Abstract. We analyse the spectral bounds of non-overlapping domain decomposition additive Schwarz preconditioners for hp-version discontinuous Galerkin finite element methods in H-type norms. Using original approximation results for discontinuous finite element spaces, it is found that these preconditioners yield a condition number bound of order 1 + Hp/hq, where H and h are respectively the co...

A component-based approach is introduced for fast and flexible solution of parameter-dependent eigenproblems. We consider a shifted version of the eigenproblem where the left hand side operator corresponds to an equilibrium between the stiffness operator and a weighted mass operator. This permits to apply the Static Condensation Reduced Basis Element method, a domain synthesis approach with red...

We analyze the use of edge finite element methods to approximate Maxwell’s equations in a bounded cavity. Using the theory of collectively compact operators, we prove h-convergence for the source and eigenvalue problems. This is the first proof of convergence of the eigenvalue problem for general edge elements, and it extends and unifies the theory for both problems. The convergence results are...

Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion. In the LHC, particles circulate at the injection energy, when multipole errors are most significant, for more than 10 million turns, but systematic tracking studies are limited to a small fraction of this total time—even on modern computers...

Abstract The matrix element of a bound electron interacting with the nucleus through exchange of a Z boson is studied for the gauge invariant case of 2s1/2 − 2p1/2 transitions in hydrogenic ions. The QED radiative correction to the matrix element, which is −α/2π in lowest order, is calculated to all orders in Zα using exact propagators. Previous calculations of the first-order binding correctio...

We present an analysis of single-moving-element zoom lenses in the thin-lens limit and show how the length of these zoom lenses is determined by the zoom-factor, sensor-dimension and the depth-of-focus. By decreasing the sensor size and extending the depth-of-focus, the lengths of these zoom lenses can be reduced significantly. As an example we present a ray-traced design of a miniaturized sing...

We present some Zermelo-Fraenkel consistency results regarding bi-orderability of groups, as well a construction groups with Conradian orders whose every action on metric spaces has bounded orbits. A classical consequence the ultrafilter lemma is that group bi-orderable if and only it locally bi-orderable. show there exists model ZF in which free (ergo bi-orderable) not bi-orderable, can be giv...

For any group G, πe(G) denotes the set of orders of its elements. If Ω is a non-empty subset of N, h(Ω) stands for the number of isomorphism classes of finite groups G such that πe(G) = Ω. We put h(G) = h(πe(G)). In this paper we show that h(P GL(2, p n)) = 1 or ∞, where p = 2 α 3 β + 1 is a prime, α ≥ 0, β ≥ 0 and n ≥ 1. In particular, we show that h(P GL(2, 7)) = h(P GL(2, 3 2)) = ∞.

A class function φ on a finite group G is said to be an order separator if, for every x and y in G\{1} , φ(x) = φ(y) is equivalent to x and y being of the same order. Similarly, φ is said to be a class-size separator if, for every x and y in G \ {1} , φ(x) = φ(y) is equivalent to |CG(x)| = |CG(y)| . In this paper, finite groups whose nonlinear irreducible complex characters are all order separa...

It is important to demonstrate the use of plasmas for focusing positron and electron beams at high energy. By reducing the transverse area of colliding beams the plasma optical element affords a potential simplicity for enhancing the luminosity in the interaction region of linear colliders. Focusing of both transverse dimensions as well as both charge states has generated interest in this techn...