Discontinuous Galerkin approximation of the Maxwell eigenproblem

A theoretical framework for the analysis of discontinuous Galerkin approximations of the Maxwell eigenproblem with discontinuous coefficients is presented. Necessary and sufficient conditions for a spurious-free approximation are established, and it is shown that, at least on conformal meshes, basically all the discontinuous Galerkin methods in the literature actually fit into this framework. Relations with the classical theory for conforming approximations are also discussed

Vekua theory for the Helmholtz operator

Vekua operators map harmonic functions defined on domain in $${\mathbb R^{2}}$$ to solutions of elliptic partial differential equations on the same domain and vice versa. In this paper, following the original work of I. Vekua (Ilja Vekua (1907-1977), Soviet-Georgian mathematician), we define Vekua operators in the case of the Helmholtz equation in a completely explicit fashion, in any space dimension N≥2. We prove (i) that they actually transform harmonic functions and Helmholtz solutions into each other; (ii) that they are inverse to each other; and (iii) that they are continuous in any Sobolev norm in star-shaped Lipschitz domains. Finally, we define and compute the generalized harmonic polynomials as the Vekua transforms of harmonic polynomials. These results are instrumental in proving approximation estimates for solutions of the Helmholtz equation in spaces of circular, spherical, and plane wave

Plane wave approximation of homogeneous Helmholtz solutions

In this paper, we study the approximation of solutions of the homogeneous Helmholtz equation Δu+ω 2 u=0 by linear combinations of plane waves with different directions. We combine approximation estimates for homogeneous Helmholtz solutions by generalized harmonic polynomials, obtained from Vekua's theory, with estimates for the approximation of generalized harmonic polynomials by plane waves. The latter is the focus of this paper. We establish best approximation error estimates in Sobolev norms, which are explicit in terms of the degree of the generalized polynomial to be approximated, the domain size, and the number of plane waves used in the approximation

An Operations management approach for radiology services

This paper focus on the application of Operations Management techniques in the context of radiological and diagnostic imaging services provision. More specifically, the outpatient appointment scheduling problem for MRI diagnostic imaging services in a radiology clinics is approached and solved taking into account set-up time minimization. This is pursued trough the design of an innovative system for the on-line assignment of appointments for specific diagnostic imaging scans. An appointment rule, a patient classification and an heuristic procedure for the booking process are defined in order to better manage uncertainty and improve system performance. The proposed approach was validated on the case of a diagnostic centre of Alliance Medical, a primary multinational company in the field of diagnostic imaging services