Optimized Schwarz methods with elliptical domain decompositions
The authors consider the domain decomposition method for solving second-order elliptic equations posed on elliptical geometries. To be more specific, an optimized Schwarz method is proposed with elliptical domain decomposition, i.e., decompositions into an ellipse and elliptical rings. First, using the technique of separation of variables, the spatial variables are decoupled and the subdomain problems are reduced to radial Mathieu-like equations defined on finite intervales. Second, the convergence of the classical Schwarz method is provided. Third, optimized Schwarz methods for both overlapping and nonoverlapping cases are considered, where a series of transmission conditions are introduced and optimized. Lastly, other related topics including the extensions to different geometric domains and the model problem with variable coefficient, and the implementation issues, are discussed.
scientific article; zbMATH DE number 7352172
scientific article