Overlapping domain decomposition for elliptic problems on locally refined meshes: Dirichlet boundary conditions
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V. V. Akimov
Abstract
- In this paper we introduce and investigate a variant of the additive Schwarz preconditioner for elliptic finite element problems on meshes with strong refinement in the vicinity of the Dirichlet part of the boundary. This type of local refinement can be due to either a sharp boundary layer in the solution of the differential equation or singularities in its derivatives.
The computational domain is decomposed into a large size subdomain containing a major part of the mesh and a number of small size subdomains containing the refined part of the mesh. The additive Schwarz method based on this sort of domain decomposition is proved to be optimal in the sense that the condition number of the preconditioned stiffness matrix is bounded from above by a constant which is independent of the mesh and the sizes of small subdomains.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Contents
- Overlapping domain decomposition for elliptic problems on locally refined meshes: Dirichlet boundary conditions
- On convergence rate of some iterative methods for bilinear and bicubic finite element schemes for the dissipative Helmholtz equation with large values of a singular parameter
- Optimization of one class of nonsymmetrizable algorithms for saddle point problems
- Combined estimates of the Monte Carlo method for the third boundary value problem for a parabolic-type equation
- Effect of grid-scale turbulence on ocean modelling
Articles in the same Issue
- Contents
- Overlapping domain decomposition for elliptic problems on locally refined meshes: Dirichlet boundary conditions
- On convergence rate of some iterative methods for bilinear and bicubic finite element schemes for the dissipative Helmholtz equation with large values of a singular parameter
- Optimization of one class of nonsymmetrizable algorithms for saddle point problems
- Combined estimates of the Monte Carlo method for the third boundary value problem for a parabolic-type equation
- Effect of grid-scale turbulence on ocean modelling
