m_bessel Module Reference

Module for Bessel functions and their zeros. More...

Functions/Subroutines
pure real(wp) function, public	bessel_jn_zero (n, m)
	Compute the m-th zero of the Bessel function of the first kind of order n.
pure real(wp) function, public	bessel_jn_prime_zero (n, m)
	Compute the m-th zero of the derivative of the Bessel function of the first kind of order n.
pure real(wp) function, public	bessel_jn_derivative (n, x)
	Compute the derivative of the Bessel function of the first kind of order n at point x.
subroutine, public	disc_laplace_eigenvalues (lambda_r, n, lambda_target)
	Compute the m-th eigenvalues of the Laplace operator on the unit disk.
subroutine, public	disc_curlcurl_eigenvalues (lambda_r, n, lambda_target)
	Compute the m-th eigenvalues of the curlcurl operator on the unit disk.
subroutine, public	init_manufactured_solution_bessel (n, m, major_radius, minor_radius)
	Initialize the parameters for the manufactured solution involving Bessel functions.
pure real(wp) function, public	toroidal_zeroform (xp, yp, zp)
	Manufactured solution for the toroidal domain, zero-form.
pure real(wp) function, public	toroidal_oneform_x (xp, yp, zp)
	Manufactured solution for the toroidal domain, one-form.
pure real(wp) function, public	toroidal_oneform_y (xp, yp, zp)
	Manufactured solution for the toroidal domain, one-form.
pure real(wp) function, public	toroidal_oneform_z (xp, yp, zp)
	Manufactured solution for the toroidal domain, one-form.
pure real(wp) function, public	toroidal_twoform_x (xp, yp, zp)
	Manufactured solution for the toroidal domain, two-form.
pure real(wp) function, public	toroidal_twoform_y (xp, yp, zp)
	Manufactured solution for the toroidal domain, two-form.
pure real(wp) function, public	toroidal_twoform_z (xp, yp, zp)
	Manufactured solution for the toroidal domain, two-form.
pure real(wp) function, public	toroidal_threeform (xp, yp, zp)
	Manufactured solution for the toroidal domain, three-form.

Detailed Description

Module for Bessel functions and their zeros.

Function/Subroutine Documentation

bessel_jn_derivative()

pure real(wp) function, public m_bessel::bessel_jn_derivative	(	integer, intent(in)	n,
		real(wp), intent(in)	x )

Compute the derivative of the Bessel function of the first kind of order n at point x.

Parameters

[in]	n	The order of the Bessel function
[in]	x	The point at which to evaluate the derivative

Returns

The value of the derivative

bessel_jn_prime_zero()

pure real(wp) function, public m_bessel::bessel_jn_prime_zero	(	integer, intent(in)	n,
		integer, intent(in)	m )

Compute the m-th zero of the derivative of the Bessel function of the first kind of order n.

Parameters

[in]	n	The order of the Bessel function
[in]	m	The index of the zero

Returns

The m-th zero of the derivative of the Bessel function of the first kind of order n

bessel_jn_zero()

pure real(wp) function, public m_bessel::bessel_jn_zero	(	integer, intent(in)	n,
		integer, intent(in)	m )

Compute the m-th zero of the Bessel function of the first kind of order n.

Parameters

[in]	n	The order of the Bessel function
[in]	m	The index of the zero

Returns

The m-th zero of the Bessel function of the first kind of order n

disc_curlcurl_eigenvalues()

subroutine, public m_bessel::disc_curlcurl_eigenvalues	(	real(wp), dimension(:), intent(out), allocatable	lambda_r,
		integer, intent(in)	n,
		real(wp), intent(in), optional	lambda_target )

Compute the m-th eigenvalues of the curlcurl operator on the unit disk.

Parameters

[in]	lambda_r	The real part of the eigenvalues
[in]	n	The number of eigenvalues to compute
[in]	lambda_target	_(optional)_ Target eigenvalue (default: 0)

disc_laplace_eigenvalues()

subroutine, public m_bessel::disc_laplace_eigenvalues	(	real(wp), dimension(:), intent(out), allocatable	lambda_r,
		integer, intent(in)	n,
		real(wp), intent(in), optional	lambda_target )

Compute the m-th eigenvalues of the Laplace operator on the unit disk.

Parameters

[in]	lambda_r	The real part of the eigenvalues
[in]	n	The number of eigenvalues to compute
[in]	lambda_target	_(optional)_ Target eigenvalue (default: 0)

init_manufactured_solution_bessel()

subroutine, public m_bessel::init_manufactured_solution_bessel	(	integer, intent(in)	n,
		integer, intent(in)	m,
		real(wp), intent(in)	major_radius,
		real(wp), intent(in)	minor_radius )

Initialize the parameters for the manufactured solution involving Bessel functions.

Parameters

[in]	n	The order of the Bessel function
[in]	m	The index of the zero
[in]	major_radius	The major radius of the torus
[in]	minor_radius	The minor radius of the torus

toroidal_oneform_x()

pure real(wp) function, public m_bessel::toroidal_oneform_x	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, one-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The first component of the one-form

toroidal_oneform_y()

pure real(wp) function, public m_bessel::toroidal_oneform_y	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, one-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The second component of the one-form

toroidal_oneform_z()

pure real(wp) function, public m_bessel::toroidal_oneform_z	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, one-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The third component of the one-form

toroidal_threeform()

pure real(wp) function, public m_bessel::toroidal_threeform	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, three-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The value of the three-form

toroidal_twoform_x()

pure real(wp) function, public m_bessel::toroidal_twoform_x	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, two-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The first component of the two-form

toroidal_twoform_y()

pure real(wp) function, public m_bessel::toroidal_twoform_y	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, two-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The second component of the two-form

toroidal_twoform_z()

pure real(wp) function, public m_bessel::toroidal_twoform_z	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, two-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The third component of the two-form

toroidal_zeroform()

pure real(wp) function, public m_bessel::toroidal_zeroform	(	real(wp), intent(in)	xp,
		real(wp), intent(in)	yp,
		real(wp), intent(in)	zp )

Manufactured solution for the toroidal domain, zero-form.

Parameters

[in]	xp	The first logical coordinate
[in]	yp	The second logical coordinate
[in]	zp	The third logical coordinate

Returns

The value of the zero-form