sll_m_spline_fem_utilities Module Reference

Description

Utilites for Maxwell solver's with spline finite elements.

Author

Katharina Kormann

Derived types and interfaces
interface	sll_i_profile_function_1d

Functions/Subroutines
subroutine, public	sll_s_spline_fem_mass_line (degree, mass_line)
	Computes the mass line for a mass matrix with degree splines. More...
subroutine, public	sll_s_spline_fem_mass_line_boundary (degree, spline, mass_line)
	Function computing the boundary part for a mass matrix with clamped splines of degree. More...
subroutine, public	sll_s_spline_fem_mass_line_boundary_full (deg, profile, spline, row, n_cells, mass_line)
	Function computing the boundary part for a mass matrix with clamped splines of degree (full version without symmetry part) More...
subroutine, public	sll_s_spline_fem_mass_line_full (deg, profile, mass_line, row, n_cells)
	Helper function to find line of mass matrix (full version without symmetry part) More...
subroutine, public	sll_s_spline_fem_mixedmass_line_boundary (deg1, deg2, profile, spline1, spline2, row, n_cells, mass_line)
	Function computing the boundary part for a mass matrix with clamped splines of degree (full version without symmetry part) More...
subroutine, public	sll_s_spline_fem_mixedmass_line_full (deg1, deg2, profile, mass_line, cell, n_cells)
	Helper function to find line of mass matrix ( N_i^p N_j^{p-1})) More...
subroutine, public	sll_s_spline_fem_mixedmass_line (deg, mass_line)
	Helper function to find line of mass matrix ( N_i^p N_j^{p-1})) More...
subroutine, public	sll_s_spline_fem_compute_mass_eig (n_cells, degree, mass_line, eig_values_mass)
	Compute eigenvalues of mass matrix with given line mass_line. More...
subroutine, public	sll_s_spline_fem_multiply_mass (n_cells, degree, mass, invec, outvec)
	Multiply the vector invec with the spline FEM mass matrix with mass line mass. More...
subroutine, public	sll_s_spline_fem_multiply_massmixed (n_cells, degree, mass, invec, outvec)
	Multiplication of the mix mass matrix given by a mass line mass. More...
subroutine, public	sll_s_spline_fem_interpolation_eigenvalues (degree, ndofs, eig)
	Compute the eigenvalues of the interpolation matrix for splines of degree degree (with first grid point as starting point of the first spline) The interpolation is for the Greville points, i.e. the grid points for odd degree and the midpoints for even degree. The grid points are numbered as they appear in the grid and the first mid point is the one in the first cell. More...
subroutine, public	sll_s_multiply_g_1d (n_dofs, delta_x, in, out)
	Multiplication of the input vector in by the derivative matrix G. More...
subroutine, public	sll_s_multiply_gt_1d (n_dofs, delta_x, in, out)
	Multiplication of the input vector in by the transposed derivative matrix G^T More...
subroutine, public	sll_s_multiply_g (n_dofs, delta_x, field_in, field_out)
	Multiply by dicrete gradient matrix (3d version) More...
subroutine, public	sll_s_multiply_gt (n_dofs, delta_x, field_in, field_out)
	Multiply by transpose of dicrete gradient matrix (3d version) More...
subroutine, public	sll_s_multiply_c (n_dofs, delta_x, field_in, field_out)
	Multiply by discrete curl matrix. More...
subroutine, public	sll_s_multiply_ct (n_dofs, delta_x, field_in, field_out)
	Multiply by transpose of discrete curl matrix. More...

Function/Subroutine Documentation

sll_s_multiply_c()

subroutine, public sll_m_spline_fem_utilities::sll_s_multiply_c	(	dimension(3), intent(in)	n_dofs,
		dimension(3), intent(in)	delta_x,
		dimension(:), intent(in)	field_in,
		dimension(:), intent(out)	field_out
	)

Multiply by discrete curl matrix.

Definition at line 927 of file sll_m_spline_fem_utilities.F90.

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sll_s_multiply_ct()

subroutine, public sll_m_spline_fem_utilities::sll_s_multiply_ct	(	dimension(3), intent(in)	n_dofs,
		dimension(3), intent(in)	delta_x,
		dimension(:), intent(in)	field_in,
		dimension(:), intent(out)	field_out
	)

Multiply by transpose of discrete curl matrix.

Definition at line 1057 of file sll_m_spline_fem_utilities.F90.

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sll_s_multiply_g()

subroutine, public sll_m_spline_fem_utilities::sll_s_multiply_g	(	dimension(3), intent(in)	n_dofs,
		dimension(3), intent(in)	delta_x,
		dimension(:), intent(in)	field_in,
		dimension(:), intent(out)	field_out
	)

Multiply by dicrete gradient matrix (3d version)

Definition at line 771 of file sll_m_spline_fem_utilities.F90.

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sll_s_multiply_g_1d()

subroutine, public sll_m_spline_fem_utilities::sll_s_multiply_g_1d	(	intent(in)	n_dofs,
		intent(in)	delta_x,
		dimension(:), intent(in)	in,
		dimension(:), intent(out)	out
	)

Multiplication of the input vector in by the derivative matrix G.

Definition at line 733 of file sll_m_spline_fem_utilities.F90.

