sll_m_maxwell_3d_fem_fft Module Reference

Description

Module interface to solve Maxwell's equations in 3D The linear systems are solved based on FFT diagnoalization.

Author

Katharina Kormann

Derived types and interfaces
type	sll_t_maxwell_3d_fem_fft

Functions/Subroutines
subroutine	sll_s_compute_e_from_b_3d_fem_fft (self, delta_t, field_in, field_out)
	compute Ey from Bz using weak Ampere formulation More...
subroutine	sll_s_compute_b_from_e_3d_fem_fft (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_3d_fem_fft (self, delta_t, efield, bfield, betar)
	Solve curl part of Maxwell's equations. More...
subroutine	sll_s_compute_e_from_rho_3d_fem_fft (self, field_in, field_out)
	Compute E_i from rho_i integrated over the time interval using weak Poisson's equation. More...
subroutine	sll_s_compute_rho_from_e_3d_fem_fft (self, field_in, field_out)
	compute rho from e using weak Gauss law ( rho = G^T M_1 e ) More...
subroutine	sll_s_compute_e_from_j_3d_fem_fft (self, current, E, component)
	Compute E_i from j_i integrated over the time interval using weak Ampere formulation. More...
subroutine	sll_s_compute_phi_from_rho_3d_fem_fft (self, field_in, field_out, efield_dofs)
	Compute phi from rho_i integrated over the time interval. More...
subroutine	sll_s_compute_phi_from_j_3d_fem_fft (self, field_in, field_out, efield_dofs)
	Compute phi from j_i integrated over the time interval, delta_t is already included. More...
subroutine	sll_s_compute_rhs_fem_fft (self, form, component, coefs_dofs, func1, func2, func3)
	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_3d_fem_fft (self, form, component, coefs_dofs, func1, func2, func3)
	Compute the L2 projection of a given function f on periodic splines of given degree. More...
real(kind=f64) function	l2norm_squared_3d_fem_fft (self, coefs, form, component)
	Compute square of the L2norm. More...
real(kind=f64) function	inner_product_3d_fem_fft (self, coefs1, coefs2, form, component)
	Compute inner product. More...
subroutine	init_3d_fem_fft (self, domain, n_dofs, s_deg_0, adiabatic_electrons, profile)
	Initialization. More...
subroutine	free_3d_fem_fft (self)
	Finalization. More...
subroutine	multiply_g (self, field_in, field_out)
	Multiply by dicrete gradient matrix. More...
subroutine	multiply_gt (self, field_in, field_out)
	Multiply by transpose of dicrete gradient matrix. More...
subroutine	multiply_c (self, field_in, field_out)
	Multiply by discrete curl matrix. More...
subroutine	multiply_ct (self, field_in, field_out)
	Multiply by transpose of discrete curl matrix. More...
subroutine	multiply_mass_3d_fem_fft (self, deg, coefs_in, coefs_out)
	Multiply by the mass matrix. More...
subroutine	multiply_mass_1form (self, coefs_in, coefs_out)
	Helper function for multiply_mass. More...
subroutine	multiply_mass_2form (self, coefs_in, coefs_out)
	Helper function for multiply_mass. More...
subroutine	multiply_mass_3dkron (self, mass_line_1, mass_line_2, mass_line_3, coefs_in, coefs_out)
	Multiply by the mass matrix. More...
subroutine	multiply_mass_all (self, deg, coefs_in, coefs_out)
	Multiply by the mass matrix. More...
subroutine	multiply_mass_inverse_all (self, form, coefs_in, coefs_out)
	Multiply by the inverse mass matrix. More...

Function/Subroutine Documentation

free_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::free_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self )

private

Finalization.

Parameters

self	Maxwell solver class

Definition at line 721 of file sll_m_maxwell_3d_fem_fft.F90.

init_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::init_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft), intent(out)  self, real(kind=f64), dimension(3,2), intent(in)  domain, integer(kind=i32), dimension(3), intent(in)  n_dofs, integer(kind=i32), dimension(3), intent(in)  s_deg_0, logical, intent(in), optional  adiabatic_electrons, type(sll_t_profile_functions), intent(in), optional  profile  )

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]	adiabatic_electrons	flag if adiabatic electrons are used
[in]	profile	temperature and density profiles

Definition at line 513 of file sll_m_maxwell_3d_fem_fft.F90.

