Module to create quadrature matrices and accompanying routines for SDC. More...

Data Types
interface	poly_eval

Functions/Subroutines
subroutine	sdc_quadrature (qtype_in, nnodes, nnodes0, nodes, nflags, qmats)
	Subroutine to create quadrature matrices. More...

logical function	not_proper (flags, node)
	Function to decide if the restriction of the nodes is pointwise, e.g. coarse nodes are every other fine node. More...

subroutine	sdc_qnodes (qnodes, flags, qtype, nnodes)
	Subroutine to compute high precision quadrature nodes. More...

subroutine	sdc_qmats (qmat, smat, dst, src, flags, ndst, nsrc)
	Subroutine to compute the quadrature matrices. More...

real(qp) function	poly_eval (p, n, x)
	Polynomial manipulation routines. More...

complex(qp) function	poly_eval_complex (p, n, x)
	Function to evaluate complex polynomial. More...

subroutine	poly_diff (p, n)
	Subroutine to differentiate polynomial (in place) More...

subroutine	poly_int (p, n)
	Subroutine to integrate polynomial (in place) More...

subroutine	poly_legendre (p, n)
	Subroutine to compute Legendre polynomial coefficients using Bonnet's recursion formula. More...

subroutine	poly_roots (roots, p0, n)
	Subroutine to compute polynomial roots using the Durand-Kerner algorithm. The roots are assumed to be real. More...

recursive subroutine	qsort (a)
	Subroutine to sort (inplace) using the quick sort algorithm. Adapted from http://www.fortran.com/qsort_c.f95. More...

subroutine, private	qsort_partition (a, marker)

Variables
integer, parameter	qp = c_long_double

integer, parameter	dp = c_double

real(qp), parameter	eps = 1.0e-23_qp

integer, parameter	sdc_gauss_lobatto = 1
	Quadrature node types. More...

integer, parameter	sdc_gauss_radau = 2

integer, parameter	sdc_clenshaw_curtis = 3

integer, parameter	sdc_uniform = 4

integer, parameter	sdc_gauss_legendre = 5

integer, parameter	sdc_proper_nodes = 2**8

integer, parameter	sdc_composite_nodes = 2**9

integer, parameter	sdc_no_left = 2**10

integer, parameter	amrex_real = c_double

Detailed Description

Module to create quadrature matrices and accompanying routines for SDC.

Function/Subroutine Documentation

◆ not_proper()

logical function sdcquadrature_mod::not_proper	(	integer(c_int), dimension(:), intent(in)	flags,
		integer, intent(in)	node
	)

Function to decide if the restriction of the nodes is pointwise, e.g. coarse nodes are every other fine node.

◆ poly_diff()

subroutine sdcquadrature_mod::poly_diff	(	real(qp), dimension(0:n), intent(inout)	p,
		integer, intent(in), value	n
	)

Subroutine to differentiate polynomial (in place)

◆ poly_eval()

real(qp) function sdcquadrature_mod::poly_eval	(	real(qp), dimension(0:n), intent(in)	p,
		integer, intent(in), value	n,
		real(qp), intent(in)	x
	)

Polynomial manipulation routines.

A polynomial p

p(x) = a_n x^n + ... + a_2 x^2 + a_1 x + a_0

is stored as a Fortran array p(0:n) according to

p = [ a_0, a_1, ..., a_n ]. Function to evaluate real polynomial

◆ poly_eval_complex()

complex(qp) function sdcquadrature_mod::poly_eval_complex	(	real(qp), dimension(0:n), intent(in)	p,
		integer, intent(in), value	n,
		complex(qp), intent(in)	x
	)

Function to evaluate complex polynomial.

◆ poly_int()

subroutine sdcquadrature_mod::poly_int	(	real(qp), dimension(0:n), intent(inout)	p,
		integer, intent(in), value	n
	)

Subroutine to integrate polynomial (in place)

◆ poly_legendre()

subroutine sdcquadrature_mod::poly_legendre	(	real(qp), dimension(0:n), intent(out)	p,
		integer, intent(in), value	n
	)

Subroutine to compute Legendre polynomial coefficients using Bonnet's recursion formula.

