I am new to domain decomposition and have been searching in google for an introduction in 1D which goes over the complete procedure from the continuous to the discrete problem as well as the algorithm for solving the discrete problem. However, I haven't had any luck and all that I've seen are on complicated geometries using FEM that skip a lot of details.

I am only interested in non-overlapping domain decomposition (substructuring) and a 1D example in finite difference would be helpful to understand the basics of transitioning from the continuous problem to applying the dirichlet-neumann method.


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    $\begingroup$ DDM is more of a framework than one specific method, so I think additional details are needed. What's the PDE? Some (poisson) nudge you towards overlapping methods, others (helmholtz) nudge you towards non-overlapping methods. Also, you might find little has been said of DDM for 1D-FEM, because the systems that arise from such discretizations can already be solved efficiently via banded solvers or nested dissection (as the separator is always O(1) unknowns). Furthermore, "corners" or "cross-points" are an important consideration in most DDM's, and are missing in 1D. $\endgroup$ Jun 30 at 16:59

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