Domain decomposition algorithms for indefinite elliptic problems
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems
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
An object-oriented framework for the development of scalable parallel multilevel preconditioners
ACM Transactions on Mathematical Software (TOMS)
BDDC methods for discontinuous Galerkin discretization of elliptic problems
Journal of Complexity
A Class of Domain Decomposition Preconditioners for hp-Discontinuous Galerkin Finite Element Methods
Journal of Scientific Computing
Journal of Scientific Computing
A parallel adaptive newton-krylov-schwarz method for 3D compressible inviscid flow simulations
Modelling and Simulation in Engineering
A BDDC algorithm for a class of staggered discontinuous Galerkin methods
Computers & Mathematics with Applications
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We consider a scalar advection-diffusion problem and a recently proposed discontinuous Galerkin approximation, which employs discontinuous finite element spaces and suitable bilinear forms containing interface terms that ensure consistency. For the corresponding sparse, nonsymmetric linear system, we propose and study an additive, two-level overlapping Schwarz preconditioner, consisting of a coarse problem on a coarse triangulation and local solvers associated to a family of subdomains. This is a generalization of the corresponding overlapping method for approximations on continuous finite element spaces. Related to the lack of continuity of our approximation spaces, some interesting new features arise in our generalization, which have no analog in the conforming case. We prove an upper bound for the number of iterations obtained by using this preconditioner with GMRES, which is independent of the number of degrees of freedom of the original problem and the number of subdomains. The performance of the method is illustrated by several numerical experiments for different test problems using linear finite elements in two dimensions.