Extensions of a coarse–fine mesh stabilized Schwarz alternating iteration domain decomposition method

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For the numerical solution of a domain decomposed discretized elliptic operator (PDE) problem a particular kind of Schwarz alternating iteration method is used, based on maximal overlap between neighboring domains. It is stabilized not by the more traditional coarse mesh method but by a combined coarse–fine mesh method. As has been demonstrated earlier for 2D problems this method can converge very rapidly and is not sensitive to how accurate the arising subdomain systems and the coarse–fine mesh system are solved. A short presentation of the method is given followed by extensions of the method to 3D problems and to porous media problems.