Detailed Description

A hierarchical cubegrid of arbitrary dimension.

This is an axis parallel hexaedral grid, with non-conform refinement structure. All vertices are explicitly generated and stored. Only practical for low dimensions, i.e. 1 to 4 or perhaps 5.

Definition at line 1 of file cubegrid.m.

Inheritance diagram for cubegrid:

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Collaboration diagram for cubegrid:

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List of all members.

Public Member Functions
	cubegrid ( varargin)
	constructor of a hierarchical cubegrid
function [ compress , new ] =	tpart_refine ( lids, new_midpoints)
	refines certain grid entities
function res =	check_consistency ()
	function checking the consistency of a polygonal grid, i.e. checking, whether the edge centroids correspond (implicit neighbour-index test)
function leaf_element =	coord2leaf_element ( coord)
	function giving the leaf_element of a grid where the values of the coord-vector can be found (coord- can for example be a set of mu-values in a parameter grid. This function utilizes a -search algorithm.
function	demo ()
	small script demonstrating the possibilities of the cubegrid class.
function	display ()
	cubegrid's display method.
function ret =	get ( propertyname, varargin)
	get-method for cubegrids
function [ p0 , p1 ] =	get_edges ( gid)
	method determining the world coordinates of the edges of a single element with global index `gid`.
function gids =	get_leafgids ()
	return leaf ids of cubegrid, i.e. vector with global element indices of leaf elements
function range =	get_ranges_of_element ( element)
	return the ranges corresponding to the element of the grid, i.e. maximum vertex range of the part_num element of the grid.
function vols =	get_volume ( gids)
	method determining the volumes of a set of elements
function lids =	gid2lid ( gids)
	function converting global element ids to leaf element ids
function gids =	lid2gid ( lids)
	function converting leaf-element ids to global element ids
function p =	plot ( params)
	plot method for a cubegrid.
function p =	plot_grid ( params)
	plot method for a cubegrid. A line plot is performed. Text can be plotted in the leafs of the grid.
function p =	plot_leafelement_data ( data, params)
	plot method for piecewise constant data on the leaf level of the grid.
function p =	plot_leafvertex_data ( data, params)
	plot method for data on the leaf level of the grid.
function ngrid =	refine ( lids)
	refinement routine for cubegrid.
function ngrid =	remove_duplicate_vertices ( epsilon)
	method to be used, if a vertex list in the grid should be compressed
function cubegrid gcopy =	copy ()
	a deep copy of the cubegrid
Public Attributes
	dimension
	dimension of grid/number of coordinates per vertex
	vertex
	`vertex(i,j)` is the j-th coordinate of i-th vertex point
	vertexindex
	`vertexindex(id,j)` is the index of j-th vertex of element `id`
	level
	`level(id)` equals refinement level of element `id`
	isleaf
	`isleaf(id)` indicates, wether element `id` is leaf or not
	firstchild
	`firstchild(id)` indicates the lowest-index of a child element
	refine_steps
	number of refinement-steps, that have been performed on the grid so far
	creation_step
	`creation_step(id)` stores the refinement step number that has led to the element `id`.

Constructor & Destructor Documentation

cubegrid.cubegrid ( varargin )

constructor of a hierarchical cubegrid

Preliminaries

In the following

gid denotes global element indices, i.e. also covering non-leaf elements,
lid denotes indices for leaf indices.

Conversion can be performed by gids = lid2gid(grid,lid) Conversion can be performed by lids = gid2lid(grid,gid)

The constructor has the following

Synopsis

cubegrid() : construction of a default cubegrid (2d unit square)
cubegrid(cgrid) : copy-constructor
cubegrid(params): generate cubegrid with certain options. The
argument params requires the following fields
1. range : cell array of intervals, where the array lengths determine the grid dimension
2. numintervals: vector with number of intervals per dimension
perhaps later: constructor by duneDGF-file?

Parameters:

varargin varargin

Generated fields of grid:

dimension — dimension of grid/number of coordinates per vertex
nelements — number of overall elements (leaf + nonleaf);
nvertices — number of vertices;
vertex — vertex(i,j) = j-th coordinate of i-th vertex point
vertexindex — vertexindex(id,j) = index of j-th vertex of element id
level — level(id) = level, i.e. refinement steps of element id
isleaf — isleaf(id) = 0 or 1 whether element id is leaf or not
refine_steps — number of refinement-steps, that have been performed on the grid so far
creation_step — creation_step(id) stores the refinement step number that has led to the element id.

Definition at line 80 of file cubegrid.m.

