Non-local variant of the optimised Schwarz method for arbitrary non-overlapping subdomain partitions

Parallel Subdomain-based Preconditioner for Non-overlapping Domain Decomposition Methods Parallel Subdomain-based Preconditioner for Non-overlapping Domain Decomposition Methods

We present a new parallelizable preconditioner that is used as the local component for a two-level preconditioner similar to BPS. On 2D model problems that exhibit either high anisotropy or discontinuity, we demonstrate its attracting numerical behaviour and compare it to the regular BPS. Finally, to alleviate the construction cost of this new preconditioner, that requires the explicit computat...

Non-crossing partitions for arbitrary Coxeter groups

Non-overlapping Schwarz algorithm for solving 2D m-DDFV schemes

We propose a non-overlapping Schwarz algorithm for solving “Discrete Duality Finite Volume” schemes (DDFV for short) on general meshes. In order to handle this problem, the first step is to propose and study a convenient DDFV scheme for anisotropic elliptic problems with mixed Dirichlet/Fourier boundary conditions. Then, we are able to build the corresponding Schwarz algorithm and to prove its ...

The method of mothers for non-overlapping non-matching DDM

In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the homogeneous Dirichlet problem for −∆u = g in Ω, our variables are i) the approximations uh of u in each sub-domain Ωs (each on its own grid), and ii) an approximation ψh of u on the skeleton (the union of the interfaces of the sub-domains) on an indepen...

27. A Non-Overlapping Optimized Schwarz Method which Converges with Arbitrarily Weak Dependence on h