相关论文: Stability and error analysis of a splitting method…
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…
We consider a fully discrete loosely coupled scheme for incompressible fluid-structure interaction based on the time semi-discrete splitting method introduced in {\emph{[Burman, Durst \& Guzm\'an, arXiv:1911.06760]}}. The splittling method…
We consider a loosely coupled algorithm for fluid-structure interaction based on a Robin interface condition for the fluid problem (explicit Robin-Neumann scheme). We study the dependence of the stability of this method on the interface…
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…
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…
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…
We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the…
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…
We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related…
We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [J. Numer. Math., 31(1):59--77, 2023] for a parabolic-parabolic interface problem and prove estimates for the discrete time derivatives of the…
This paper studies a non-singular coupling scheme for solving the acoustic and elastic wave scattering problems and its extension to the problems of Laplace and Lam\'e equations and the problem with a compactly supported inhomogeneity is…
We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [Numer. Algorithms, 99:921-948, 2025] for a parabolic-parabolic interface problem. We modify the first step of the scheme so that several…
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…
A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for a rigid…
Robin boundary conditions are a natural consequence of employing Nitsche's method for imposing the kinematic velocity constraint at the fluid-solid interface. Loosely-coupled FSI schemes based on Dirichlet-Robin or Robin-Robin coupling have…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary…
Several methods for handling sloping fluid-solid interfaces with the elastic parabolic equation are tested. A single-scattering approach that is modified for the fluid-solid case is accurate for some problems but breaks down when the…