Schwarz alternating method

In mathematics, the Schwarz alternating method, named after Hermann Schwarz, is an iterative method to find the solution of a partial differential equations on a domain which is the union of two overlapping subdomains, by solving the equation on each of the two subdomains in turn, taking always the latest values of the approximate solution as the boundary conditions. A modification of the method, known as the additive Schwarz method, has become a practical domain decomposition method. An abstract formulation of the original method is then referred to as the multiplicative Schwarz method.

Historical notice

It was first formulated by H. A. Schwarz and served as a theoretical tool: its convergence for general second order elliptic partial differential equations was first proved much later, in 1951, by Solomon Mikhlin.

See also

• Additive Schwarz method
• Solomon Mikhlin
• Hermann Schwarz

References

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