Detailed Description

an ldg shape functions implementation

Definition at line 1 of file ldgdiscfunc.m.

Collaboration diagram for ldgdiscfunc:

Public Member Functions
	ldgdiscfunc ( varargin)
	initialize ldg function on triangular grids with input
function	display ()
function res =	evaluate ( eindices, lcoord)
function res =	subsasgn ( S, val)
function res =	subsref ( S)
function sdf =	scalar_component ( ncomp)
	extraction of scalar component of vectorial ldg function
function p =	plot ( params)
	plot as colormap
Public Attributes
	nelements
	number of elements
	pdeg
	polynomial degree
	ndofs_per_element
	number of DOFs per grid elment
	ndofs
	number of DOFs
	dimrange
	dimension of range space
	dofs
	the DOF vector
::gridbase	grid
	grid object

Constructor & Destructor Documentation

ldgdiscfunc.ldgdiscfunc ( varargin )

initialize ldg function on triangular grids with input

note, the only use of this class is, that by local storage of the dof vector and a (..) as evaluation routine, these objects can be used identically as analytical functions in integration, matrix assembly, etc. But in general the ../ldg directory contains methods for handling ldg functions based on seperate dof and parameter storage. These methods are more efficient as the class&methods.

arguments

varargin: This can be one of

inp = ldgdiscfunc : copy constructor

- inp = {dofs, params}: optional vector of dofs to be stored in the ldg function

- inp = params: Generate an empty ldg function,

where the required fields of params are

pdeg - polynomial degree on each element
dimrange - dimension of function
nelements - number of triangles

df has a field dofs, which are sorted as follows

for all elements
- for all degrees
  - for all dimensions

i.e. dofs with number 1,1+dimrange,1+2 dimrange ... are the dofs of the first scalar component, etc.

let $\hat phi_i i=1...m$ be an orthonormal basis on the reference triangle $\hat T$ . Let T be an arbitrary triangle and $F_T$ be the reference mapping from $\hat T$ to $T$ . Then for all global dof indices $j=1,...,N$ there exists an element $T(j)$ and local index $i(j)$ such that $phi_j (x) = \hat phi_i(j) ( F_T^-1(x))$