Related papers: Schur complement Domain Decomposition Methods for …
This paper studies the $d$-dimensional extension of a fictitious domain penalization technique that we previously proposed for Neumann or Robin boundary conditions. We apply Droniou's approach for non-coercive linear elliptic problems to…
Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is…
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…
Domain decomposition methods are essential in solving applied problems on parallel computer systems. For boundary value problems for evolutionary equations the implicit schemes are in common use to solve problems at a new time level…
This paper presents a class of boundary integral equation methods for the numerical solution of acoustic and electromagnetic time-domain scattering problems in the presence of unbounded penetrable interfaces in two-spatial dimensions. The…
We study the homogeneous Cauchy-Dirichlet Problem (CDP) for a nonlinear and nonlocal diffusion equation of singular type of the form $\partial_t u =-\mathcal{L} u^m$ posed on a bounded Euclidean domain $\Omega\subset\mathbb{R}^N$ with…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…
In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain,…
Accelerating iterative eigenvalue algorithms is often achieved by employing a spectral shifting strategy. Unfortunately, improved shifting typically leads to a smaller eigenvalue for the resulting shifted operator, which in turn results in…
Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We…
Consider the scattering of a time-harmonic electromagnetic plane wave by an open cavity which is embedded in a perfectly electrically conducting infinite ground plane. This paper concerns the numerical solutions of the open cavity…
This paper is concerned with a numerical solution of the acoustic scattering by a bounded impenetrable obstacle in three dimensions. The obstacle scattering problem is formulated as a boundary value problem in a bounded domain by using a…
We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub…
In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
Non-overlapping domain decomposition methods necessarily have to exchange Dirichlet and Neumann traces at interfaces in order to be able to converge to the underlying mono-domain solution. Well known such non-overlapping methods are the…
We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…