Related papers: Space-Time Domain Decomposition Methods for Diffus…
This paper develops a physics-informed neural network (PINN) based on the Schwarz waveform relaxation (SWR) method for solving local and nonlocal advection-diffusion-reaction equations. Specifically, we derive the formulation by…
We present a Waveform Relaxation (WR) version of the Neumann-Neumann algorithm for the wave equation in space-time. The method is based on a non-overlapping spatial domain decomposition, and the iteration involves subdomain solves in…
Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of…
In this paper, we are concerned with the global pressure formulation of immiscible incompressible two-phase flow between different rock types. We develop for this problem two robust schemes based on domain decomposition (DD) methods and…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann algorithm, formulated specially for multiple subdomains splitting for general parabolic and hyperbolic problems. This method is based on a non-overlapping spatial domain…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann and Neumann-Neumann algorithms for the wave equation in space time. Each method is based on a non-overlapping spatial domain decomposition, and the iteration involves…
This paper is devoted to the derivation of a pleasingly parallel Galerkin method for the time-independent $N$-body Schr\"odinger equation, and its time-dependent version modeling molecules subject to an external electric field. In this…
Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset node data can be designed with a few discrete frequencies hence allowing for compact volume of data to be managed. Moreover, attenuation effects can be…
Non-overlapping Schwarz methods with generalized Robin transmission conditions were originally introduced by B. Despr\'es for time-harmonic wave propagation problems and have largely developed over the past thirty years. The aim of the…
In this paper we propose on continuous level a class of domain decomposition methods of Robin-Robin type to solve the problems of unilateral contact between elastic bodies with nonlinear Winkler covers. These methods are based on abstract…
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 study for the first time Schwarz domain decomposition methods for the solution of the Navier equations modeling the propagation of elastic waves. These equations in the time harmonic regime are difficult to solve by iterative methods,…
The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
This paper proposes a frequency-time hybrid solver for the time-dependent wave equation in two-dimensional interior spatial domains. The approach relies on four main elements, namely, 1) A multiple scattering strategy that decomposes a…
The Schwarz Waveform Relaxation algorithm (SWR) exchanges the waveform of boundary value between neighbouring sub-domains, which provides a more efficient way than the other Schwarz algorithms to realize distributed computation. However,…
A space-time domain decomposition approach is presented as a natural extension of the enhanced velocity mixed finite element (EVMFE) [Wheeler et. al] for spatial domain decomposition. The proposed approach allows for different space-time…
In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in…
Inpainting-based compression methods are qualitatively promising alternatives to transform-based codecs, but they suffer from the high computational cost of the inpainting step. This prevents them from being applicable to time-critical…
This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…