I’ve written a finite element code in Matlab, for a multi-physics problem. The problem is when I change mesh sizing, the code doesn’t converge. I guess it is because the employed variables are not dimensionless and the stiffness matrix depends on the units (i.e. mm or m). How can I make my variables dimensionless? For example how can I make geometry lengths dimensionless? I will be glad if you can help me or give me suitable references.
Start by doing non-dimensional the original PDE equations. Use a characteristic velocity, lengh and so on..
Hi,
It is possible that the multi-physics problem is dependent on grid scale/ element size, for example if there is a singularity. Then you could use a mesh size that you think describe the phenomena or rewrite the model (to do that, that there are many options; gradients, integrals, BE-methods)
If it is a normal linear problem it ought to converge, but also then if for example a thickness varies much, the stiffness matrix may have entries of both small and large magnitudes.
Some codes cannot easily do inv of such matrices, and one programmer said one should write solve instead, but it would be better if the program replies and tells why inv is not possible?
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