Abstract additive Schwarz method

In mathematics, the abstract additive Schwarz method, named after Hermann Schwarz, is an abstract version of the additive Schwarz method for boundary value problems on partial differential equations, formulated only in terms of linear algebra without reference to domains, subdomains, etc. Many if not all domain decomposition methods can be cast as abstract additive Schwarz method, which is often the first and most convenient approach to their analysis.^[1]

References

↑ Dryja, Maksymilian; Widlund, Olof B. (1990), "Towards a unified theory of domain decomposition algorithms for elliptic problems", in Chan, Tony; Glowinski, Roland; Périaux, Jacques; Widlund, Olof B., Third International Symposium on Domain Decomposition Methods for Partial Differential Equations (Houston, Texas, March 20–22, 1989) (PDF), Philadelphia, PA: SIAM, pp. 3–21 .

Parabolic	Forward-time central-space (FTCS) Crank–Nicolson

Hyperbolic	Lax–Friedrichs Lax–Wendroff MacCormack Upwind Method of characteristics

Others	Alternating direction-implicit (ADI) Finite-difference time-domain (FDTD)

Others

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