A nonoverlapped domain decomposition for a class of convection-diffusion problems

An overlapping domain decomposition preconditioner for a class of discontinuous Galerkin approximations of advection-diffusion problems

We consider a scalar advection{di usion problem and a recently proposed discontinuous Galerkin approximation, which employs discontinuous nite 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 coars...

Acceleration of a Domain Decomposition Method for Advection-Diffusion Problems

in a bounded polyhedral domain Ω ⊂ R with a Lipschitz boundary ∂Ω and 0 < ǫ ≤ 1,b ∈ [H(Ω) ∩ L∞(Ω)]d, c ∈ L∞(Ω), f ∈ L(Ω), c− 1 2∇ · b ≥ 0. Let {Ωk} be a non-overlapping macro partition with Ω = ∪k=1Ωk. The goal of the well-known DDM of Robin type (Lions [1990]) is to enforce (in appropriate trace spaces) continuity of the solution u and of the diffusive and advective fluxes ǫ∇u·nkj resp.− 1 2 (...

Domain Decomposition Preconditioning for Discontinuous Galerkin Approximations of Convection-Diffusion Problems

Tool-box for parallel adaptive computations of 3-D convection-diffusion problems using domain decomposition

In this report we describe the tools that we have used, developed, and implemented in a computer system for simulation of flows in porous media. Our goal was to create a simulator that uses various tools and that is based on discretization by finite elements and finite volumes and uses efficient preconditioning iterative methods for the resulting large sparse system. Also important features are...

Equidistribution grids for two-parameter convection–diffusion boundary-value problems

In this article, we propose an adaptive grid based on mesh equidistribution principle for two-parameter convection-diffusion boundary value problems with continuous and discontinuous data. A numerical algorithm based on an upwind finite difference operator and an appropriate adaptive grid is constructed. Truncation errors are derived for both continuous and discontinuous problems. Parameter uni...