Sparse Aitken–Schwarz domain decomposition with application to Darcy flow

Algebraic Domain Decomposition Methods for Darcy flow in heterogeneous media

Application of domain decomposition methods to indoor air flow simulation

A framework for solving the nonisothermal URANS equations with emphasis on applications to thermal building simulation is prescribed in this paper. Different domain decomposition techniques are used (i) for the treatment of boundary layers, (ii) for the efficient solution of the arising linear subproblems, and (iii) for coupling the indoor air flow field with the ambient. The approach is then a...

Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling

In this paper we consider a coupled system made of the Stokes and Darcy equations, and we propose some iteration-by-subdomain methods based on Robin conditions on the interface. We prove the convergence of these algorithms, and for suitable finite element approximations we show that the rate of convergence is independent of the mesh size h. A special attention is paid to the optimization of the...

Decomposition of sparse graphs, with application to game coloring number

Let k be a nonnegative integer, and let mk = 4(k+1)(k+3) k2+6k+6 . We prove that every simple graph with maximum average degree less than mk decomposes into a forest and a subgraph with maximum degree at most k. It follows that every simple graph with maximum average degree less than mk has game coloring number at most 4 + k.

Interface control domain decomposition (ICDD) method for Stokes-Darcy coupling

We propose the ICDD method to solve the coupling between Stokes and Darcy equations. According to this approach, the problem is formulated as an optimal control problem whose control variables are the traces of the velocity and the pressure on the internal boundaries of the subdomains that provide an overlapping decomposition of the original computational domain. A theoretical analysis is carri...