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sll_s_multiply_gt()

subroutine, public sll_m_spline_fem_utilities::sll_s_multiply_gt	(	dimension(3), intent(in)	n_dofs,
		dimension(3), intent(in)	delta_x,
		dimension(:), intent(in)	field_in,
		dimension(:), intent(out)	field_out
	)

Multiply by transpose of dicrete gradient matrix (3d version)

Definition at line 845 of file sll_m_spline_fem_utilities.F90.

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sll_s_multiply_gt_1d()

subroutine, public sll_m_spline_fem_utilities::sll_s_multiply_gt_1d	(	intent(in)	n_dofs,
		intent(in)	delta_x,
		dimension(:), intent(in)	in,
		dimension(:), intent(out)	out
	)

Multiplication of the input vector in by the transposed derivative matrix G^T

Definition at line 752 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_compute_mass_eig()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_compute_mass_eig	(	intent(in)	n_cells,
		intent(in)	degree,
		dimension(0:degree), intent(in)	mass_line,
		dimension(n_cells), intent(out)	eig_values_mass
	)

Compute eigenvalues of mass matrix with given line mass_line.

Definition at line 571 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_interpolation_eigenvalues()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_interpolation_eigenvalues	(	intent(in)	degree,
		intent(in)	ndofs,
		dimension(ndofs), intent(out)	eig
	)

Compute the eigenvalues of the interpolation matrix for splines of degree degree (with first grid point as starting point of the first spline) The interpolation is for the Greville points, i.e. the grid points for odd degree and the midpoints for even degree. The grid points are numbered as they appear in the grid and the first mid point is the one in the first cell.

Definition at line 689 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mass_line()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mass_line	(	intent(in)	degree,
		dimension(degree+1), intent(out)	mass_line
	)

Computes the mass line for a mass matrix with degree splines.

Definition at line 64 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mass_line_boundary()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mass_line_boundary	(	intent(in)	degree,
		type(sll_t_spline_pp_1d), intent(in)	spline,
		dimension(:), intent(out)	mass_line
	)

Function computing the boundary part for a mass matrix with clamped splines of degree.

Parameters

[in]

spline

pp spline class

Definition at line 98 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mass_line_boundary_full()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mass_line_boundary_full	(	intent(in)	deg,
		procedure(sll_i_profile_function_1d)	profile,
		type(sll_t_spline_pp_1d), intent(in)	spline,
		intent(in)	row,
		intent(in)	n_cells,
		dimension((7*deg**2-deg-2)/2), intent(out)	mass_line
	)

Function computing the boundary part for a mass matrix with clamped splines of degree (full version without symmetry part)

Parameters

	profile	profile function
[in]	spline	pp spline class

Definition at line 234 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mass_line_full()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mass_line_full	(	intent(in)	deg,
		procedure(sll_i_profile_function_1d)	profile,
		dimension(2*deg+1), intent(out)	mass_line,
		intent(in)	row,
		intent(in)	n_cells
	)

Helper function to find line of mass matrix (full version without symmetry part)

Parameters

profile

profile function

Definition at line 309 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mixedmass_line()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mixedmass_line	(	intent(in)	deg,
		dimension(deg*2), intent(out)	mass_line
	)

Helper function to find line of mass matrix ( N_i^p N_j^{p-1}))

Definition at line 525 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mixedmass_line_boundary()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mixedmass_line_boundary	(	intent(in)	deg1,
		intent(in)	deg2,
		procedure(sll_i_profile_function_1d)	profile,
		type(sll_t_spline_pp_1d), intent(in)	spline1,
		type(sll_t_spline_pp_1d), intent(in)	spline2,
		intent(in)	row,
		intent(in)	n_cells,
		dimension( (deg1+deg2)**2+(2*deg2+deg1-deg1**2)/2 ), intent(out)	mass_line
	)

Function computing the boundary part for a mass matrix with clamped splines of degree (full version without symmetry part)

Parameters

	profile	profile function
[in]	spline1	1D pp-spline
[in]	spline2	1D pp-spline

Definition at line 365 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_mixedmass_line_full()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_mixedmass_line_full	(	intent(in)	deg1,
		intent(in)	deg2,
		procedure(sll_i_profile_function_1d)	profile,
		dimension(deg1+deg2+1), intent(out)	mass_line,
		intent(in)	cell,
		intent(in)	n_cells
	)

Helper function to find line of mass matrix ( N_i^p N_j^{p-1}))

Parameters

profile

profile function

Definition at line 465 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_multiply_mass()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_multiply_mass	(	intent(in)	n_cells,
		intent(in)	degree,
		dimension(degree+1), intent(in)	mass,
		dimension(:), intent(in)	invec,
		dimension(:), intent(out)	outvec
	)

Multiply the vector invec with the spline FEM mass matrix with mass line mass.

Definition at line 593 of file sll_m_spline_fem_utilities.F90.

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sll_s_spline_fem_multiply_massmixed()

subroutine, public sll_m_spline_fem_utilities::sll_s_spline_fem_multiply_massmixed	(	intent(in)	n_cells,
		intent(in)	degree,
		dimension(degree*2), intent(in)	mass,
		dimension(:), intent(in)	invec,
		dimension(:), intent(out)	outvec
	)

Multiplication of the mix mass matrix given by a mass line mass.

Definition at line 643 of file sll_m_spline_fem_utilities.F90.

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