Formal definition of mesh bias parameter

[LukeFisherUKAEA]

I have looked for, but have been unable to find, a quantitative definition for how the mesh bias variable behaves. Is this essentially a geometric series, where the distance between node 0 and n for n > 0 is given by:

distance = sum (a r^(n - 1) ) = a(1 - r^(n-1)) / 1 - r

where a is the first spacing (i.e. between nodes 0 and 1), r is the bias value and n is the node number?

I suspect there is a very simple explanation for this but I run into problems as there are three parameters to define in the mesh block: the number of nodes, the distance spanned and the bias value. Does this mean that by choosing the length of a particular dimension and the number of nodes I wish to use, the bias value is fixed? But if the geometric nature is true then one should also be able to define the first spacing, a. The more I look at it the further away I get from understanding it! If there is a definition on the MOOSE help pages then I would appreciate a link to it. Many thanks in advance for the help.

[GiudGiud]

Hello

Which mesh generator is this for?
https://mooseframework.inl.gov/source/mesh/GeneratedMesh.html ?

I looked at the code, and the a (standard spacing in the non-biased case, not the first spacing anymore) is being modified to respect the number of nodes, the bias value and the distance in that generator.

Guillaume

[GiudGiud]

On a quick note we re getting more mesh biasing work in this PR. Not sure that is relevant for you
#20638