sll_m_maxwell_2d_fem_fft Module Reference

Description

Module interface to solve Maxwell's equations in 2D The linear systems are solved based on FFT diagnoalization.

Author

Katharina Kormann

Derived types and interfaces
type	sll_t_maxwell_2d_fem_fft
interface	sll_i_function_2d_real64
	2d real function More...

Functions/Subroutines
subroutine	compute_rho_from_e_2d_fem (self, efield, rho)
	compute rho from e using weak Gauss law ( rho = G^T M_1 e ) More...
subroutine	sll_s_compute_e_from_b_2d_fem (self, delta_t, field_in, field_out)
	compute Ey from Bz using weak Ampere formulation More...
subroutine	sll_s_compute_b_from_e_2d_fem (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	compute_e_from_j_2d_fem (self, current, component, E)
	Compute E_i from j_i integrated over the time interval using weak Ampere formulation. More...
subroutine	sll_s_compute_e_from_rho_2d_fem (self, rho, E)
subroutine	sll_s_compute_fem_rhs (self, func, component, form, 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_2d_fem (self, func, component, form, coefs_dofs)
	Compute the L2 projection of a given function f on periodic splines of given degree. More...
real(kind=f64) function	l2norm_squared_2d_fem (self, coefs_dofs, component, form)
	Compute square of the L2norm. More...
real(kind=f64) function	inner_product_2d_fem (self, coefs1_dofs, coefs2_dofs, component, form)
subroutine	init_2d_fem (self, domain, n_dofs, s_deg_0)
subroutine	free_2d_fem (self)
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_gt (self, field_in, field_out)
	Multiply by transpose of dicrete gradient matrix. More...
subroutine	multiply_mass_1form (self, coefs_in, coefs_out)
subroutine	multiply_mass_2form (self, coefs_in, coefs_out)
subroutine	multiply_mass_2dkron (self, mass_line_1, mass_line_2, 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...

Function/Subroutine Documentation

compute_e_from_j_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::compute_e_from_j_2d_fem ( class(sll_t_maxwell_2d_fem_fft)  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 178 of file sll_m_maxwell_2d_fem_fft.F90.

compute_rho_from_e_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::compute_rho_from_e_2d_fem	(	class(sll_t_maxwell_2d_fem_fft)	self,
		real(kind=f64), dimension(:), intent(in)	efield,
		real(kind=f64), dimension(:), intent(inout)	rho
	)

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

Definition at line 119 of file sll_m_maxwell_2d_fem_fft.F90.

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free_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::free_2d_fem ( class(sll_t_maxwell_2d_fem_fft)  self )

private

Definition at line 479 of file sll_m_maxwell_2d_fem_fft.F90.

init_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::init_2d_fem ( class(sll_t_maxwell_2d_fem_fft), intent(out)  self, real(kind=f64), dimension(2,2), intent(in)  domain, integer(kind=i32), dimension(2), intent(in)  n_dofs, integer(kind=i32), intent(in)  s_deg_0  )

private

Parameters

[out]

self

solver object

Definition at line 398 of file sll_m_maxwell_2d_fem_fft.F90.

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inner_product_2d_fem()

real(kind=f64) function sll_m_maxwell_2d_fem_fft::inner_product_2d_fem ( class(sll_t_maxwell_2d_fem_fft)  self, real(kind=f64), dimension(:)  coefs1_dofs, real(kind=f64), dimension(:)  coefs2_dofs, integer(kind=i32)  component, integer(kind=i32)  form  )

private

Parameters

self	Maxwell solver object
coefs1_dofs	Coefficient for each DoF
coefs2_dofs	Coefficient for each DoF
component	Specify the component
form	Specify 0,1,2 or 3 form

Returns

Result: squared L2 norm

Definition at line 337 of file sll_m_maxwell_2d_fem_fft.F90.

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l2norm_squared_2d_fem()

real(kind=f64) function sll_m_maxwell_2d_fem_fft::l2norm_squared_2d_fem ( class(sll_t_maxwell_2d_fem_fft)  self, real(kind=f64), dimension(:)  coefs_dofs, integer(kind=i32)  component, integer(kind=i32)  form  )

private

Compute square of the L2norm.

