An iterative method for elliptic problems on regions partitioned into substructures
Mathematics of Computation
Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Timely Communicaton: An Analysis for a Nonoverlapping Domain Decomposition Iterative Procedure
SIAM Journal on Scientific Computing
Absorbing boundary conditions for domain decomposition
Applied Numerical Mathematics - Special issue on absorbing boundary conditions
Some Nonoverlapping Domain Decomposition Methods
SIAM Review
Optimized Schwarz Methods without Overlap for the Helmholtz Equation
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
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Optimized Schwarz methods form a class of domain decomposition methods for the solution of elliptic partial differential equations. Optimized Schwarz methods employ a first or higher order boundary condition along the artificial interface to accelerate convergence. In the literature, the analysis of optimized Schwarz methods relies on Fourier analysis and so the domains are restricted to be regular (rectangular). In this paper, we express the interface operator of an optimized Schwarz method in terms of Poincare-Steklov operators. This enables us to derive an upper bound of the spectral radius of the operator arising in this method of 1-O(h^1^/^4) on a class of general domains, where h is the discretization parameter. This is the predicted rate for a second order optimized Schwarz method in the literature on rectangular subdomains and is also the observed rate in numerical simulations.