smod_legendre_1D Submodule

Legendre_1D is a submodule used to generate arrays of coeffiecents used for developing finite element basis functions in 1D. Finite element basis functions are defined at internal nodes and used to iterpolate some value between those nodes.

calculate the coeffiecents associated with a univarate Lagrangian polynomial

$$1, x, x^2, ..., x^N$$

In the end you end up with a group of basis functions similar to this:

Contents

Module Functions

getArow1D getx getAlpha1D pascal_1D_line basis_1D

Module Functions

pure function getArow1D(N, xi) result(row)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	N
real(kind=wp),	intent(in)			::	xi

Return Value real(kind=wp), dimension(N)

function getx(N) result(x)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	N

Return Value real(kind=wp), dimension(N)

function getAlpha1D(N) result(alpha)

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	N

Return Value real(kind=wp), dimension(N,N)

pure function pascal_1D_line(N, x) result(row)

Generates the elements of an array associated with a univarate Lagrange polynomial.

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	N
real(kind=wp),	intent(in)			::	x

Return Value real(kind=wp), dimension(N+1)

pure function basis_1D(x, alpha, dx) result(y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(:)	::	x
real(kind=wp),	intent(in),		dimension(:)	::	alpha
integer,	intent(in)			::	dx

Return Value real(kind=wp), dimension(:), allocatable