Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps
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Victorita Dolean
,
Frédéric Nataf
Abstract
Coarse grid correction is a key ingredient in order to have scalable domain decomposition methods. For smooth problems, the theory and practice of such two-level methods is well established, but this is not the case for problems with complicated variation and high contrasts in the coefficients. In a previous study, two of the authors introduced a coarse space adapted to highly heterogeneous coefficients using the low frequency modes of the subdomain DtN maps. In this work, we present a rigorous analysis of a two-level overlapping additive Schwarz method with this coarse space, which provides an automatic criterion for the number of modes that need to be added per subdomain to obtain a convergence rate of the order of the constant coefficient case. Our method is suitable for parallel implementation and its efficiency is demonstrated by numerical examples on some challenging problems with high heterogeneities for automatic partitionings.
© Institute of Mathematics, NAS of Belarus
Articles in the same Issue
- Editorial
- Schwarz Type Solvers for -FEM Discretizations of Mixed Problems
- Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps
- Robust Two-level Domain Decomposition Preconditioners for High-contrast Anisotropic Flows in Multiscale Media
- Regular Decompositions for H(div) Spaces
- Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods
- Domain Decomposition Preconditioning for Problems with Highly Varying Coefficients
- A Simplified Calculation of Reduced HCT--Basis Functions in a Finite Element Context
- Norms of Discrete Trace Functions of (Ω) and (Ω)
Articles in the same Issue
- Editorial
- Schwarz Type Solvers for -FEM Discretizations of Mixed Problems
- Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps
- Robust Two-level Domain Decomposition Preconditioners for High-contrast Anisotropic Flows in Multiscale Media
- Regular Decompositions for H(div) Spaces
- Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods
- Domain Decomposition Preconditioning for Problems with Highly Varying Coefficients
- A Simplified Calculation of Reduced HCT--Basis Functions in a Finite Element Context
- Norms of Discrete Trace Functions of (Ω) and (Ω)