Parameters

self	Maxwell solver object
coefs_dofs	Coefficient for each DoF
component	Specify the component
form	Specify 0,1,2 or 3 form

Returns

Result: squared L2 norm

Definition at line 323 of file sll_m_maxwell_2d_fem_fft.F90.

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l2projection_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::l2projection_2d_fem ( class(sll_t_maxwell_2d_fem_fft)  self, procedure(sll_i_function_2d_real64)  func, integer(kind=i32)  component, integer(kind=i32)  form, 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

component	Specify the component
form	Specify 0,1,2 or 3 form

Definition at line 294 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_c()

subroutine sll_m_maxwell_2d_fem_fft::multiply_c ( class(sll_t_maxwell_2d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

Multiply by discrete curl matrix.

Definition at line 490 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_ct()

subroutine sll_m_maxwell_2d_fem_fft::multiply_ct ( class(sll_t_maxwell_2d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

Multiply by transpose of discrete curl matrix.

Parameters

	self	Maxwell solver object
[in]	field_in	Matrix to be multiplied
[in,out]	field_out	C*field_in

Definition at line 601 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_gt()

subroutine sll_m_maxwell_2d_fem_fft::multiply_gt ( class(sll_t_maxwell_2d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  field_in, real(kind=f64), dimension(:), intent(inout)  field_out  )

private

Multiply by transpose of dicrete gradient matrix.

Parameters

	self	Maxwell solver object
[in]	field_in	Matrix to be multiplied
[in,out]	field_out	C*field_in

Definition at line 712 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_mass_1form()

subroutine sll_m_maxwell_2d_fem_fft::multiply_mass_1form ( class(sll_t_maxwell_2d_fem_fft), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Definition at line 768 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_mass_2dkron()

subroutine sll_m_maxwell_2d_fem_fft::multiply_mass_2dkron ( class(sll_t_maxwell_2d_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)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Multiply by the mass matrix.

Definition at line 824 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_mass_2form()

subroutine sll_m_maxwell_2d_fem_fft::multiply_mass_2form ( class(sll_t_maxwell_2d_fem_fft), intent(inout)  self, real(kind=f64), dimension(:), intent(in)  coefs_in, real(kind=f64), dimension(:), intent(out)  coefs_out  )

private

Definition at line 795 of file sll_m_maxwell_2d_fem_fft.F90.

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multiply_mass_all()

subroutine sll_m_maxwell_2d_fem_fft::multiply_mass_all ( class(sll_t_maxwell_2d_fem_fft), intent(inout)  self, integer(kind=i32), dimension(2), 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

[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)

Definition at line 863 of file sll_m_maxwell_2d_fem_fft.F90.

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sll_s_compute_b_from_e_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::sll_s_compute_b_from_e_2d_fem ( class(sll_t_maxwell_2d_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}) $.

Definition at line 163 of file sll_m_maxwell_2d_fem_fft.F90.

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sll_s_compute_e_from_b_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::sll_s_compute_e_from_b_2d_fem ( class(sll_t_maxwell_2d_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

[in]	delta_t	Time step
[in]	field_in	B
[in,out]	field_out	E

Definition at line 137 of file sll_m_maxwell_2d_fem_fft.F90.

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sll_s_compute_e_from_rho_2d_fem()

subroutine sll_m_maxwell_2d_fem_fft::sll_s_compute_e_from_rho_2d_fem ( class(sll_t_maxwell_2d_fem_fft)  self, real(kind=f64), dimension(:), intent(in)  rho, real(kind=f64), dimension(:), intent(out)  E  )

private

Definition at line 194 of file sll_m_maxwell_2d_fem_fft.F90.

sll_s_compute_fem_rhs()

subroutine sll_m_maxwell_2d_fem_fft::sll_s_compute_fem_rhs ( class(sll_t_maxwell_2d_fem_fft)  self, procedure(sll_i_function_2d_real64)  func, integer(kind=i32)  component, integer(kind=i32)  form, 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

component	Specify the component
form	Specify 0,1,2 or 3 form

Definition at line 206 of file sll_m_maxwell_2d_fem_fft.F90.

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