Annalisa Buffa

Containment Control in Mobile Networks

In this paper, the problem of driving a collection of mobile robots to a given target destination is studied. In particular, we are interested in achieving this transfer in an orderly manner so as to ensure that the agents remain in the convex polytope spanned by the leader-agents, while the remaining agents, only employ local interaction rules. To this aim we exploit the theory of partial difference equations and propose hybrid control schemes based on stop-go rules for the leader-agents. Non-Zenoness, liveness and convergence of the resulting system are also analyzed.

A Multiplicative Calderon Preconditioner for the Electric Field Integral Equation

In this paper, a new technique for preconditioning electric field integral equations (EFIEs) by leveraging Calderon identities is presented. In contrast to all previous Calderon preconditioners, the proposed preconditioner is purely multiplicative in nature, applicable to open and closed structures, straightforward to implement, and easily interfaced with existing method of moments (MoM) code. Numerical results demonstrate that the MoM EFIE system obtained using the proposed preconditioning converges rapidly, independently of the discretization density.

On traces for H(curl, Ω) in Lipschitz domains

Abstract We study tangential vector fields on the boundary of a bounded Lipschitz domain Ω in R 3 . Our attention is focused on the definition of suitable Hilbert spaces corresponding to fractional Sobolev regularities and also on the construction of tangential differential operators on the non-smooth manifold. The theory is applied to the characterization of tangential traces for the space H ( curl ,Ω) . Hodge decompositions are provided for the corresponding trace spaces, and an integration by parts formula is proved.

On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra

The aim of this paper is to study the tangential trace and tangential components of fields which belong to the space H(curl, Omega), when Omega is a polyhedron with Lipschitz continuous boundary. The appropriate functional setting is developed in order to suitably define these traces on the whole boundary and on a part of it (for partially vanishing fields and general ones.) In both cases it is possible to define ad hoc dualities among tangential trace and tangential components. In addition, the validity of two related integration by parts formulae is provided. Copyright (C) 2001 John Wiley & Sons, Ltd.

A dual finite element complex on the barycentric refinement

Given a two dimensional oriented surface equipped with a simplicial mesh, the standard lowest order finite element spaces provide a complex X* centered on Raviart-Thomas divergence conforming vector fields. It can be seen as a realization of the simplicial cochain complex. We construct a new complex Y* of finite element spaces on the barycentric refinement of the mesh which can be seen as a realization of the simplicial chain complex on the original (unrefined) mesh, such that the L 2 duality is non-degenerate on Y i × X 2-i for each i ∈ {0,1,2}. In particular Y 1 is a space of curl-conforming vector fields which is L 2 dual to Raviart-Thomas div-conforming elements. When interpreted in terms of differential forms, these two complexes provide a finite-dimensional analogue of Hodge duality.

On traces for functional spaces related to Maxwell's equations Part II: Hodge decompositions on the boundary of Lipschitz polyhedra and applications

Hodge decompositions of tangential vector fields defined on piecewise regular manifolds are provided. The first step is the study of L2 tangential fields and then the attention is focused on some particular Sobolev spaces of order

A justification of eddy currents model for the Maxwell equations

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Mathematical analysis of variational isogeometric methods

\nopagenumbers\end. In order to reach this goal, it is required to properly define the first order differential operators and to investigate their properties. When the manifold Γ is the boundary of a polyhedron Ω, these spaces are important in the analysis of tangential trace mappings for vector fields in H(curl, Ω) on the whole boundary or on a part of it. By means of these Hodge decompositions, one can then provide a complete characterization of these trace mappings: general extension theorems, from the boundary, or from a part of it, to the inside; definition of suitable dualities and validity of integration by parts formulae. Copyright

Laplacian sheep: a hybrid, stop-go policy for leader-based containment control

This paper is concerned with the approximation of the Maxwell equations by the eddy currents model, which appears as a correction of the quasi-static model. The eddy currents model is obtained by neglecting the displacement currents in the Maxwell equations and exhibits an elliptic character in the time-harmonic formulation. Our main concern in this paper is to show that the eddy currents model approximates the full Maxwell system up to the second order with respect to the frequency if and only if an additional condition on the current source is fulfilled. Otherwise, it is a first-order approximation to the Maxwell equations. We also study the well-posedness of the eddy currents model and investigate the time-dependent case. All our results strongly depend on the topology properties of the domains under consideration. This dependence which is specific to Maxwells equations does not appear for the two- or the three-dimensional Helmholtz operator.

Discontinuous Galerkin Approximation of the Maxwell Eigenproblem

This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error estimates in several cases of interest. The theory presented also includes estimates for T-splines, which are an extension of splines allowing for local refinement. In particular, we focus our attention on elliptic and saddle point problems, and we define spline edge and face elements. Our theoretical results are demonstrated by a rich set of numerical examples. Finally, we discuss implementation and efficiency together with preconditioning issues for the final linear system.