On Nonoverlapping Domain Decomposition Methods for the Incompressible Navier-stokes Equations

BDDC Algorithms for Incompressible Stokes Equations

The purpose of this paper is to extend the BDDC (balancing domain decomposition by constraints) algorithm to saddle-point problems that arise when mixed finite element methods are used to approximate the system of incompressible Stokes equations. The BDDC algorithms are iterative substructuring methods, which form a class of domain decomposition methods based on the decomposition of the domain ...

Newton-krylov Domain Decomposition Solvers for Adaptive Hp Approximations of the Steady Incompressible Navier-stokes Equations with Discontinuous Pressure Fields

Domain Decomposition for Discontinuous Galerkin Method with Application to Stokes Flow

We report on recent results related to domain decomposition methods based on the Discontinuous Galerkin discretizations of Stokes equations. We analyze the efficiency of a block nonoverlapping Schwarz preconditioner based on the approach by Feng and Karakashian [2001]. We also prove the inf-sup stability of a substructuring method.

Schwarz domain decomposition for the incompressible Navier-Stokes equations in general co-ordinates

This report describes a domain decomposition method for the incompressible NavierStokes equations in general coordinates. Domain decomposition techniques are needed if we want to solve ows in complex geometries. The discretization is performed by a nite volume method combined with a staggered grid arrangement. The domain decomposition technique is of Schwarz type combined with a GMRES accelerat...

A Stable Penalty Method for the Compressible Navier-Stokes Equations: II. One-Dimensional Domain Decomposition Schemes

This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier–Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a result the patching of subdomains is local in space. The scheme is studied in detail for Burgers’s equa...