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March 16, 2010 7:58pm UTC

why we do meshing in comsol?

hi all,

I have one question that why we do meshing in comsol and why we some times refine meshing on specific
boundaries?

i hope you people give me detail idea and logic of meshing.

Thanks

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March 18, 2010 7:12am UTC in response to kashif hussain

Re: why we do meshing in comsol?

Please refer
http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/
(It is nicely written)

The basic concept is the subdivision of the mathematical model into non-overlapping components called elements. The response of each element is expressed by unknown functions and the response of the whole model is then considered to be approximated by assembling the collection of all elements. Therefore, Finite-element requires discretization of the domain. We do that by meshing it, so that, we would have nodal representation of the geometry and functional representation of the domain. And, FEM is heavily mesh dependent. Refining is needed for two main reasons. One geometrical and other is mathematical.

Geometric > i.e., if you have curved edges, you will have better representation with smaller elements. Example, you have a circle, and you want to represent it by using straight lines. Obviously, result will be closer to actual circle, if you use higher number of smaller sized lines.
REFER > http://www.colorado.edu/engineering/cas/courses.d/IFEM.d/IFEM.Ch01.d/IFEM.Ch01.pdf
and slide to Page 1-6. There are some visuals.

Mathematical > In finite difference, we get the solution on the grid points only. In Finite Element, we get the solution over the domain (i.e. at the nodes and anywhere in between). Now, unlike FDM, to get the solution on entire element, we use piecewise and well-behaved shape functions to interpolate from integration points. So, lets say you have a quadratic shape function and very large elements; while going from one node to another node, you might not be able to capture the whole transition. However, if you have smaller elements with same degreed shape functions, you will have a better representation. Lets say, axially loaded plate with a center hole on it. We know that there will be a stress gradient around the hole. We need to use an adaptivity or denser meshes in that area to get the better presentation. Or you can still use coarser mesh but then you should to use higher order polynomials for interpolation. These two called, h-method and p-method.

I hope it helps.

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