We consider in this paper numerical approximation of the linear fluid-structure interaction (FSI). We construct a new class of pressure-correction schemes for the linear FSI problem with a fixed interface, and prove rigorously that they are unconditionally stable. These schemes are computationally very efficient, as they lead to, at each time step, a coupled linear elliptic system for the veloc...

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...

We design and implement the first polynomial-based spectral method on graphic processing units (GPUs). The key to success lies in the seamless integration of the matrix diagonalization technique and new generation CUDA tools. The method is applicable to elliptic equations with general boundary conditions in both 2-D and 3-D cases. We show remarkable speedups of more than 10 times in the 2-D cas...

Keywords: Predator–prey model Stage-structure Stability Cross-diffusion Non-constant positive steady states a b s t r a c t This paper is concerned with the reaction diffusion version with homogeneous Neumann boundary conditions of a stage-structured predator–prey model. We first show that the nonnegative constant steady states are globally stable, which implies that corresponding elliptic syst...

In this paper we present an incremental formulation of the phase field model for a fluid filled crack in a poroelastic medium. The mathematical model represents a linear elasticity system with fading elastic moduli as the crack grows that is coupled with an elliptic variational inequality for the phase field variable. The convex constraint of the variational inequality assures the irreversibili...

Transmission eigenvalues are points in the spectrum of the interior transmission operator, a coupled 2x2 system of elliptic partial differential equations, where one unknown function must satisfy two boundary conditions and the other must satisfy none. We show that the interior transmission eigenvalues are discrete and depend continuously on the contrast by proving that the interior transmissio...

We study a finite volume discretization of a strongly coupled elliptic-parabolic PDE system describing miscible displacement in a porous medium. We discretize each equation by a finite volume scheme which allows a wide variety of unstructured grids (in any space dimension) and gives strong enough convergence for handling the nonlinear coupling of the equations. We prove the convergence of the s...

We present a class of domain decomposition (DD) preconditioners for the solution of elliptic linear-quadratic optimal control problems. Our DD preconditioners are extensions of Neumann–Neumann DD preconditioners, which have been successfully applied to the solution of single PDEs. The DD preconditioners are based on a decomposition of the optimality conditions for the elliptic linear-quadratic ...

the paper is concerned with the bifurcation of limit cycles in general quadratic perturbations of a quadratic reversible and non-hamiltonian system, whose period annulus is bounded by an elliptic separatrix related to a singularity at infinity in the poincar'{e} disk. attention goes to the number of limit cycles produced by the period annulus under perturbations. by using the appropriate p...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...