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inner_product_3d_fem_fft()

real(kind=f64) function sll_m_maxwell_3d_fem_fft::inner_product_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:)  coefs1, real(kind=f64), dimension(:)  coefs2, integer(kind=i32)  form, integer(kind=i32), optional  component  )

private

Compute inner product.

Parameters

self	Maxwell solver class
coefs1	Coefficient for each DoF
coefs2	Coefficient for each DoF
form	Specify 0,1,2 or 3 form
component	Specify the component

Returns

Result: squared L2 norm

Definition at line 451 of file sll_m_maxwell_3d_fem_fft.F90.

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l2norm_squared_3d_fem_fft()

real(kind=f64) function sll_m_maxwell_3d_fem_fft::l2norm_squared_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:)  coefs, integer(kind=i32)  form, integer(kind=i32)  component  )

private

Compute square of the L2norm.

Parameters

self	Maxwell solver class
coefs	Coefficient for each DoF
form	Specify 0,1,2 or 3-form
component	Specify the component of the form

Returns

Result: squared L2 norm

Definition at line 438 of file sll_m_maxwell_3d_fem_fft.F90.

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l2projection_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::l2projection_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, integer(kind=i32), intent(in)  form, integer(kind=i32), intent(in)  component, real(kind=f64), dimension(:), intent(out)  coefs_dofs, procedure(sll_i_function_3d_real64)  func1, procedure(sll_i_function_3d_real64), optional  func2, procedure(sll_i_function_3d_real64), optional  func3  )

private

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

Parameters

	self	Maxwell solver class
[in]	form	Specify if the function is a0,1,2 or 3-form
[in]	component	Specify the component of the function
[out]	coefs_dofs	Finite Element right-hand-side
	func1	Function first component
	func2	Function second component
	func3	Function third component

Definition at line 411 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_c()

subroutine sll_m_maxwell_3d_fem_fft::multiply_c ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Multiply by discrete curl matrix.

Parameters

	self	Maxwell solver class
[out]	field_out	C*field_in

Definition at line 777 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_ct()

subroutine sll_m_maxwell_3d_fem_fft::multiply_ct ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Multiply by transpose of discrete curl matrix.

Parameters

	self	Maxwell solver class
[out]	field_out	C^T*field_in

Definition at line 788 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_g()

subroutine sll_m_maxwell_3d_fem_fft::multiply_g ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Multiply by dicrete gradient matrix.

Parameters

	self	Maxwell solver class
[out]	field_out	G*field_in

Definition at line 755 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_gt()

subroutine sll_m_maxwell_3d_fem_fft::multiply_gt ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Multiply by transpose of dicrete gradient matrix.

Parameters

	self	Maxwell solver class
[out]	field_out	G^T*field_in

Definition at line 766 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_mass_1form()

subroutine sll_m_maxwell_3d_fem_fft::multiply_mass_1form ( class(sll_t_maxwell_3d_fem_fft), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Helper function for multiply_mass.

Parameters

[in,out]	self	Maxwell solver class
[in]	coefs_in	Coefficient for each DoF
[out]	coefs_out	Coefficient for each DoF

Definition at line 826 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_mass_2form()

subroutine sll_m_maxwell_3d_fem_fft::multiply_mass_2form ( class(sll_t_maxwell_3d_fem_fft), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Helper function for multiply_mass.

Parameters

[in,out]	self	Maxwell solver class
[in]	coefs_in	Coefficient for each DoF
[out]	coefs_out	Coefficient for each DoF

Definition at line 853 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_mass_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::multiply_mass_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, integer(kind=i32), dimension(:), intent(in)  deg, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Multiply by the mass matrix.

Parameters

	self	Maxwell solver class
[in]	deg	deg/form specifies if we multiply the mass to a 1- or 2-form or a mix of both
[in]	coefs_in	Coefficient for each DoF
[out]	coefs_out	Coefficient for each DoF

Definition at line 799 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_mass_3dkron()

subroutine sll_m_maxwell_3d_fem_fft::multiply_mass_3dkron ( class(sll_t_maxwell_3d_fem_fft), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  mass_line_1, real(kind=f64), dimension(:), intent(in)  mass_line_2, real(kind=f64), dimension(:), intent(in)  mass_line_3, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Multiply by the mass matrix.

