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Khalel A. April 7, 1999 10:04

URGENT Multi-Domains calculation
I have to take an exam tomorrow of meshing technics, and I don't understand how the multi-domain calculation is done? I don't need an accurate answer , only an overview of the method. Thank you for your answers. Khalel.

Marco April 8, 1999 05:41

Re: URGENT Multi-Domains calculation
The idea of multi-domain is to split the domain of the numerical calculation into many sub-domains and to solve equations onto these ones. The solution algorithm will be iterative, because solution of each sub-domain will need values on adjacent domains to construct boundary condition for itself. This process can be usefull, for example, to efficiently parallelize the code or to build structured grids on multi connected topologies.

I hope this can be usefull for your exam. Good luck. Marco

Rémi Demersseman April 15, 1999 02:31

Re: URGENT Multi-Domains calculation
Do all the sub-domains meshes correspond to their neighbours? I mean, it must be difficult if the meshes are different, because of the needed step of converting the data of one mesh' nodes to the other meshes ones. How to get through that? Rémi.

Marco April 15, 1999 04:15

Re: URGENT Multi-Domains calculation
If you think to study just one case and write an application just for it, you can let meshes to correspond with the adjacent ones. This can let you save time in programming and calculation, but you will be no more able to draw your grid as you like. On the other side, if you intend to have a more general code, suitable for many cases, it is foundamental to implement some tool to interpolate values on boundaries of a block and then re-discretize them on the adjacent grid (or grids if you have non-conformal sub-domains). This will be more expensive in programming and much more in calculation ( in general, you will need to pass trough interfaces Dirichlet as well as Neumann conditions), but interpolation will let you take full advantage of domain decomposition, reducing the global number of points by placing them where you really need. The increment in time of calculation can be reduced if you have of a good amount of RAM, because coefficientes to transform values across sub-domains boundaries can be stored and not calculated at each iteration on blocks.

Rémi April 15, 1999 04:37

Re: URGENT Multi-Domains calculation
Is there any restriction about the interpolation? Maybe the difference created between the first grid results and their interpolation on the second grid can be so important that the coupled calculation would diverge. Have you any example of that kind of interpolation tool published? Rémi

Marco April 15, 1999 05:43

Re: URGENT Multi-Domains calculation
I am sorry but I have not found any published example of interpolation between sub-domains.

I have used a very simple second order interpolation, and it seems to work pretty fine if coarseness of adjacent blocks are not much different in areas where the solution is "bad". Where the solution is plain, it works even with much different density of discretization (3-4 times). I tried this with incompressible N.S. equations in vorticity-stream function formulation with low Reynolds and I had'nt the possibility to test effects of changing the kind of interpolation.

I guess there are cases where interpolation accuracy is a limiting factor in convergence, but I think that iterations over sub-domains reduce this problem if the time step is not too big.

Ramendra Sahoo April 15, 1999 09:17

Re: URGENT Multi-Domains calculation
Hi Remi,

As far as multi-domain calculations are concerned with different grids there are two different approaches : either you can go for matching boundaries with mismatching grids or everything mismatching i.e. overlapping grids. If you are not using adaptive grids you can save a lot of time in calculations as well as no. of grids. For the first type of calculations you can use a lot of interpolations techniques both for geometric, flux as well as fundamental variables along the domain boundaries. Some of the standard interpolation techniques are available by Akima (Refer to his papers in ACM Trans. 1971,1976,1996..) in both two dimension and three dimensions. You should make sure that these interpolation techniques are satisfying either Newman or Dirichlet boundary conditions. In fact for simple cases since the interpolations deal with higher order derivatives, they usually satisfy atleast one of these two type of boundary conditions. For complex interfaces like different materials/fluids you can slightly modify the interpolation routines to match your criteria or you can impose further satisfying conditions. I have used similar conditions alongwith adaptive grids and found to be working nice and saving lot of computation time. If you are using overlapping grids, you can refer to Bill Henshaw/ Chesshire groups papers (LANL) for the implementations. I hope this will help you to solve your problems.

Good luck.


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