sll_m_maxwell_1d_fem Module Reference

Description

Solve Maxwell's equations in 1D.

This version corresponds to conforming spline finite elements

Authors

Katharina Kormann Eric Sonnendrücker

Derived types and interfaces
type	sll_t_maxwell_1d_fem
	Maxwell solver class. More...

Functions/Subroutines
subroutine	sll_s_compute_e_from_b_1d_fem (self, delta_t, field_in, field_out)
	compute Ey from Bz using weak Ampere formulation More...
subroutine	sll_s_compute_b_from_e_1d_fem (self, delta_t, field_in, field_out)
subroutine	sll_s_compute_curl_part_1d_fem (self, delta_t, efield, bfield, betar)
subroutine	weak_curl (self, delta_t, field_in, field_out)
	compute Ey from Bz using weak Ampere formulation More...
subroutine	strong_curl (self, delta_t, field_in, field_out)
	Compute Bz from Ey using strong 1D Faraday equation for spline coefficients $B_z^{new}(x_j) = B_z^{old}(x_j) - \frac{\Delta t}{\Delta x} (E_y(x_j) - E_y(x_{j-1}) $. More...
subroutine	sll_s_compute_e_from_rho_1d_fem (self, field_in, field_out)
subroutine	compute_rho_from_e_1d_fem (self, field_in, field_out)
	Compute rho from Gauss law for given efield. More...
subroutine	choose_interpolation (self, current, component, E)
	Choose between compute_E_from_j_1d_fem and compute_E_from_j_1d_fem_shape. More...
subroutine	compute_e_from_j_1d_fem (self, current, component, E)
	Compute E_i from j_i integrated over the time interval using weak Ampere formulation More...
subroutine	compute_e_from_j_1d_fem_shape (self, current, component, E)
subroutine	multiply_interpolation_inverse_transpose (self, in, out)
subroutine	solve_e_b_1d_fem (self, delta_t, bfield, efield)
	Solves for the efield part in a implicit curl part solve. More...
subroutine	solve_circulant (self, eigvals, rhs, res)
subroutine	compute_phi_from_rho_1d_fem (self, in, phi, efield)
	For model with adiabatic electrons. More...
subroutine	compute_phi_from_j_1d_fem (self, in, phi, efield)
	For model with adiabatic electrons. More...
subroutine	sll_s_compute_fem_rhs (self, func, degree, coefs_dofs)
	Compute the FEM right-hand-side for a given function f and periodic splines of given degree Its components are $\int f N_i dx$ where $N_i$ is the B-spline starting at $x_i$. More...
real(kind=f64) function	l2norm_squared_1d_fem (self, coefs_dofs, degree)
	Compute square of the L2norm. More...
real(kind=f64) function	inner_product_1d_fem (self, coefs1_dofs, coefs2_dofs, degree, degree2)
subroutine	l2projection_1d_fem (self, func, degree, coefs_dofs)
	Compute the L2 projection of a given function f on periodic splines of given degree. More...
subroutine	init_1d_fem (self, domain, n_dofs, s_deg_0, delta_t, strong_ampere, solver_tolerance, force_sign, adiabatic_electrons)
subroutine	free_1d_fem (self)
subroutine	multiply_g (self, in, out)
subroutine	multiply_gt (self, in, out)
subroutine	multiply_mass_1d_fem (self, in, out, degree)
subroutine	invert_mass_1d_fem (self, in, out, degree)
	Invert the mass matrix. More...
subroutine	transform_dofs_1d_fem (self, in, out, degree)
	Invert the mass matrix. More...

Function/Subroutine Documentation

choose_interpolation()

subroutine sll_m_maxwell_1d_fem::choose_interpolation ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  current, integer(kind=i32), intent(in)  component, real(kind=f64), dimension(:), intent(inout)  E  )

private

Choose between compute_E_from_j_1d_fem and compute_E_from_j_1d_fem_shape.

Parameters

	self	Maxwell solver class
[in]	current	Component component of the current integrated over time interval
[in]	component	Component of the Efield to be computed
[in,out]	e	Updated electric field

Definition at line 326 of file sll_m_maxwell_1d_fem.F90.

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compute_e_from_j_1d_fem()

subroutine sll_m_maxwell_1d_fem::compute_e_from_j_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  current, integer(kind=i32), intent(in)  component, real(kind=f64), dimension(:), intent(inout)  E  )

private

Compute E_i from j_i integrated over the time interval using weak Ampere formulation

Parameters

	self	Maxwell solver class
[in]	current	Component component of the current integrated over time interval
[in]	component	Component of the Efield to be computed
[in,out]	e	Updated electric field

Definition at line 342 of file sll_m_maxwell_1d_fem.F90.

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compute_e_from_j_1d_fem_shape()

subroutine sll_m_maxwell_1d_fem::compute_e_from_j_1d_fem_shape ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  current, integer(kind=i32), intent(in)  component, real(kind=f64), dimension(:), intent(inout)  E  )

private

Parameters

	self	Maxwell solver class
[in]	current	Component component of the current integrated over time interval
[in]	component	Component of the Efield to be computed
[in,out]	e	Updated electric field

Definition at line 363 of file sll_m_maxwell_1d_fem.F90.

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compute_phi_from_j_1d_fem()

subroutine sll_m_maxwell_1d_fem::compute_phi_from_j_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  phi, real(kind=f64), dimension(:), intent(out)  efield  )

private

For model with adiabatic electrons.

Parameters

	self	Maxwell solver class
[in]	in	Current integrated over time interval
[out]	efield	E

Definition at line 455 of file sll_m_maxwell_1d_fem.F90.

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compute_phi_from_rho_1d_fem()

subroutine sll_m_maxwell_1d_fem::compute_phi_from_rho_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  phi, real(kind=f64), dimension(:), intent(out)  efield  )

private

For model with adiabatic electrons.

Parameters

	self	Maxwell solver class
[in]	in	rho
[out]	efield	E

Definition at line 438 of file sll_m_maxwell_1d_fem.F90.

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compute_rho_from_e_1d_fem()

subroutine sll_m_maxwell_1d_fem::compute_rho_from_e_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Compute rho from Gauss law for given efield.

Parameters

	self	Maxwell solver class
[out]	field_out	rho

Definition at line 294 of file sll_m_maxwell_1d_fem.F90.

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free_1d_fem()

subroutine sll_m_maxwell_1d_fem::free_1d_fem ( class(sll_t_maxwell_1d_fem)  self )

private

Parameters

self	Maxwell solver class

Definition at line 863 of file sll_m_maxwell_1d_fem.F90.

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init_1d_fem()

subroutine sll_m_maxwell_1d_fem::init_1d_fem ( class(sll_t_maxwell_1d_fem), intent(out)  self, real(kind=f64), dimension(2), intent(in)  domain, integer(kind=i32), intent(in)  n_dofs, integer(kind=i32), intent(in)  s_deg_0, real(kind=f64), intent(in)  delta_t, logical, intent(in), optional  strong_ampere, real(kind=f64), intent(in), optional  solver_tolerance, real(kind=f64), intent(in), optional  force_sign, logical, intent(in), optional  adiabatic_electrons  )

private

Parameters

[out]	self	Maxwell solver class
[in]	domain	xmin, xmax
[in]	n_dofs	number of degrees of freedom (here number of cells and grid points)
[in]	s_deg_0	highest spline degree
[in]	delta_t	Time step
[in]	strong_ampere	flag to switch between strong and weak Ampere formulation
[in]	solver_tolerance	tolerance for Schur complement solver
[in]	force_sign	sign of particle force
[in]	adiabatic_electrons	flag if adiabatic electrons are used

Definition at line 615 of file sll_m_maxwell_1d_fem.F90.

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inner_product_1d_fem()

real(kind=f64) function sll_m_maxwell_1d_fem::inner_product_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:)  coefs1_dofs, real(kind=f64), dimension(:)  coefs2_dofs, integer(kind=i32)  degree, integer(kind=i32), optional  degree2  )

private

Parameters

self	Maxwell solver class
coefs1_dofs	Coefficient for each DoF
coefs2_dofs	Coefficient for each DoF
degree	Specify the degree of the basis functions
degree2	Specify the degree of the basis functions

Returns

Result: squared L2 norm

Definition at line 541 of file sll_m_maxwell_1d_fem.F90.

