sll_m_maxwell_1d_fem_sm Module Reference

Description

Solve Maxwell's equations in 1D based on spline FEM, version based on sparse matrices.

Author

Katharina Kormann, Benedikt Perse

Derived types and interfaces
type	sll_t_maxwell_1d_fem_sm
	Maxwell solver class for spline FEM with sparse matrix solvers. More...

Functions/Subroutines
subroutine	sll_s_compute_e_from_b_1d_fem_sm (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_sm (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_fem_sm (self, delta_t, efield, bfield, betar)
	Solve curl part of Maxwell's equations. More...
subroutine	sll_s_compute_e_from_rho_1d_fem_sm (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_fem_sm (self, field_in, field_out)
	Compute rho from Gauss law for given efield. More...
subroutine	compute_e_from_j_1d_fem_sm (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_fem_sm (self, in, phi, efield)
	For model with adiabatic electrons. More...
subroutine	compute_phi_from_j_1d_fem_sm (self, in, phi, efield)
	For model with adiabatic electrons. More...
subroutine	sll_s_compute_rhs_fem_sm (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...
subroutine	l2projection_1d_fem_sm (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_fem_sm (self, coefs_dofs, degree)
	Compute square of the L2norm. More...
real(kind=f64) function	inner_product_1d_fem_sm (self, coefs1_dofs, coefs2_dofs, degree, degree2)
	Compute inner product. More...
subroutine	init_1d_fem_sm (self, domain, n_dofs, s_deg_0, delta_t, mass_tolerance, poisson_tolerance, solver_tolerance, force_sign, adiabatic_electrons)
	Initialization. More...
subroutine	init_from_file_1d_fem_sm (self, domain, n_dofs, s_deg_0, nml_file, force_sign, adiabatic_electrons)
	Initialization from nml file. More...
subroutine	free_1d_fem_sm (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_fem_sm (self, in, out, degree)
	Multiply by the mass matrix. More...
subroutine	invert_mass_1d_fem_sm (self, in, out, degree)
	Multiply by the inverse mass matrix. More...

Function/Subroutine Documentation

compute_e_from_j_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::compute_e_from_j_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 233 of file sll_m_maxwell_1d_fem_sm.F90.

compute_phi_from_j_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::compute_phi_from_j_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 272 of file sll_m_maxwell_1d_fem_sm.F90.

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compute_phi_from_rho_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::compute_phi_from_rho_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 255 of file sll_m_maxwell_1d_fem_sm.F90.

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compute_rho_from_e_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::compute_rho_from_e_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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
[in]	field_in	E
[out]	field_out	rho

Definition at line 220 of file sll_m_maxwell_1d_fem_sm.F90.

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free_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::free_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  self )

private

Finalization.

Parameters

self	Maxwell solver class

Definition at line 608 of file sll_m_maxwell_1d_fem_sm.F90.

init_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::init_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm), 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, real(kind=f64), intent(in), optional  mass_tolerance, real(kind=f64), intent(in), optional  poisson_tolerance, real(kind=f64), intent(in), optional  solver_tolerance, real(kind=f64), intent(in), optional  force_sign, logical, intent(in), optional  adiabatic_electrons  )

private

Initialization.

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]	mass_tolerance	tolerance for mass solver
[in]	poisson_tolerance	tolerance for Poisson solver
[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 425 of file sll_m_maxwell_1d_fem_sm.F90.

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init_from_file_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::init_from_file_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm), 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, character(len=*)  nml_file, real(kind=f64), intent(in), optional  force_sign, logical, intent(in), optional  adiabatic_electrons  )

private

Initialization from nml file.

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
	nml_file	nml-file
[in]	force_sign	sign of particle force
[in]	adiabatic_electrons	flag if adiabatic electrons are used

Definition at line 527 of file sll_m_maxwell_1d_fem_sm.F90.

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inner_product_1d_fem_sm()

real(kind=f64) function sll_m_maxwell_1d_fem_sm::inner_product_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 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 375 of file sll_m_maxwell_1d_fem_sm.F90.

invert_mass_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::invert_mass_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm), 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 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 664 of file sll_m_maxwell_1d_fem_sm.F90.

l2norm_squared_1d_fem_sm()

real(kind=f64) function sll_m_maxwell_1d_fem_sm::l2norm_squared_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 355 of file sll_m_maxwell_1d_fem_sm.F90.

l2projection_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::l2projection_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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
[out]	coefs_dofs	spline coefficients of projection

Definition at line 332 of file sll_m_maxwell_1d_fem_sm.F90.

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multiply_g()

subroutine sll_m_maxwell_1d_fem_sm::multiply_g ( class(sll_t_maxwell_1d_fem_sm), 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 solver class
[in]	in	field_in
[out]	out	G*field_in

Definition at line 620 of file sll_m_maxwell_1d_fem_sm.F90.

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multiply_gt()

subroutine sll_m_maxwell_1d_fem_sm::multiply_gt ( class(sll_t_maxwell_1d_fem_sm), 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 solver class
[in]	in	field_in
[out]	out	G^T*field_in

Definition at line 631 of file sll_m_maxwell_1d_fem_sm.F90.

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multiply_mass_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::multiply_mass_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm), 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 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 642 of file sll_m_maxwell_1d_fem_sm.F90.

sll_s_compute_b_from_e_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::sll_s_compute_b_from_e_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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

Definition at line 149 of file sll_m_maxwell_1d_fem_sm.F90.

sll_s_compute_curl_part_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::sll_s_compute_curl_part_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 solver class

Definition at line 163 of file sll_m_maxwell_1d_fem_sm.F90.

sll_s_compute_e_from_b_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::sll_s_compute_e_from_b_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 131 of file sll_m_maxwell_1d_fem_sm.F90.

sll_s_compute_e_from_rho_1d_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::sll_s_compute_e_from_rho_1d_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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 solver class
[in]	field_in	rho
[out]	field_out	E

Definition at line 206 of file sll_m_maxwell_1d_fem_sm.F90.

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sll_s_compute_rhs_fem_sm()

subroutine sll_m_maxwell_1d_fem_sm::sll_s_compute_rhs_fem_sm ( class(sll_t_maxwell_1d_fem_sm)  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
[out]	coefs_dofs	Finite Element right-hand-side

Definition at line 294 of file sll_m_maxwell_1d_fem_sm.F90.

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