Related papers: Nonlocal Optimized Schwarz Methods for time-harmon…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
In this paper we are interested in the "fast path" fracture and we aim to use global-in-time, nonoverlapping domain decomposition methods to model flow and transport problems in a porous medium containing such a fracture. We consider a…
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…
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…
In this paper, we apply the optimized Schwarz method to the two dimensional nonlinear Schr{\"o}dinger equation and extend this method to the simulation of Bose-Einstein condensates (Gross-Pitaevskii equation). We propose an extended version…
Over the last two decades, classical Schwarz methods have been extended to systems of hyperbolic partial differential equations, and it was observed that the classical Schwarz method can be convergent even without overlap in certain cases.…
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the…
This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
We introduce in this paper a new tool to prove the convergence of the Overlapping Optimized Schwarz Methods with multisubdomains. The technique is based on some estimates of the errors on the boundaries of the overlapping strips. Our…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
We prove that the time-harmonic solutions to Maxwell's equations in a 3D exterior domain converge to a certain static solution as the frequency tends to zero. We work in weighted Sobolev spaces and construct new compactly supported…
This paper gives a geometric description of functional spaces related to Domain Decomposition techniques for computing solutions of Laplace and Helmholtz equations. Understanding the geometric structure of these spaces leads to algorithms…
In this paper we prove a stable determination of the coefficients of the time-harmonic Maxwell equations from local boundary data. The argument --due to Isakov-- requires some restrictions on the domain.
This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schr\"{o}dinger system with rapidly oscillating discontinuous coefficients arising from the modeling of a heterogeneous nanostructure with a…
In this paper, we develop a new representation for outgoing solutions to the time harmonic Maxwell equations in unbounded domains in $\bbR^3.$ This representation leads to a Fredholm integral equation of the second kind for solving the…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…