R_elementProperties: Compute some properties for each triangular element of the...

Description Usage Arguments Value

View source: R/fdaPDE.smoothing_R.R

Description

Only executed when the function create.FEM.basis is run with the option CPP_CODE = FALSE. It computes some quantities associated to the linear map that transforms the ith triangle in the reference triangular element. These are used for the computation of the integrals necessary to build the mass and stiffness matrix.

Usage

1

Arguments

mesh

A MESH2D mesh object representing the triangular mesh. This can be created with create.MESH.2D.

Value

A list with the following variables:

detJ

A vector of length #triangles. The ith element contains the determinant of the transformation from the reference triangle to the nodes of the i-th triangle. It's values is also the double of the area of each triangle of the basis.

transf

A matrix #triangles-by-2-by-2. transf[i,,] is the 2-by-2 tranformation matrix that transforms the nodes of the reference triangle to the nodes of the i-th triangle.

metric

A matrix #triangles-by-2-by-2. metric[i,,] is the 2-by-2 matrix
transf[i,,]^{-1}*transf[i,,]^{-T}. This matrix is usuful for the computation of the integrals over the elements of the mesh.


fdaPDE documentation built on May 29, 2017, 9:06 a.m.