We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation...
Three non-overlapping domain decomposition methods are proposed for the numerical approximation of time-harmonic Maxwell equations with damping (i.e., in a conductor). For each method convergence is proved and, for the discrete problem, the rate of convergence of the iterative algorithm is shown to be independent of the number of degrees of freedom.
Three non-overlapping domain decomposition methods are proposed for the
numerical
approximation of time-harmonic Maxwell equations with damping (, in a conductor). For
each method convergence is proved and, for the discrete problem, the rate of
convergence
of the iterative algorithm is shown to be independent of the number of
degrees of freedom.
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