Related papers: Stable Coupling of Nonconforming, High-Order Finit…
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…
We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a…
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations. In contrast to conventional interpolation operators, these new interpolation operators maintain the strict…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
We consider a nonlinear variational wave equation that models the dynamics of the director field in nematic liquid crystals with high molecular rotational inertia. Being derived from an energy principle, energy stability is an intrinsic…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
This article presents a unified mathematical framework for modeling coupled poro-viscoelastic and thermo-viscoelastic phenomena, formulated as a system of first-order in time partial differential equations. The model describes the evolution…
Concurrent multiscale methods play an important role in modeling and simulating materials with defects, aiming to achieve the balance between accuracy and efficiency. Atomistic-to-continuum (a/c) coupling methods, a typical class of…
This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators…
We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for…
We consider the coupled system of equations that describe flow in fractured porous media. To describe such types of problems, multicontinuum and multiscale approaches are used. Because in multicontinuum models, the permeability of each…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
We present and analyze an unconditionally energy stable and convergent finite difference scheme for the Functionalized Cahn-Hilliard equation. One key difficulty associated with the energy stability is based on the fact that one nonlinear…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and…
In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic…
A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…