We present an algorithm for characterising the generalised Dirichlet to Neumann map for moving initial-boundary value problems. This algorithm is derived by combining the so-called global relation, which couples the initial and boundary values of the problem, with a new method for inverting certain one-dimensional integrals. This new method is based on the spectral analysis of an associated ODE...

Let Ω ⊂ Rd be a bounded domain with smooth boundary and let A ⊂⊂ Ω be a smooth, compactly embedded subdomain. Consider the operator − 1 2 ∆ in Ω − Ā with the Dirichlet boundary condition at ∂A and the Neumann boundary condition at ∂Ω, and let λ0(Ω, A) > 0 denote its principal eigenvalue. We discuss the question of monotonicity of λ0(Ω, A) in its dependence on the domain Ω. The main point of thi...

The paper studies finite element methods for the simulation of time–dependent convection–diffusion–reaction equations with small diffusion: the SUPG method, a SOLD method and two types of FEM– FCT methods. The methods are assessed, in particular with respect to the size of the spurious oscillations in the computed solutions, at a 3D example with nonhomogeneous Dirichlet boundary conditions and ...

Boundary conditions play a non trivial role in string theory. For instance the rich structure of D-branes is generated by choosing appropriate combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an antisymmetric background is present at the string end-points (corresponding to mixed boundary conditions) space time becomes non-commutative there. We show here how to build ...

The purpose of this paper is to present a new fictitious domain approach inspired by the extended finite element method introduced by Moës, Dolbow and Belytschko in [18]. An optimal method is obtained thanks to an additional stabilization technique. Some a priori estimates are established and numerical experiments illustrate different aspects of the method. The presentation is made on a simple ...

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates ar...

The diamagnetic inequality for the magnetic Schrödinger semigroup is extended to the difference of the semigroups of magnetic Schrödinger operators with Neumann and Dirichlet boundary conditions on arbitrary open domains and rather general magnetic vector potentials A and potentials V . In particular, this bound renders moot all the technical issues in the recent proofs of the independence of t...

We consider a second-order, selfadjoint elliptic operator L on a smooth one-parameter family of domains {Ωt}t∈[a,b] with no assumptions on the geometry of the Ωt’s. It is shown that the Morse index of L can be equated with the Maslov index of an appropriately defined path in a symplectic Hilbert space constructed on the boundary of Ωb. Our result is valid for a wide variety of boundary conditio...

The aim of this paper is to show certain properties of the Green’s functions related to the Hill’s equation coupled with various two point boundary value conditions. We will obtain the expression of the Green’s function of Neumann, Dirichlet, Mixed and anti-periodic problems as a combination of the Green’s function related to periodic ones. As a consequence we will prove suitable results in spe...

Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of motion leaves a Poisson equation for the pressure to be solved. But Poisson equations require boundary conditions. For the case of rectangular periodic boun...