9,457 research outputs found
Remarks on the stability of Cartesian PMLs in corners
This work is a contribution to the understanding of the question of stability
of Perfectly Matched Layers (PMLs) in corners, at continuous and discrete
levels. First, stability results are presented for the Cartesian PMLs
associated to a general first-order hyperbolic system. Then, in the context of
the pressure-velocity formulation of the acoustic wave propagation, an unsplit
PML formulation is discretized with spectral mixed finite elements in space and
finite differences in time. It is shown, through the stability analysis of two
different schemes, how a bad choice of the time discretization can deteriorate
the CFL stability condition. Some numerical results are finally presented to
illustrate these stability results
A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains
The numerical analysis of elastic wave propagation in unbounded media may be
difficult due to spurious waves reflected at the model artificial boundaries.
This point is critical for the analysis of wave propagation in heterogeneous or
layered solids. Various techniques such as Absorbing Boundary Conditions,
infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers)
lead to an important reduction of such spurious reflections. In this paper, a
simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey
damping formulation which is often already available in existing Finite Element
softwares. The principle of the Caughey Absorbing Layer Method is first
presented (including a rheological interpretation). The efficiency of the
method is then shown through 1D Finite Element simulations considering
homogeneous and heterogeneous damping in the absorbing layer. 2D models are
considered afterwards to assess the efficiency of the absorbing layer method
for various wave types and incidences. A comparison with the PML method is
first performed for pure P-waves and the method is shown to be reliable in a
more complex 2D case involving various wave types and incidences. It may thus
be used for various types of problems involving elastic waves (e.g. machine
vibrations, seismic waves, etc)
Elliptic harbor wave model with perfectly matched layer and exterior bathymetry effects
Standard strategies for dealing with the Sommerfeld condition in elliptic mild-slope models require strong assumptions on the wave field in the region exterior to the computational domain. More precisely, constant bathymetry along (and beyond) the open boundary, and parabolic approximations–based boundary conditions are usually imposed. Generally, these restrictions require large computational domains, implying higher costs for the numerical solver. An alternative method for coastal/harbor applications is proposed here. This approach is based on a perfectly matched layer (PML) that incorporates the effects of the exterior bathymetry. The model only requires constant exterior depth in the alongshore direction, a common approach used for idealizing the exterior bathymetry in elliptic models. In opposition to standard open boundary conditions for mild-slope models, the features of the proposed PML approach include (1) completely noncollinear coastlines, (2) better representation of the real unbounded domain using two different lateral sections to define the exterior bathymetry, and (3) the generation of reliable solutions for any incoming wave direction in a small computational domain. Numerical results of synthetic tests demonstrate that solutions are not significantly perturbed when open boundaries are placed close to the area of interest. In more complex problems, this provides important performance improvements in computational time, as shown for a real application of harbor agitation.Peer ReviewedPostprint (author's final draft
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
A new construction of perfectly matched layers for the linearized Euler equations
Based on a PML for the advective wave equation, we propose two PML models for
the linearized Euler equations. The derivation of the first model can be
applied to other physical models. The second model was implemented. Numerical
results are shown.Comment: submitted for publication on February 1st 2005 What's new: interface
conditions for the first PML model, a 3D section, more numerical result
Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver
Due to discretization effects and truncation to finite domains, many
electromagnetic simulations present non-physical modifications of Maxwell's
equations in space that may generate spurious signals affecting the overall
accuracy of the result. Such modifications for instance occur when Perfectly
Matched Layers (PMLs) are used at simulation domain boundaries to simulate open
media. Another example is the use of arbitrary order Maxwell solver with domain
decomposition technique that may under some condition involve stencil
truncations at subdomain boundaries, resulting in small spurious errors that do
eventually build up. In each case, a careful evaluation of the characteristics
and magnitude of the errors resulting from these approximations, and their
impact at any frequency and angle, requires detailed analytical and numerical
studies. To this end, we present a general analytical approach that enables the
evaluation of numerical discretization errors of fully three-dimensional
arbitrary order finite-difference Maxwell solver, with arbitrary modification
of the local stencil in the simulation domain. The analytical model is
validated against simulations of domain decomposition technique and PMLs, when
these are used with very high-order Maxwell solver, as well as in the infinite
order limit of pseudo-spectral solvers. Results confirm that the new analytical
approach enables exact predictions in each case. It also confirms that the
domain decomposition technique can be used with very high-order Maxwell solver
and a reasonably low number of guard cells with negligible effects on the whole
accuracy of the simulation.Comment: 33 pages, 14 figure
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