Member Function Documentation

function res = cubegrid.check_consistency ( )

function checking the consistency of a polygonal grid, i.e. checking, whether the edge centroids correspond (implicit neighbour-index test)

Todo:: : perhaps later further extensions

Return values:

res	boolean value which is `true` if the check succeeds, or `false` if it fails.

Reimplemented from gridbase.

Definition at line 2 of file check_consistency.m.

function leaf_element = cubegrid.coord2leaf_element ( coord )

function giving the leaf_element of a grid where the values of the coord-vector can be found (coord- can for example be a set of mu-values in a parameter grid. This function utilizes a $O(log(n))$ -search algorithm.

coord : vector of coord-values (must have same dimension as grid)

15.02.2010 Markus Dihlmann

Parameters:

coord coord

Return values:

leaf_element leaf element

Definition at line 2 of file coord2leaf_element.m.

function cubegrid gcopy = cubegrid.copy ( ) [virtual]

a deep copy of the cubegrid

Return values:

gcopy a deep copy of this instance also

Implements gridbase.

Definition at line 382 of file cubegrid.m.

function cubegrid.display ( )

cubegrid's display method.

All scalar quantities are displayed. Internal pointlists, vectors and flags of elements are not displayed. These can be accessed by the get() method.

Reimplemented from gridbase.

Definition at line 2 of file display.m.

function ret = cubegrid.get	(	propertyname,
		varargin
	)

get-method for cubegrids

Parameters:

propertyname

A property name of the grid which can be one of the following

level : get vector of levels of all elements
dimension : get dimension of grid
nvertices : get number of vertices of grid
nelements : get number of elements of grid
isleaf : get vector of isleaf-indices of all elements
vertexindex returns a matrix (i,j) index of j-th vertex of element i a further optional argument with element indices can be passed, then only the vertices of these elements are returned,
```
 get(grid,'vertexindex',[2,3]) 
```
returns a 2 x nvertices_per_element matrix with indices
vertex : returns a matrix of all vertex coordinates, i.e. ret(i,j) => j-th coordinate of i-th vertex point optionally, a subset of vertex-indices can be determined as further parameter, i.e.
```
 get(grid,'vertex',[2 3 4]) 
```
produces a 3 x dim matrix with the coordinates of the points

or property can be equal to one of the following strings returning quantities which are derived from the above grid properties

nleafelements : get number of leaf elements of grid
leafelements : get vector of indices of elements that are leaf elements
leafcogs : returns a matrix of all centers of gravity of the leaf elements. ret(i,j) is the j-th coordinate of the i-th leaf element

varargin An optional list of arguments as described above.

Return values:

ret ret

Definition at line 2 of file get.m.

function [ p0 , p1 ] = cubegrid.get_edges ( gid )

method determining the world coordinates of the edges of a single element with global index gid.

i-th edge goes from p0(:,i) to p1(:,i)

Note:: vectorized version for multiple elements not yet implemented

Parameters:

gid	global index of element for which edge coordinates are requested

Return values:

p0	lowest coordinate of the edge
p1	highest coordinate of the edge

Definition at line 2 of file get_edges.m.

function gids = cubegrid.get_leafgids ( )

return leaf ids of cubegrid, i.e. vector with global element indices of leaf elements

Bernard Haasdonk 27.3.2007

Return values:

gids	gids
vector	of global leaf indices

Definition at line 2 of file get_leafgids.m.

function range = cubegrid.get_ranges_of_element ( element )

return the ranges corresponding to the element of the grid, i.e. maximum vertex range of the part_num element of the grid.

Markus Dihlmann 16.02.2010

Parameters:

element element

Return values:

range range

Definition at line 2 of file get_ranges_of_element.m.

function vols = cubegrid.get_volume ( gids )

method determining the volumes of a set of elements

A simple product of edge-lengths is computed, i.e. the edges are assumed to be axis-parallel.

Note:: The computation for multiple gids is trivially performed by a loop. Vectorization must be done sometime!!

Parameters:

gids	Global indices

Return values:

vols	The volumes for the elements given by `gids`.

Definition at line 2 of file get_volume.m.

function lids = cubegrid.gid2lid ( gids )

function converting global element ids to leaf element ids

Parameters:

gids	global indices of elements to which the local indices shall be computed.

Return values:

lids	leaf element ids or `-1` if a global id was not a leaf element

Definition at line 2 of file gid2lid.m.

function gids = cubegrid.lid2gid ( lids )

function converting leaf-element ids to global element ids

Parameters:

lids	local indices for which the global ones shall be computed

Return values:

gids	global indices of leaf indices

Definition at line 2 of file lid2gid.m.

function p = cubegrid.plot ( params )

plot method for a cubegrid.

