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Paper	Title	Other Keywords	Page
MOA1MP02	Geometry of Electromagnetism and its Implications in Field and Wave Analysis	electromagnetic-fields, focusing	42
	L. Kettunen, A. Tarhasaari TUT, Tampere
	Electromagnetism has a strong geometrical structure which, however, is hidden when the theory is examined in terms of classical vector analysis. Consequently a more powerful framework of algebraic topology and differential geometry is needed to view the subject. Recently, the geometric view has become rather popular among the community of computational electromagnetism, but still it has been asked, whether the more generic view truly enables one to develop new tools applicable to pragmatic field and wave analysis which could not be discovered otherwise. In other words, is the investment needed to study the new subject justified by the advantages brought by the more accurate viewpoint? Such a question is, evidently, not trivial to answer. Not because the larger framework did not have clear advantages, but rather for it takes a considerable effort to understand the difference between the "old" and "new" approach. Second, the advantages tend to be rather generic in the sense, that the geometric viewpoint tends to be more useful in building a software system to solve electromagnetic boundary value problems instead of in finding some handy techniques to solve certain specific problems. This paper makes an attempt to highlight some keypoints of the geometric nature of electromagnetism and to explain which way the geometric viewpoint is known to be useful in numerical analysis of electromagnetic field and wave problems. We start from the basics of electromagnetism and end up with more specific questions related to computing.
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MOAPMP03	Geometrical Methods in Computational Electromagnetism	controls, simulation	75
	A. Bossavit LGEP, Gif-sur-Yvette
	From almost one century, it has been known that vector fields E, H, D, B, etc., in the Maxwell equations are just "proxies" for more fundamental objects, the differential forms e, h, d, b, etc., that when integrated on lines or surfaces, as the case may be, yield physically meaningful quantities such as emf's, mmf's, fluxes, etc. This viewpoint helps separate the "non-metric" part of the equations (Faraday and Ampère), fully covariant, from the "metric" one (the constitutive laws), with more restricted (Lorentz) covariance. The usefulness of this viewpoint in computational issues has been realized more recently, and will be the main topic addressed in this survey. It makes the association of degrees of freedom with mesh elements such as edges, facets, etc. (instead of nodes as in traditioanl finite element techniques), look natural, whereas the very notion of "edge element" seemed exotic twenty years ago. It explains why all numerical schemes treat Faraday and Ampère the same way, and only differ in the manner they discretize metric-dependent features, i.e., constitutive laws. What finite elements, finite volumes, and finite differences, have in common, is thus clearly seen. Moreover, this seems to be the right way to advance the "mimetic discretization" or "discrete differential calculus" research programs, which many dream about: a kind of functorial transformation of the partial differential equations of physics into discrete models, when space-time continuum is replaced by a discrete structure such as a lattice, a simplicial complex, etc. Though total fulfillment of this dream is still ahead, we already have something that engineers –especially programmers keen on object-oriented methods– should find valuable: A discretization toolkit, offering ready-to-use, natural "discrete" counterparts to virtually all "continuous" objects discernible in the equations, fields, differential operators, v x B force fields, Maxwell tensor, etc.
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THM2IS01	Accelerator Description Formats	lattice, simulation, controls, quadrupole	297
	N. Malitsky BNL, Upton, Long Island, New York R. M. Talman CLASSE, Ithaca, New York
	Being an integral part of accelerator software, accelerator description aims to provide an external representation of an accelerator’s internal model and associative effects. As a result, the choice of description formats is driven by the scope of accelerator applications and is usually implemented as a tradeoff between various requirements: completeness and extensibility, user and developer orientation, and others. Moreover, an optimal solution does not remain static but instead evolves with new project tasks and computer technologies. This talk presents an overview of several approaches, the evolution of accelerator description formats, and a comparison with similar efforts in the neighboring high-energy physics domain. Following the UAL Accelerator-Algorithm-Probe pattern, we will conclude with a next logical specification, Accelerator Propagator Description Format (APDF), providing a flexible approach for associating physical elements and evolution algorithms most appropriate for the immediate tasks.
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