Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Speed-up the computing efficiency of waveform relaxation method for power system transient stability
Proceedings of the first international workshop on High performance computing, networking and analytics for the power grid
Advances in Engineering Software
Advances in Engineering Software
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Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergence rate than both the algebraic and the geometric one. We complement our results by numerical experiments.