Related papers: Design and analysis of a Schwarz coupling method f…
Local-nonlocal coupling approaches provide a means to combine the computational efficiency of local models and the accuracy of nonlocal models. To facilitate the coupling of the two models, non-matching grids are often desirable as nonlocal…
The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of…
We present here nonoverlapping optimized Schwarz methods applied to heat transfer problems with heterogeneous diffusion coefficients. After a Laplace transform in time, we derive the error equation and obtain the convergence factor. The…
The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace…
This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…
We design and analyze a Schwarz waveform relaxation algorithm for domain decomposition of advection-diffusion-reaction problems with strong heterogeneities. The interfaces are curved, and we use optimized Robin or Ventcell transmission…
Parabolic optimal control problems arise in numerous scientific and engineering applications. They typically lead to large-scale coupled forward-backward systems that cannot be treated with classical time-stepping schemes and are…
In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate…
The dynamic iteration method with a restricted additive Schwarz splitting is investigated to co-simulate linear differential algebraic equations system coming from RLC electrical circuit with linear components. We show the pure linear…
We present an adaptive simulation framework for binary-fluid flows, based on the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical…
The aim of this paper is to develop new optimized Schwarz algorithms for the one dimensional Schr{\"o}dinger equation with linear or nonlinear potential. After presenting the classical algorithm which is an iterative process, we propose a…
In this study we present a non-overlapping Schwarz waveform relaxation (SWR) method applied to a one dimensional model problem representative of the coupling between the ocean and the atmosphere. This problem includes nonlinear interface…
We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
In this paper, we introduce a novel parallel contact algorithm designed to run efficiently in High-Performance Computing based supercomputers. Particular emphasis is put on its computational implementation in a multiphysics finite element…
This study introduces a recursive method for computing asymptotic solutions of the Laplace equation in corner domains with the homogeneous Dirichlet boundary condition on one side and the Robin boundary condition with a power-law…
Numerical solution of heterogeneous Helmholtz problems presents various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable…
In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not…
Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an accelerated Schwarz method for radiative transfer equations…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…