Parameters

[in,out]	self	Maxwell solver class
[in]	mass_line_1	massline
[in]	mass_line_2	massline
[in]	mass_line_3	massline
[in]	coefs_in	Coefficient for each DoF
[out]	coefs_out	Coefficient for each DoF

Definition at line 880 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_mass_all()

subroutine sll_m_maxwell_3d_fem_fft::multiply_mass_all ( class(sll_t_maxwell_3d_fem_fft)  self, integer(kind=i32), dimension(:), intent(in)  deg, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Multiply by the mass matrix.

Parameters

	self	Maxwell solver class
[in]	deg	deg(i) specifies the degree of the 1d mass matrix in dimension i (Note: 1 for 0-form, 2 for 1-form, 3 for 0-1-form mix)
[in]	coefs_in	Coefficient for each DoF
[out]	coefs_out	Coefficient for each DoF

Definition at line 939 of file sll_m_maxwell_3d_fem_fft.F90.

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multiply_mass_inverse_all()

subroutine sll_m_maxwell_3d_fem_fft::multiply_mass_inverse_all ( class(sll_t_maxwell_3d_fem_fft)  self, integer(kind=i32), intent(in)  form, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Multiply by the inverse mass matrix.

Parameters

	self	Maxwell solver class
[in]	form	form specifies the form (Note: 0 for 0-form, 1 for 1-form, 2 for 2-form, 3 for 0-1-form mix)
[in]	coefs_in	Coefficient for each DoF
[out]	coefs_out	Coefficient for each DoF

Definition at line 1020 of file sll_m_maxwell_3d_fem_fft.F90.

sll_s_compute_b_from_e_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_b_from_e_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  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	E
[in,out]	field_out	B

Definition at line 179 of file sll_m_maxwell_3d_fem_fft.F90.

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sll_s_compute_curl_part_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_curl_part_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  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 193 of file sll_m_maxwell_3d_fem_fft.F90.

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sll_s_compute_e_from_b_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_e_from_b_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  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	B
[in,out]	field_out	E

Definition at line 153 of file sll_m_maxwell_3d_fem_fft.F90.

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sll_s_compute_e_from_j_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_e_from_j_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  current, real(kind=f64), dimension(:), intent(inout)  E, integer(kind=i32), intent(in), optional  component  )

private

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

Parameters

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

Definition at line 256 of file sll_m_maxwell_3d_fem_fft.F90.

sll_s_compute_e_from_rho_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_e_from_rho_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

Compute E_i from rho_i integrated over the time interval using weak Poisson's equation.

Parameters

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

Definition at line 231 of file sll_m_maxwell_3d_fem_fft.F90.

sll_s_compute_phi_from_j_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_phi_from_j_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out, real(kind=f64), dimension(:), intent(out)  efield_dofs  )

private

Compute phi from j_i integrated over the time interval, delta_t is already included.

Parameters

	self	Maxwell solver class
[in]	field_in	Current integrated over time interval
[in,out]	field_out	phi
[out]	efield_dofs	E

Definition at line 290 of file sll_m_maxwell_3d_fem_fft.F90.

sll_s_compute_phi_from_rho_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_phi_from_rho_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out, real(kind=f64), dimension(:), intent(out)  efield_dofs  )

private

Compute phi from rho_i integrated over the time interval.

Parameters

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

Definition at line 276 of file sll_m_maxwell_3d_fem_fft.F90.

sll_s_compute_rho_from_e_3d_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_rho_from_e_3d_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(out)  field_out  )

private

compute rho from e using weak Gauss law ( rho = G^T M_1 e )

Parameters

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

Definition at line 243 of file sll_m_maxwell_3d_fem_fft.F90.

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sll_s_compute_rhs_fem_fft()

subroutine sll_m_maxwell_3d_fem_fft::sll_s_compute_rhs_fem_fft ( class(sll_t_maxwell_3d_fem_fft)  self, integer(kind=i32), intent(in)  form, integer(kind=i32), intent(in)  component, real(kind=f64), dimension(:), intent(out)  coefs_dofs, procedure(sll_i_function_3d_real64)  func1, procedure(sll_i_function_3d_real64), optional  func2, procedure(sll_i_function_3d_real64), optional  func3  )

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
[in]	form	Specify if the function is a0,1,2 or 3-form
[in]	component	Specify the component of the function
[out]	coefs_dofs	Finite Element right-hand-side
	func1	Function first component
	func2	Function second component
	func3	Function third component

Definition at line 308 of file sll_m_maxwell_3d_fem_fft.F90.

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