# Algorithm for assembling quadrilateral mesh in FEM

1. Apr 30, 2014

### mdn

Hi all,
I have co-ordinates of 4 vertices of quadrilateral for every element in mesh. I assembled such elements by moving single, separate point in whole domain and compared it's coordinate with all vertices of quadrilateral.
Above technique work properly, but it required rectangle element with fixed width and height for all elements.
my question is, what is best algorithm to assemble quadrilateral mesh with only information of 4 vertices of each elements in mesh?
please note that this question is not based on Delaunay triangulation or any other advancing front method (this technique gives all information while making meshes), rather to consider computational geometry.

2. Apr 30, 2014

### SteamKing

Staff Emeritus
Your question is open to different interpretations.

What does "I assembled such elements by moving single, separate point in whole domain and compared it's coordinate with all vertices of quadrilateral" mean? Are you trying to determine to which elements or elements a particular point belongs?

3. Apr 30, 2014

### mdn

Dear steamking,
thanks for replay, i will explain the stuff in detail.
*************Geometry to Mesh*************
my approach of generating automatic quadrilateral mesh is as follows...
1. draw any polygonal shape using mouse (convex, concave no restriction)
2. fill whole domain by rectangle (it is object in java, it will take track of its own vertices while moving in domain)
3. now in this stage, i had to do assembling means ... give global number to each vertices of element..find which node shares how many element for local global numbering.
in this technique i have used two dimensional array of coordinate to search every vertices of element and then given global number to each vertices. now next you know what is assembling...
I have used above technique for rectangle element and found no problem.

now question is, i know 4 vertices of rectangle of each element, can i assemble (off course automatic) elements, with only information of coordinates of vertices?

4. Apr 30, 2014

### SteamKing

Staff Emeritus
I think you want to know if it is possible for the elements of your mesh to be assembled automatically using just the nodal coordinate data.

I think the answer to this question is 'No' except for the simplest region geometries, like the rectangular region mentioned in the OP.

I believe what automatic mesh generators do is allow the user to describe the overall boundary to be analyzed, and then by means of triangulation or other procedures, generate internal nodal coordinates and elements without the user having to do this drudge work himself. Of course, there should be checks to ensure that the elements generated are well-behaved and that a sufficient number of elements is generated to provide an accurate solution.

It is problem of computational geometry, which is why I believe research is continuing.

A related problem is, once the elements and nodes have been generated, finding the arrangement of node numbering which minimizes the bandwidth of the corresponding stiffness matrix, in order to speed solution calculation.

A similar situation occurs when using lasers or other devices to measure objects in 3-D. The measuring device essentially produces a number of 3-D coordinates, but this information must be organized in some fashion in order to describe the surface of the object mathematically. A related field is how you would be able to engineer some sort of 'robot vision', which would allow a machine to 'see' objects and navigate around them without intervention by a human operator.

5. Apr 30, 2014

### mdn

but i did that for arbitrary shape also!

6. Apr 30, 2014

### mdn

let's forget about above stuff, i will ask question in different way
how to find neighbour of one with other element ? i have only information of nodal coordinate data of all elements and nothing else.