sll_m_maxwell_clamped_1d_trafo Module Reference

Description

Solve Maxwell's equations in curvilinear coordinates with boundary conditions in 1D based on spline FEM, version based on sparse matrices.

Author

Benedikt Perse

Derived types and interfaces
type	sll_t_maxwell_clamped_1d_trafo

Functions/Subroutines
subroutine	sll_s_compute_e_from_b_1d_trafo (self, delta_t, field_in, field_out)
	compute Ey from Bz using weak Ampere formulation More...
subroutine	sll_s_compute_b_from_e_1d_trafo (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_curl_part_1d_trafo (self, delta_t, efield, bfield, betar)
	Solve curl part of Maxwell's equations. More...
subroutine	sll_s_compute_e_from_rho_1d_trafo (self, field_in, field_out)
	compute e from rho using weak Poisson's equation ( rho = G^T M_1 G \phi, e = -G \phi ) More...
subroutine	compute_rho_from_e_1d_trafo (self, field_in, field_out)
	Compute rho from Gauss law for given efield. More...
subroutine	compute_e_from_j_1d_trafo (self, current, component, E)
	Compute E_i from j_i integrated over the time interval using weak Ampere formulation. More...
subroutine	compute_phi_from_rho_1d_trafo (self, in, phi, efield)
	For model with adiabatic electrons. More...
subroutine	compute_phi_from_j_1d_trafo (self, in, phi, efield)
	For model with adiabatic electrons. More...
subroutine	sll_s_compute_rhs_trafo (self, func, degree, coefs_dofs)
	Compute the FEM right-hand-side for a given function f and clamped splines of given degree Its components are $\int f N_i dx$ where $N_i$ is the B-spline starting at $x_i$. More...
subroutine	l2projection_1d_trafo (self, func, degree, coefs_dofs)
	Compute the L2 projection of a given function f on periodic splines of given degree. More...
real(kind=f64) function	l2norm_squared_1d_trafo (self, coefs_dofs, degree)
	Compute square of the L2norm. More...
real(kind=f64) function	inner_product_1d_trafo (self, coefs1_dofs, coefs2_dofs, degree, degree2)
	Compute inner product. More...
subroutine	init_1d_trafo (self, domain, n_cells, s_deg_0, boundary, map, mass_tolerance, poisson_tolerance, solver_tolerance)
	Initialization. More...
subroutine	init_from_file_1d_trafo (self, domain, n_cells, s_deg_0, boundary, map, nml_file)
	Initialization from nml file. More...
subroutine	free_1d_trafo (self)
	Finalization. More...
subroutine	multiply_g (self, in, out)
	Multiply by dicrete gradient matrix. More...
subroutine	multiply_gt (self, in, out)
	Multiply by transpose of dicrete gradient matrix. More...
subroutine	multiply_mass_1d_trafo (self, in, out, degree)
	Multiply by the mass matrix. More...
subroutine	invert_mass_1d_trafo (self, in, out, degree)
	Multiply by the inverse mass matrix. More...
subroutine	compute_field_energy (self, efield_dofs1, efield_dofs2, bfield_dofs, energy)
	Compute field energy. More...

Function/Subroutine Documentation

compute_e_from_j_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::compute_e_from_j_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped 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 234 of file sll_m_maxwell_clamped_1d_trafo.F90.

compute_field_energy()

subroutine sll_m_maxwell_clamped_1d_trafo::compute_field_energy ( class(sll_t_maxwell_clamped_1d_trafo)  self, real(kind=f64), dimension(:), intent(in)  efield_dofs1, real(kind=f64), dimension(:), intent(in)  efield_dofs2, real(kind=f64), dimension(:), intent(in)  bfield_dofs, real(kind=f64), intent(out)  energy  )

private

Compute field energy.

Parameters

	self	Maxwell_Clamped solver class
[in]	efield_dofs1	Ex
[in]	efield_dofs2	Ey
[in]	bfield_dofs	Bz
[out]	energy	field energy

Definition at line 770 of file sll_m_maxwell_clamped_1d_trafo.F90.

compute_phi_from_j_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::compute_phi_from_j_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped solver class
[in]	in	Current integrated over time interval
[out]	efield	E

Definition at line 272 of file sll_m_maxwell_clamped_1d_trafo.F90.

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compute_phi_from_rho_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::compute_phi_from_rho_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped solver class
[in]	in	rho
[out]	efield	E

Definition at line 255 of file sll_m_maxwell_clamped_1d_trafo.F90.

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compute_rho_from_e_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::compute_rho_from_e_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped solver class
[in]	field_in	E
[out]	field_out	rho

Definition at line 221 of file sll_m_maxwell_clamped_1d_trafo.F90.

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free_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::free_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  self )

private

Finalization.

Parameters

self	Maxwell_Clamped solver class

Definition at line 684 of file sll_m_maxwell_clamped_1d_trafo.F90.

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init_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::init_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo), intent(out)  self, real(kind=f64), dimension(2), intent(in)  domain, integer(kind=i32), intent(in)  n_cells, integer(kind=i32), intent(in)  s_deg_0, integer(kind=i32), intent(in)  boundary, type(sll_t_mapping_3d), intent(inout), target  map, real(kind=f64), intent(in), optional  mass_tolerance, real(kind=f64), intent(in), optional  poisson_tolerance, real(kind=f64), intent(in), optional  solver_tolerance  )

private

Initialization.

Parameters

[out]	self	Maxwell_Clamped solver class
[in]	domain	xmin, xmax
[in]	n_cells	number of cells
[in]	s_deg_0	highest spline degree
[in]	boundary	field boundary conditions
[in,out]	map	coordinate transformation
[in]	mass_tolerance	tolerance for mass solver
[in]	poisson_tolerance	tolerance for Poisson solver
[in]	solver_tolerance	tolerance for Schur complement solver

Definition at line 519 of file sll_m_maxwell_clamped_1d_trafo.F90.

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init_from_file_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::init_from_file_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo), intent(out)  self, real(kind=f64), dimension(2), intent(in)  domain, integer(kind=i32), intent(in)  n_cells, integer(kind=i32), intent(in)  s_deg_0, integer(kind=i32), intent(in)  boundary, type(sll_t_mapping_3d), intent(inout), target  map, character(len=*), intent(in)  nml_file  )

private

Initialization from nml file.

Parameters

[out]	self	Maxwell_Clamped solver class
[in]	domain	xmin, xmax
[in]	n_cells	number of degrees of freedom (here number of cells and grid points)
[in]	s_deg_0	highest spline degree
[in]	boundary	field boundary conditions
[in,out]	map	coordinate transformation
[in]	nml_file	nml-file

Definition at line 621 of file sll_m_maxwell_clamped_1d_trafo.F90.

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inner_product_1d_trafo()

real(kind=f64) function sll_m_maxwell_clamped_1d_trafo::inner_product_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  self, real(kind=f64), dimension(:)  coefs1_dofs, real(kind=f64), dimension(:)  coefs2_dofs, integer(kind=i32)  degree, integer(kind=i32), optional  degree2  )

private

Compute inner product.

Parameters

self	Maxwell_Clamped 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 472 of file sll_m_maxwell_clamped_1d_trafo.F90.

invert_mass_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::invert_mass_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out, integer(kind=i32), intent(in)  degree  )

private

Multiply by the inverse mass matrix.

Parameters

[in,out]	self	Maxwell_Clamped 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 749 of file sll_m_maxwell_clamped_1d_trafo.F90.

l2norm_squared_1d_trafo()

real(kind=f64) function sll_m_maxwell_clamped_1d_trafo::l2norm_squared_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  self, real(kind=f64), dimension(:)  coefs_dofs, integer(kind=i32)  degree  )

private

Compute square of the L2norm.

Parameters

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

Returns

Result: squared L2 norm

Definition at line 452 of file sll_m_maxwell_clamped_1d_trafo.F90.

l2projection_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::l2projection_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped solver class
	func	Function
[in]	degree	Specify the degree of the basis functions
[out]	coefs_dofs	Spline coefficients of projection

Definition at line 430 of file sll_m_maxwell_clamped_1d_trafo.F90.

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multiply_g()

subroutine sll_m_maxwell_clamped_1d_trafo::multiply_g ( class(sll_t_maxwell_clamped_1d_trafo), intent(in)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out  )

private

Multiply by dicrete gradient matrix.

Parameters

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

Definition at line 706 of file sll_m_maxwell_clamped_1d_trafo.F90.

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multiply_gt()

subroutine sll_m_maxwell_clamped_1d_trafo::multiply_gt ( class(sll_t_maxwell_clamped_1d_trafo), intent(in)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out  )

private

Multiply by transpose of dicrete gradient matrix.

Parameters

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

Definition at line 717 of file sll_m_maxwell_clamped_1d_trafo.F90.

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multiply_mass_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::multiply_mass_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  in, real(kind=f64), dimension(:), intent(out)  out, integer(kind=i32), intent(in)  degree  )

private

Multiply by the mass matrix.

Parameters

[in,out]	self	Maxwell_Clamped 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 728 of file sll_m_maxwell_clamped_1d_trafo.F90.

sll_s_compute_b_from_e_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::sll_s_compute_b_from_e_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped solver class
[in]	delta_t	Time step

Definition at line 151 of file sll_m_maxwell_clamped_1d_trafo.F90.

sll_s_compute_curl_part_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::sll_s_compute_curl_part_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  self, intent(in)  delta_t, dimension(:), intent(inout)  efield, dimension(:), intent(inout)  bfield, optional  betar  )

private

Solve curl part of Maxwell's equations.

Parameters

self	Maxwell_Clamped solver class

Definition at line 165 of file sll_m_maxwell_clamped_1d_trafo.F90.

sll_s_compute_e_from_b_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::sll_s_compute_e_from_b_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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_Clamped solver class
[in]	delta_t	Time step
[in]	field_in	Bz
[in,out]	field_out	Ey

Definition at line 133 of file sll_m_maxwell_clamped_1d_trafo.F90.

sll_s_compute_e_from_rho_1d_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::sll_s_compute_e_from_rho_1d_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

compute e from rho using weak Poisson's equation ( rho = G^T M_1 G \phi, e = -G \phi )

Parameters

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

Definition at line 208 of file sll_m_maxwell_clamped_1d_trafo.F90.

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sll_s_compute_rhs_trafo()

subroutine sll_m_maxwell_clamped_1d_trafo::sll_s_compute_rhs_trafo ( class(sll_t_maxwell_clamped_1d_trafo)  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 clamped 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_Clamped solver class
	func	Function
[in]	degree	Specify the degree of the basis functions
[out]	coefs_dofs	Finite Element right-hand-side

Definition at line 294 of file sll_m_maxwell_clamped_1d_trafo.F90.

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