So this may be the wrong forum, mods feel free to move. Some background- I am solving some complex flow through porous media equations. Currently the simulator works well, but I would like to begin coupling vertical domains. I've got my set of equations, which breaks down into a primarily block-diagonal system. There are a few elements outside of the diagonal blocks that connect the domains. It seems to me that this would work well using either an iterative schwarz solver (additive or multiplicative) or a schwarz preconditioner. I've coded several versions up (AS and MS solvers, and an AS preconditioned GMRES solve), but for all but the most simple systems, am having issues with convergence.(adsbygoogle = window.adsbygoogle || []).push({});

I suspect that I have some coding bugs, but before searching for them, I wanted to make sure my algorithm is correct. Any thoughts on the AS solver algorithm below would be appreciated. So..

Given a system of equations, Ax=b, where A can be divided into several blocks along the diagonal (A_{1}-A_{N}) and what I call a "background matrix", which are the elements not in the blocks, that provide connection between domains. I am proposing the following pseudo-code algorithm:

where there is an initial guess for x andCode (Text):

while(!converged) {

b' = b-A[SUB]background[/SUB]*x

for(i=1,N) {

local_solver(A[SUB]i[/SUB], x[SUB]i[/SUB], b'[SUB]i[/SUB])

}

}

is a solver appropriate to the block matrix ACode (Text):local_solver(A[SUB]i[/SUB], x[SUB]i[/SUB], b'[SUB]i[/SUB])_{i}that solves for x_{i}, given b'_{i}.

Does this seem like an appropriate way to go about an additive schwarz solve? And is the correct way to use the additive schwarz algorithm as a preconditioner to simply go through one iteration applied to the vector I want to condition? Thoughts?

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# Schwarz iterative methods.

Can you offer guidance or do you also need help?

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