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Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These methods typically involve solving…
Linear elastic fracture mechanics admit analytic solutions that have low regularity at crack tips. Current numerical methods for partial differential equations (PDEs) of this type suffer from the constraint of such low regularity, and fail…
We develop and analyze a splitting method for fluid-poroelastic structure interaction. The fluid is described using the Stokes equations and the poroelastic structure is described using the Biot equations. The transmission conditions on the…
This paper deals with the problem of identification of a Robin coefficient (also known as impedance coefficient) in a parabolic PDE from terminal observations of the temperature distributions. The problem is ill-posed in the sense that…
We propose an explicit partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed to achieve high computational efficiency in modern engineering simulations. The FSI problem under…
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides.…
One of the major challenges of coupled problems is to manage nonconforming meshes at the interface between two models and/or domains, due to different numerical schemes or domains discretizations employed. Moreover, very often complex…
In the current work we study a nonlocal parabolic problem with Robin boundary conditions. The problem arises from the study of an idealized electrically actuated MEMS (Micro-Electro-Mechanical System) device. Initially we study the…
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics…
Multiscale phenomena manifest across various scientific domains, presenting a ubiquitous challenge in accurately and effectively simulating multiscale dynamics in complex systems. In this paper, a novel decoupling solving paradigm is…
We propose a lattice model to study the dynamics of a driven interface in a medium with random pinning forces. For driving forces F smaller than a threshold force F_c the whole interface gets pinned. The depinning transition can be…
Dynamical decoupling is a technique aimed at suppressing the interaction between a quantum system and its environment by applying frequent unitary operations on the system alone. In the present paper, we analytically study the dynamical…
Physics-informed neural networks (PINNs) are emerging as popular mesh-free solvers for partial differential equations (PDEs). Recent extensions decompose the domain, apply different PINNs to solve the problem in each subdomain, and stitch…
We study numerically a stochastic differential equation describing an interface driven along the hard direction of an anisotropic random medium. The interface is subject to a homogeneous driving force, random pinning forces and the surface…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
We introduce two global-in-time domain decomposition methods, namely the Steklov-Poincare method and the Robin method, for solving a fluid-structure interaction system. These methods allow us to formulate the coupled system as a space-time…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
We present a loosely coupled, non-iterative time-splitting scheme based on Robin-Robin coupling conditions. We apply a novel unified analysis for this scheme applied to both a Parabolic/Parabolic coupled system and a Parabolic/Hyperbolic…
Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non Gaussian random numerical integration that capture the highly oscillatory behavior of the involved…
This paper deals with an existence and uniqueness result of the weak solution for a quasilinear elliptic PDE with nonlinear Robin boundary conditions.This problem is defined on a domain whose boundary is the union of two disjoint…