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invert_mass_1d_fem()

subroutine sll_m_maxwell_1d_fem::invert_mass_1d_fem ( class(sll_t_maxwell_1d_fem), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out, integer(kind=i32), intent(in)  degree  )

private

Invert the mass matrix.

Parameters

[in,out]	self	Maxwell solver class
[in]	degree	Specify the degree of the basis functions
[in]	in	spline coefficients of projection
[out]	out	spline coefficients of projection

Definition at line 928 of file sll_m_maxwell_1d_fem.F90.

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l2norm_squared_1d_fem()

real(kind=f64) function sll_m_maxwell_1d_fem::l2norm_squared_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:)  coefs_dofs, integer(kind=i32)  degree  )

private

Compute square of the L2norm.

Parameters

self	Maxwell solver class
coefs_dofs	Coefficient for each DoF
degree	Specify the degree of the basis functions

Returns

Result: squared L2 norm

Definition at line 516 of file sll_m_maxwell_1d_fem.F90.

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l2projection_1d_fem()

subroutine sll_m_maxwell_1d_fem::l2projection_1d_fem ( class(sll_t_maxwell_1d_fem)  self, procedure(sll_i_function_1d_real64)  func, integer(kind=i32), intent(in)  degree, real(kind=f64), dimension(:), intent(out)  coefs_dofs  )

private

Compute the L2 projection of a given function f on periodic splines of given degree.

Parameters

	self	Maxwell solver class
	func	function
[in]	degree	Specify the degree of the basis functions

Definition at line 590 of file sll_m_maxwell_1d_fem.F90.

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multiply_g()

subroutine sll_m_maxwell_1d_fem::multiply_g ( class(sll_t_maxwell_1d_fem), intent(in)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out  )

private

Parameters

[in]	self	Maxwell_Clamped solver class
[in]	in	field_in
[out]	out	G*field_in

Definition at line 881 of file sll_m_maxwell_1d_fem.F90.

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multiply_gt()

subroutine sll_m_maxwell_1d_fem::multiply_gt ( class(sll_t_maxwell_1d_fem), intent(in)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out  )

private

Parameters

[in]	self	Maxwell_Clamped solver class
[in]	in	field_in
[out]	out	G^T*field_in

Definition at line 891 of file sll_m_maxwell_1d_fem.F90.

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multiply_interpolation_inverse_transpose()

subroutine sll_m_maxwell_1d_fem::multiply_interpolation_inverse_transpose ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(inout)  out  )

private

Parameters

	self	Maxwell solver class
[in]	in	input
[in,out]	out	output

Definition at line 378 of file sll_m_maxwell_1d_fem.F90.

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multiply_mass_1d_fem()

subroutine sll_m_maxwell_1d_fem::multiply_mass_1d_fem ( class(sll_t_maxwell_1d_fem), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out, integer(kind=i32), intent(in)  degree  )

private

Parameters

[in,out]	self	Maxwell solver class
[in]	in	Coefficient for each DoF
[out]	out	Coefficient for each DoF
[in]	degree	Specify the degree of the basis functions

Definition at line 901 of file sll_m_maxwell_1d_fem.F90.

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sll_s_compute_b_from_e_1d_fem()

subroutine sll_m_maxwell_1d_fem::sll_s_compute_b_from_e_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), intent(in)  delta_t, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

Parameters

	self	Maxwell solver class
[in]	delta_t	Time step
[in]	field_in	Ey
[in,out]	field_out	Bz

Definition at line 169 of file sll_m_maxwell_1d_fem.F90.

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sll_s_compute_curl_part_1d_fem()

subroutine sll_m_maxwell_1d_fem::sll_s_compute_curl_part_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), intent(in)  delta_t, real(kind=f64), dimension(:), intent(inout)  efield, real(kind=f64), dimension(:), intent(inout)  bfield, real(kind=f64), optional  betar  )

private

Parameters

	self	Maxwell solver class
[in]	delta_t	Time step
[in,out]	efield	Ey
[in,out]	bfield	Bz
	betar	1/beta

Definition at line 184 of file sll_m_maxwell_1d_fem.F90.

sll_s_compute_e_from_b_1d_fem()

subroutine sll_m_maxwell_1d_fem::sll_s_compute_e_from_b_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), intent(in)  delta_t, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

compute Ey from Bz using weak Ampere formulation

Parameters

	self	Maxwell solver class
[in]	delta_t	Time step
[in]	field_in	Bz
[in,out]	field_out	Ey

Definition at line 153 of file sll_m_maxwell_1d_fem.F90.

