We present a domain decomposition method on a semilinear hyperbolic system with multiple relaxation times. In the region where the relaxation time is small, an asymptotic equilibrium equation can be used for computational efficiency. An interface condition based on the sign of the characteristic speed at the interface is provided to couple the two systems in a domain decomposition setting. A ri...

The finite element method is a numerical simulation technique for solving partial differential equations. Domain decomposition provides a means for parallelizing the expensive simulation with modern computing architecture. Choosing the sub-domains for domain decomposition is a non-trivial task, and in this paper we show how this can be addressed with machine learning. Our method starts with a b...

Abstract. A BDDC (balancing domain decomposition by constraints) algorithm is developed for elliptic problems with mortar discretizations for geometrically non-conforming partitions in both two and three spatial dimensions. The coarse component of the preconditioner is defined in terms of one mortar constraint for each edge/face which is an intersection of the boundaries of a pair of subdomains...

We analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive Banach space. This method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations. In particular, the method generalizes the additive Schwarz domain decomposition methods to allow for as...

In this paper we present a balancing domain decomposition method of Neumann– Neumann type for the numerical approximation of an age-structured population diffusing in a multilayer environment. We give a quasi optimal convergence result for the algorithm via Fourier analysis in a two-layers case, and we address the variational generalization to an arbitrary number of layers as well as its finite...

Abstract. A BDDC (balancing domain decomposition by constraints) algorithm is developed for elasticity problems in three dimensions with mortar discretization on geometrically nonconforming subdomain partitions. Coarse basis functions in the BDDC algorithm are constructed from primal constraints on faces. These constrains are similar to the average matching condition and the moment matching con...

The paper summarises the ambient vibration-based assessment of an historic suspension footbridge, dating back to 1928. The footbridge is characterised by the timber floor system supported by two couples of cables, that were recently replaced. After the retrofit, the actual structural behaviour of the bridge were assessed by experimental and theoretical methods. The field tests included geometri...

The Balancing Domain Decomposition algorithm uses in each iteration solution of local problems on the subdomains coupled with a coarse problem that is used to propagate the error globally and to guarantee that the possibly singular local problems are consistent. The abstract theory introduced recently by the first-named author is used to develop condition number bounds for conforming linear ele...

The Overlapping Balancing Domain Decomposition (OBDD) methods can be considered as an extension of the Balancing Domain Decomposition (BDD) methods to the case of overlapping subdomains. This new approach, has been proposed and studied in [4, 3]. In this paper, we will discuss its practical parallel implementation and present numerical experiments on large unstructured meshes.