Detailed Description

an ldg shape functions implementation

Definition at line 17 of file ldgdiscfunc.m.

Inheritance diagram for ldgdiscfunc:

Collaboration diagram for ldgdiscfunc:

Public Member Functions
	ldgdiscfunc (varargin)
	initialize ldg function on triangular grids with input More...

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 More...

function p =	plot (params)
	plot as colormap More...

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, df_info}

optional vector of dofs to be stored in the ldg function

inp = df_info: A descriptive object of type ldginfo.

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 \(phi_j (x) = \hat phi_i(j) ( F_T^-1(x))\)

Then an ldg-discrete function is given by

\[ df (x) = sum_j=1^N dof(j) * phi_j(x)= sum_j=1^N dof(j) * \hat phi_i(j) (F_T(j)^-1 (x) )= \]

Parameters

varargin varargin

Definition at line 86 of file ldgdiscfunc.m.

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