6 research outputs found
Spatial decay in transient heat conduction for general elongated regions
Zanaboni's procedure for establishing Saint-Venant's principle is ex-
tended to anisotropic homogeneous transient heat conduction on regions
that are successively embedded in each other to become indefinitely elon-
gated. No further geometrical restrictions are imposed. The boundary
of each region is maintained at zero temperature apart from the common
surface of intersection which is heated to the same temperature assumed
to be of bounded time variation. Heat sources are absent. Subject to
these conditions, the thermal energy, supposed bounded in each region,
becomes vanishingly small in those parts of the regions suficiently remote
from the heated common surface. As with the original treatment, the
proof involves certain monotone bounded sequences, and does not depend
upon differential inequalities or the maximum principle. A definition is
presented of an elongated region.Peer ReviewedPostprint (author's final draft
Simulating 3D periodic structures at oblique incidences with discontinuous Galerkin time-domain methods: theoretical and practical considerations
International audienceIn this work, we focus on the development of the use of Periodic Boundary Conditions (PBC) with sources at oblique incidence in a Discontinuous Galerkin Time Domain (DGTD) framework. Whereas in the context of the Finite Difference Time Domain (FDTD) methods, an abundant literature can be found, for DGTD, the amount of contributions reporting on such methods is remarkably low. In this paper, we supplement the existing references using the field transform technique with an analysis of the continuous system using the method of characteristics and provide an energy estimate. Furthermore, we also study the discrete stability of the resulting DGTD scheme. Additional details about sources, observables (reflectance, transmittance and diffraction efficiency), and the use of Complex Frequency-Shifted Perfectly-Matched Layers (CFS-PMLs) in this framework are also given. After numerical validations, two realistic test-cases are considered in the context of nanophotonics with the Diogenes DGTD solver (http://diogenes.inria.fr)