Optimized Schwarz Methods

By Martin J. Gander. SIAM Journal on Numerical Analysis, 2006

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Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods (2012, methodology): “A ll these observations and further developments led at the turn of the century to the inv ntion of the new class of optimized Schwarz methods [34], with specialized v ariants for Helmholtz problems [35, 33].”
New development in freefem++ (2012, background): “Nataf for the all the discussion to implementation of this algorithm (see [28] for the theory).”
A Parallel Space-Time Algorithm (2012, methodology): “In practice, one must replace the Dirichlet boundary conditions with more general transmission operators, resulting in optimized and optimal Schwarz methods; see, for example, [15, 13, 16, 19].”
A FEM domain decomposition method for photonic and electromagnetic band gap structures (2006, methodology): “However, we note that the direct application of the DtD and/ or DtN DDM will not converge for Helmholtz or Maxwell type of problems [14], [30].”