LagrangeDegree

This subroutine returns the monomial degrees (basis) for lagrange polynomials.

Lagrange polynomial of order $p,q,r$ is given by

$$l(x,y,z) = \text{span} \left\{ x^{a} y^{b} z^{c} \vert a=0,1,\cdots, p; b=0, 1, \cdots, q; c=0,1,\cdots, r \right\}$$

Calling example:

degree = LagrangeDegree_Hexahedron(order)
degree = LagrangeDegree_Hexahedron(p, q, r)

Interface 1

܀ Interface

INTERFACE LagrangeDegree_Hexahedron
  MODULE PURE FUNCTION LagrangeDegree_Hexahedron1(order) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: order
    INTEGER(I4B), ALLOCATABLE :: ans(:, :)
  END FUNCTION LagrangeDegree_Hexahedron1
END INTERFACE LagrangeDegree_Hexahedron

️܀ Example 1

PROGRAM main
USE easifembase
IMPLICIT NONE
INTEGER(i4b) :: i1, i2, order
TYPE(string) :: astr
INTEGER(I4B), ALLOCATABLE :: deg(:, :)
order = 1
deg = LagrangeDegree_Hexahedron(order=order)

CALL display(mdencode(deg), "degrees: ")

END PROGRAM main

See results

degrees:

a	b	c
0	0	0
1	0	0
0	1	0
1	1	0
0	0	1
1	0	1
0	1	1
1	1	1

$$1, x, y, xy, z, xz, yz, xyz$$

܀ Example 2

PROGRAM main
USE easifembase
IMPLICIT NONE
INTEGER(i4b) :: i1, i2, order
TYPE(string) :: astr
INTEGER(I4B), ALLOCATABLE :: deg(:, :)
order = 2
deg = LagrangeDegree_Hexahedron(order=order)

CALL display(mdencode(deg), "degrees: ")

END PROGRAM main

See results

degrees:

a	b	c
0	0	0
1	0	0
2	0	0
0	1	0
1	1	0
2	1	0
0	2	0
1	2	0
2	2	0
0	0	1
1	0	1
2	0	1
0	1	1
1	1	1
2	1	1
0	2	1
1	2	1
2	2	1
0	0	2
1	0	2
2	0	2
0	1	2
1	1	2
2	1	2
0	2	2
1	2	2
2	2	2

↢

Interface 2

܀ Interface

INTERFACE LagrangeDegree_Hexahedron
  MODULE PURE FUNCTION LagrangeDegree_Hexahedron2(p, q, r) RESULT(ans)
    INTEGER(I4B), INTENT(IN) :: p
    INTEGER(I4B), INTENT(IN) :: q
    INTEGER(I4B), INTENT(IN) :: r
    INTEGER(I4B), ALLOCATABLE :: ans(:, :)
  END FUNCTION LagrangeDegree_Hexahedron2
END INTERFACE LagrangeDegree_Hexahedron

p, q, r

• p is order in x direction
• q is order in y direction
• r is order in z direction

️܀ See example

PROGRAM main
USE easifembase
IMPLICIT NONE
INTEGER(i4b) :: i1, i2, p, q, r
TYPE(string) :: astr
INTEGER(I4B), ALLOCATABLE :: deg(:, :)
p = 2; q = 1; r = 1
deg = LagrangeDegree_Hexahedron(p, q, r)

CALL display(mdencode(deg), "degrees: ")

END PROGRAM main

See results

degrees:

a	b	c
0	0	0
1	0	0
2	0	0
0	1	0
1	1	0
2	1	0
0	0	1
1	0	1
2	0	1
0	1	1
1	1	1
2	1	1

↢