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1.4 Solution by domain decomposition

The numerical solution of large problems by domain decomposition techniques   is very well adapted to current generation parallel computers. However, the efficiency of these techniques depend strongly on the algorithm chosen and its implementation.

The approach proposed in the MODULEF code divides the computational domain into non-structured sub-domains of arbitrary form, and reduces the initial problem to an interface problem. The corresponding operator (the Steklov-Poincaré operator at the continuous level, the Schur complement matrix at the discrete level) is inverted by an preconditioned conjugate gradient algorithm . This algorithm requires, at each step, the solution of a Dirichlet and a Neumann problem on each sub-domain.

For a detailed description of the algorithm implemented in MODULEF, consult [2].

Note:

The notion of sub-domains has, here, a different meaning to the the one generally used in MODULEF. In fact, here it is synonym to sub-structure, whereas in general, (COMACO, COMILI, COFORC) it is rather synonym to material number.