This work focuses on the derivation and analysis of a novel, strongly-coupled partitioned method for fluid–structure interaction problems. The flow is assumed to be viscous incompressible, structure modeled using linear elastodynamics equations. We assume that thick, i.e., same number spatial dimensions as fluid. Our newly developed numerical based Robin boundary conditions, well refactorizatio...

Abstract Our aim is to study the backward problem, i.e. recover initial data from terminal observation, of subdiffusion with time dependent coefficients. First all, by using smoothing property solution operators and a perturbation argument freezing diffusion coefficients, we show stability estimate in Sobolev spaces, under some smallness/largeness condition on time. Moreover, case noisy data, a...

A time discretization scheme based on the third-order backward difference formula has been embedded into a Chebyshev tau spectral method for the Navier-Stokes equations. The time discretization is a variant of the second-order backward scheme proposed by Krasnov et al. (J. Fluid Mech., 2008). Highresolution direct numerical simulations of turbulent incompressible channel flow have been performe...

This article proposes an implicit discontinuous Galerkin scheme for solving the 2D model of drug release from cardiovascular drug-eluting stents, given binding that is saturated and reversible. The uses discretization based on bubble modal basis functions in space backward Euler time. For this purpose, we have divided each domain into several sub-domains. In sub-domain, used a as local bases. T...

A finite element method for the Cahn-Hilliard equation (a semilinear parabolic equation of fourth order) is analyzed, both in a spatially semidisCrete case and in a completely discrete case based on the backward Euler method. Error bounds of optimal order over a finite time interval are obtained for solutions with smooth and nonsmooth initial data. A detailed study of the regularity of the exac...

We propose a preconditioned nonlinear conjugate gradient method coupled with a spectral spatial discretization scheme for computing the ground states (GS) of rotating Bose-Einstein condensates (BEC), modeled by the Gross-Pitaevskii Equation (GPE). We first start by reviewing the classical gradient flow (also known as imaginary time (IMT)) method which considers the problem from the PDE standpoi...

Implicit integration methods have contributed to large performance enhancements in the field of simulation of particle-system mechanical models. While Backward Euler and BDF-2 methods are now widely used for cloth simulation applications, the Implicit Midpoint method is often overlooked, because of its poor stability properties. It is however as simple to implement as Backward Euler, and offers...

In this report it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the spurious oscillations which are pointed out elsewhere when an explicit method is used, are avoided. Moreover the method (an event-capturing, or time-stepping ...

In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed fo...