1. History
1.1 Schwarz method
Schwarz methods have their origins in an alternating algorithm devised by H.A. Schwarz to demonstrate the existence of harmonic functions (i.e. twice continuously derivable solutions of the Laplace equation Δu = 0) in a composite domain, with a prescribed edge value g. He began by considering a domain composed of a disk T1 and a square T2 (see figure 1a), domains for which an explicit solution by means of Fourier series exists.
The respective boundaries of these two domains are denoted ∂T1 and ∂T2. The part of ∂T1 lying in T2 is denoted L2, the complementary...
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History
Schwarz methods
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