolerance	iteration tolerance
[in]	max_iter	maximal number of iterations
[in]	force_sign	sign of particle force
[in]	rhob	charge at the boundary
[in]	jmean	logical for mean value of current

Definition at line 741 of file sll_m_time_propagator_pic_vm_1d2v_trafo_helper.F90.