A line plot is performed. Currently implementation for more than 3D not implemented, as this would be a line-mess

Bernard Haasdonk 1.3.2007

Parameters:

params params

Return values:

p	this is the list of handles to the graphics primitives

Required fields of params:

LineStyle — LineStyle

Optional fields of params:

color — RGB vector
shrink_factor — if this flag is given, the elements are plotted shrinked
plot_level — if this flag is nonzero, a level plot is performed
level — this integer must be specified in case of level-plot
plot_patch — if this flag is set (only 2D and 3D) the plot is done by colored patches
axis_equal — if this flag is set, set axis to equal scale

Definition at line 2 of file plot.m.

function p = cubegrid.plot_grid ( params )

plot method for a cubegrid. A line plot is performed. Text can be plotted in the leafs of the grid.

p is the list of handles to the graphics primitives

optional params: color : RGB vector shrink_factor: if this flag is given, the elements are plotted shrinked plot_level: if this flag is nonzero, a level plot is performed level : this integer must be specified in case of level-plot plot_patch : if this flag is set (only 2D and 3D) the plot is done by colored patches axis_equal : if this flag is set, set axis to equal scale

leaftext : vector of strings. Length must be equal to number of leafelements. The text is shown in the cogs (center of gravities) of the leafelements.

Markus Dihlmann 18.02.2010

Parameters:

params params

Return values:

p p

Required fields of params:

text — text

Definition at line 2 of file plot_grid.m.

function p = cubegrid.plot_leafelement_data	(	data,
		params
	)

plot method for piecewise constant data on the leaf level of the grid.

Currently only implemented for 2D. A patch plot is performed.

See also:: plot_element_data() for general possible options in params

Parameters:

data	data
params	params

Return values:

p	this is the list of handles to the graphics primitives

Definition at line 2 of file plot_leafelement_data.m.

function p = cubegrid.plot_leafvertex_data	(	data,
		params
	)

plot method for data on the leaf level of the grid.

Currently only implemented for 2D. A patch plot is performed, such that the vertices have corresponding values as given by data, the values in between are interpolated by MATLAB.

See also:: plot_vertex_data() for optional params fields

Parameters:

data	data
params	params

Return values:

p	this is the list of handles to the graphics primitives

Definition at line 2 of file plot_leafvertex_data.m.

function ngrid = cubegrid.refine ( lids )

refinement routine for cubegrid.

Refinement rule is a simple division into $2^dim$ smaller cubes After refinement, a condensation of the vertex list is performed by remove_duplicate_vetrices(), i.e. duplicate vertices generated during refinement are removed.

Parameters:

lids	List of leaf-element ids of the to-be-refined codim `0` entities. Only leaf-elements can reasonably be refined, so do not pass global elements here, as internally a translation into global element ids is performed.

Return values:

ngrid the refined grid

Definition at line 2 of file refine.m.

function ngrid = cubegrid.remove_duplicate_vertices ( epsilon )

method to be used, if a vertex list in the grid should be compressed

This might be required after refinement of a grid, merging of grids, etc. Duplicate detection is based on l2-error deviation thresholded by epsilon.

Parameters:

epsilon l2-error deviation threshold. (Default = 1e-6)

Return values:

ngrid the compressed grid

Generated fields of ngrid:

vertex — vertex
vertexindex — vertexindex
nvertices — nvertices

Definition at line 2 of file remove_duplicate_vertices.m.

function [ compress , new ] = cubegrid.tpart_refine	(	lids,
		new_midpoints
	)

refines certain grid entities

Parameters:

lids	ids of grid entities to be refined
new_midpoints	the newly created vertices of the refined grid.

Return values:

compress	the ids of entities which are getting smaller due to the refinement.
new	ids of the newly created elements

Definition at line 317 of file cubegrid.m.

The documentation for this class was generated from the following files:

grid/@cubegrid/cubegrid.m
grid/@cubegrid/check_consistency.m
grid/@cubegrid/coord2leaf_element.m
grid/@cubegrid/demo.m
grid/@cubegrid/display.m
grid/@cubegrid/get.m
grid/@cubegrid/get_edges.m
grid/@cubegrid/get_leafgids.m
grid/@cubegrid/get_ranges_of_element.m
grid/@cubegrid/get_volume.m
grid/@cubegrid/gid2lid.m
grid/@cubegrid/lid2gid.m
grid/@cubegrid/plot.m
grid/@cubegrid/plot_grid.m
grid/@cubegrid/plot_leafelement_data.m
grid/@cubegrid/plot_leafvertex_data.m
grid/@cubegrid/refine.m
grid/@cubegrid/remove_duplicate_vertices.m

Detailed Description

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation