482 research outputs found
Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems
In this paper, we propose and study the uniaxial perfectly matched layer
(PML) method for three-dimensional time-domain electromagnetic scattering
problems, which has a great advantage over the spherical one in dealing with
problems involving anisotropic scatterers. The truncated uniaxial PML problem
is proved to be well-posed and stable, based on the Laplace transform technique
and the energy method. Moreover, the -norm and -norm error
estimates in time are given between the solutions of the original scattering
problem and the truncated PML problem, leading to the exponential convergence
of the time-domain uniaxial PML method in terms of the thickness and absorbing
parameters of the PML layer. The proof depends on the error analysis between
the EtM operators for the original scattering problem and the truncated PML
problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3)
(2020), 1918-1940).Comment: 23 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1907.0890
Spectral-Domain Computation of Fields Radiated by Sources in Non-Birefringent Anisotropic Media
We derive the key expressions to robustly address the eigenfunction
expansion-based analysis of electromagnetic (EM) fields produced by current
sources within planar non-birefringent anisotropic medium (NBAM) layers. In
NBAM, the highly symmetric permeability and permittivity tensors can induce
directionally-dependent, but polarization independent, propagation properties
supporting "degenerate" characteristic polarizations, i.e. four
linearly-independent eigenvectors associated with only two (rather than four)
unique, non-defective eigenvalues. We first explain problems that can arise
when the source(s) specifically reside within NBAM planar layers when using
canonical field expressions. To remedy these problems, we exhibit alternative
spectral-domain field expressions, immune to such problems, that form the
foundation for a robust eigenfunction expansion-based analysis of time-harmonic
EM radiation and scattering within such type of planar-layered media. Numerical
results demonstrate the high accuracy and stability achievable using this
algorithm.Comment: The official (preliminary) published version of this manuscript,
along with copyright information, can be found using the provided DOI. IEEE
Antennas Wireless Propag. Lett., 201
Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media
To analyze seismic wave propagation in geological structures, it is possible
to consider various numerical approaches: the finite difference method, the
spectral element method, the boundary element method, the finite element
method, the finite volume method, etc. All these methods have various
advantages and drawbacks. The amplification of seismic waves in surface soil
layers is mainly due to the velocity contrast between these layers and,
possibly, to topographic effects around crests and hills. The influence of the
geometry of alluvial basins on the amplification process is also know to be
large. Nevertheless, strong heterogeneities and complex geometries are not easy
to take into account with all numerical methods. 2D/3D models are needed in
many situations and the efficiency/accuracy of the numerical methods in such
cases is in question. Furthermore, the radiation conditions at infinity are not
easy to handle with finite differences or finite/spectral elements whereas it
is explicitely accounted in the Boundary Element Method. Various absorbing
layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the
spurious wave reflections especially in some difficult cases such as shallow
numerical models or grazing incidences. Finally, strong earthquakes involve
nonlinear effects in surficial soil layers. To model strong ground motion, it
is thus necessary to consider the nonlinear dynamic behaviour of soils and
simultaneously investigate seismic wave propagation in complex 2D/3D geological
structures! Recent advances in numerical formulations and constitutive models
in such complex situations are presented and discussed in this paper. A crucial
issue is the availability of the field/laboratory data to feed and validate
such models.Comment: of International Journal Geomechanics (2010) 1-1
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