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sll_s_compute_e_from_rho_1d_fem()

subroutine sll_m_maxwell_1d_fem::sll_s_compute_e_from_rho_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Parameters

	self	Maxwell solver class
[in]	field_in	rho
[out]	field_out	E

Definition at line 265 of file sll_m_maxwell_1d_fem.F90.

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sll_s_compute_fem_rhs()

subroutine sll_m_maxwell_1d_fem::sll_s_compute_fem_rhs ( class(sll_t_maxwell_1d_fem)  self, procedure(sll_i_function_1d_real64)  func, integer(kind=i32), intent(in)  degree, real(kind=f64), dimension(:), intent(out)  coefs_dofs  )

private

Compute the FEM right-hand-side for a given function f and periodic splines of given degree Its components are $\int f N_i dx$ where $N_i$ is the B-spline starting at $x_i$.

Parameters

	self	Maxwell solver class
	func	function
[in]	degree	Specify the degree of the basis functions

Definition at line 477 of file sll_m_maxwell_1d_fem.F90.

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solve_circulant()

subroutine sll_m_maxwell_1d_fem::solve_circulant ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), dimension(:), intent(in)  eigvals, real(kind=f64), dimension(:), intent(in)  rhs, real(kind=f64), dimension(:), intent(out)  res  )

private

Parameters

	self	Maxwell solver class
[in]	eigvals	eigenvalues of circulant matrix
[out]	res	result

Definition at line 405 of file sll_m_maxwell_1d_fem.F90.

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solve_e_b_1d_fem()

subroutine sll_m_maxwell_1d_fem::solve_e_b_1d_fem ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), intent(in)  delta_t, real(kind=f64), dimension(:), intent(in)  bfield, real(kind=f64), dimension(:), intent(inout)  efield  )

private

Solves for the efield part in a implicit curl part solve.

Parameters

	self	Maxwell solver class
[in]	delta_t	Time step
[in]	bfield	Component component of the current integrated over time interval
[in,out]	efield	Updated electric field

Definition at line 390 of file sll_m_maxwell_1d_fem.F90.

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strong_curl()

subroutine sll_m_maxwell_1d_fem::strong_curl ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), intent(in)  delta_t, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

Compute Bz from Ey using strong 1D Faraday equation for spline coefficients $B_z^{new}(x_j) = B_z^{old}(x_j) - \frac{\Delta t}{\Delta x} (E_y(x_j) - E_y(x_{j-1}) $.

Parameters

	self	Maxwell solver class
[in]	delta_t	Time step
[in]	field_in	Ey
[in,out]	field_out	Bz

Definition at line 246 of file sll_m_maxwell_1d_fem.F90.

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transform_dofs_1d_fem()

subroutine sll_m_maxwell_1d_fem::transform_dofs_1d_fem ( class(sll_t_maxwell_1d_fem), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out, integer(kind=i32), intent(in)  degree  )

private

Invert the mass matrix.

Parameters

[in,out]	self	Maxwell solver class
[in]	degree	Specify the degree of the basis functions ! this is 0 for 0 form and 1 for 1 form
[in]	in	spline coefficients of projection
[out]	out	spline coefficients of projection

Definition at line 950 of file sll_m_maxwell_1d_fem.F90.

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weak_curl()

subroutine sll_m_maxwell_1d_fem::weak_curl ( class(sll_t_maxwell_1d_fem)  self, real(kind=f64), intent(in)  delta_t, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

compute Ey from Bz using weak Ampere formulation

Parameters

	self	Maxwell solver class
[in]	delta_t	Time step
[in]	field_in	input field
[in,out]	field_out	output_field

Definition at line 226 of file sll_m_maxwell_1d_fem.F90.

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