Optimized Schwarz methods for a diffusion problem with discontinuous coefficient

DOI10.1007/s11075-014-9884-2zbMath1314.65155OpenAlexW2002504778MaRDI QIDQ2346277

Martin J. Gander, Olivier Dubois

Publication date: 1 June 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: http://doc.rero.ch/record/331706/files/11075_2014_Article_9884.pdf

zbMATH Keywords

domain decompositionparallel preconditioningoptimized Schwarz methodsoptimized transmission conditions

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Finite volume methods for boundary value problems involving PDEs (65N08)

Related Items (26)

Optimized Schwarz Methods for Heterogeneous Helmholtz and Maxwell’s Equations ⋮ On the scalability of classical one-level domain-decomposition methods ⋮ Optimized Schwarz methods with nonoverlapping circular domain decomposition ⋮ Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution ⋮ Optimized Schwarz methods with ventcell transmission conditions for model problems with continuously variable coefficients ⋮ Localized model order reduction and domain decomposition methods for coupled heterogeneous systems ⋮ Domain decomposition methods to model heat exchanges between a well and a rock mass ⋮ A stable and accurate partitioned algorithm for conjugate heat transfer ⋮ Analysis of Schwarz Methods for Convected Helmholtz-Like Equations ⋮ Optimized Overlapping DDFV Schwarz Algorithms ⋮ A non-overlapping optimized Schwarz method for the heat equation with non linear boundary conditions and with applications to de-icing ⋮ The optimised Schwarz method and the two-Lagrange multiplier method for heterogeneous problems in general domains with two general subdomains ⋮ A Linear Domain Decomposition Method for Non-equilibrium Two-Phase Flow Models ⋮ A posteriori stopping criteria for optimized Schwarz domain decomposition algorithms in mixed formulations ⋮ Discrete optimization of Robin transmission conditions for anisotropic diffusion with discrete duality finite volume methods ⋮ A substructuring preconditioner with vertex-related interface solvers for elliptic-type equations in three dimensions ⋮ Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis ⋮ Heterogeneous Optimized Schwarz Methods for Second Order Elliptic PDEs ⋮ A domain decomposition method to couple nonisothermal compositional gas liquid Darcy and free gas flows ⋮ Unnamed Item ⋮ On the choice of Robin parameters for the optimized Schwarz method for domains with non-conforming heterogeneities ⋮ Optimized Schwarz and finite element cell-centered method for heterogeneous anisotropic diffusion problems ⋮ Optimized Schwarz Methods for Model Problems with Continuously Variable Coefficients ⋮ A linear domain decomposition method for partially saturated flow in porous media ⋮ Is There More Than One Dirichlet--Neumann Algorithm for the Biharmonic Problem? ⋮ A Complex Homographic Best Approximation Problem. Application to Optimized Robin--Schwarz Algorithms, and Optimal Control Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Robin-Robin preconditioner for advection-diffusion equations with discontinuous coefficients
• Optimized Schwarz methods without overlap for highly heterogeneous media
• Numerical experiments on a domain decomposition algorithm for nonlinear elliptic boundary value problems
• A relaxation procedure for domain decomposition methods using finite elements
• Improved ad hoc interface conditions for Schwarz solution procedure tuned to highly heterogeneous media
• Non-overlapping additive Schwarz methods tuned to highly heterogeneous media
• The Optimized Schwarz Method with a Coarse Grid Correction
• A homographic best approximation problem with application to optimized Schwarz waveform relaxation
• Generalized Schwarz Splittings
• A method of finite element tearing and interconnecting and its parallel solution algorithm
• Optimal Schwarz Waveform Relaxation for the One Dimensional Wave Equation
• The optimized order 2 method
• FACTORIZATION OF THE CONVECTION-DIFFUSION OPERATOR AND THE SCHWARZ ALGORITHM
• Optimized Schwarz Methods without Overlap for the Helmholtz Equation
• Absorbing boundary conditions for the wave equation and parallel computing
• Optimized Schwarz methods for unsymmetric layered problems with strongly discontinuous and anisotropic coefficients
• Optimized Schwarz Waveform Relaxation Methods for Advection Reaction Diffusion Problems
• Optimized Schwarz Methods
• An optimized Schwarz waveform relaxation method for the unsteady convection diffusion equation in two dimensions

This page was built for publication: Optimized Schwarz methods for a diffusion problem with discontinuous coefficient