Structure

The structure of this data type is given by:

TYPE :: QuadraturePoint_
  REAL(DFP), ALLOCATABLE :: Points( :, : )
  INTEGER( I4B ) :: tXi = 0
END TYPE QuadraturePoint_

Points

The number of rows in Points is tXi+1, and the number of columns in Points is equal to the number of quadrature points.

• Points(1:tXi, :) denotes the quadrature points.
• Points(tXi+1, :) denotes the weights.

tXi

• In 1D tXi is 1
• In 2D tXi is 2
• In 3D tXi is 3

QuadratureType

Currently, easifem provides following quadrature points:

Legendre polynomial based

• GaussLegendre
• GaussLegendreLobatto
• GaussLegendreRadau
• GaussLegendreRadauLeft
• GaussLegendreRadauRight

Chebyshev polynomial based

• GaussChebyshev
• GaussChebyshevLobatto
• GaussChebyshevRadau
• GaussChebyshevRadauLeft
• GaussChebyshevRadauRight

Jacobi polynomial based

• GaussJacobi
• GaussJacobiLobatto
• GaussJacobiRadau
• GaussJacobiRadauLeft
• GaussJacobiRadauRight

Ultraspherical polynomial based

• GaussUltraSpherical
• GaussUltraSphericalLobatto
• GaussUltraSphericalRadau
• GaussUltraSphericalRadauLeft
• GaussUltraSphericalRadauRight