◆ poly_roots()

subroutine sdcquadrature_mod::poly_roots	(	real(qp), dimension(n), intent(out)	roots,
		real(qp), dimension(0:n), intent(in)	p0,
		integer, intent(in), value	n
	)

Subroutine to compute polynomial roots using the Durand-Kerner algorithm. The roots are assumed to be real.

◆ qsort()

recursive subroutine sdcquadrature_mod::qsort ( real(qp), dimension(:), intent(inout) a )

Subroutine to sort (inplace) using the quick sort algorithm. Adapted from http://www.fortran.com/qsort_c.f95.

◆ qsort_partition()

subroutine, private sdcquadrature_mod::qsort_partition	(	real(qp), dimension(:), intent(inout)	a,
		integer, intent(out)	marker
	)

private

◆ sdc_qmats()

subroutine sdcquadrature_mod::sdc_qmats	(	real(amrex_real), dimension(ndst-1, nsrc), intent(out)	qmat,
		real(amrex_real), dimension(ndst-1, nsrc), intent(out)	smat,
		real(c_long_double), dimension(ndst), intent(in)	dst,
		real(c_long_double), dimension(nsrc), intent(in)	src,
		integer(c_int), dimension(nsrc), intent(in)	flags,
		integer(c_int), intent(in), value	ndst,
		integer(c_int), intent(in), value	nsrc
	)

Subroutine to compute the quadrature matrices.

Parameters

[in]	ndst	Number of destination points
[in]	nsrc	Number of source points
[in]	dst	Destination points
[in]	src	Source points
[out]	qmat	O to dst quadrature weights
[out]	smat	dst(m) to dst(m+1) quadrature weights

◆ sdc_qnodes()

subroutine sdcquadrature_mod::sdc_qnodes	(	real(c_long_double), dimension(nnodes), intent(out)	qnodes,
		integer(c_int), dimension(nnodes), intent(out)	flags,
		integer(c_int), intent(in), value	qtype,
		integer(c_int), intent(in), value	nnodes
	)

Subroutine to compute high precision quadrature nodes.

Parameters

[in]	nnodes	Number of nodes
[in]	qtype	Type of nodes (see pf_dtype)
[out]	qnodes	The computed quadrature nodes

◆ sdc_quadrature()

subroutine sdcquadrature_mod::sdc_quadrature	(	integer, intent(in)	qtype_in,
		integer, intent(in)	nnodes,
		integer, intent(in)	nnodes0,
		real(amrex_real), dimension(nnodes), intent(inout)	nodes,
		integer, dimension(nnodes), intent(out)	nflags,
		real(amrex_real), dimension(nnodes,nnodes-1,4), intent(inout)	qmats
	)

Subroutine to create quadrature matrices.

Variable Documentation

◆ amrex_real

integer, parameter sdcquadrature_mod::amrex_real = c_double

◆ dp

integer, parameter sdcquadrature_mod::dp = c_double

◆ eps

real(qp), parameter sdcquadrature_mod::eps = 1.0e-23_qp

◆ qp

integer, parameter sdcquadrature_mod::qp = c_long_double

◆ sdc_clenshaw_curtis

integer, parameter sdcquadrature_mod::sdc_clenshaw_curtis = 3

◆ sdc_composite_nodes

integer, parameter sdcquadrature_mod::sdc_composite_nodes = 2**9

◆ sdc_gauss_legendre

integer, parameter sdcquadrature_mod::sdc_gauss_legendre = 5

◆ sdc_gauss_lobatto

integer, parameter sdcquadrature_mod::sdc_gauss_lobatto = 1

Quadrature node types.

◆ sdc_gauss_radau

integer, parameter sdcquadrature_mod::sdc_gauss_radau = 2

◆ sdc_no_left

integer, parameter sdcquadrature_mod::sdc_no_left = 2**10

◆ sdc_proper_nodes

integer, parameter sdcquadrature_mod::sdc_proper_nodes = 2**8

◆ sdc_uniform

integer, parameter sdcquadrature_mod::sdc_uniform = 4

Data Types

Functions/Subroutines

Variables