52,023 research outputs found
Boundary conditions for coupled quasilinear wave equations with application to isolated systems
We consider the initial-boundary value problem for systems of quasilinear
wave equations on domains of the form , where is
a compact manifold with smooth boundaries . By using an
appropriate reduction to a first order symmetric hyperbolic system with maximal
dissipative boundary conditions, well posedness of such problems is established
for a large class of boundary conditions on . We show that our
class of boundary conditions is sufficiently general to allow for a well posed
formulation for different wave problems in the presence of constraints and
artificial, nonreflecting boundaries, including Maxwell's equations in the
Lorentz gauge and Einstein's gravitational equations in harmonic coordinates.
Our results should also be useful for obtaining stable finite-difference
discretizations for such problems.Comment: 22 pages, no figure
Application of edge-based finite elements and vector ABCs in 3D scattering
A finite element absorbing boundary condition (FE-ABC) solution of the scattering by arbitrary 3-D structures is considered. The computational domain is discretized using edge-based tetrahedral elements. In contrast to the node-based elements, edge elements can treat geometries with sharp edges, are divergence-less, and easily satisfy the field continuity condition across dielectric interfaces. They do, however, lead to a higher unknown count but this is balanced by the greater sparsity of the resulting finite element matrix. Thus, the computation time required to solve such a system iteratively with a given degree of accuracy is less than the traditional node-based approach. The purpose is to examine the derivation and performance of the ABC's when applied to 2-D and 3-D problems and to discuss the specifics of our FE-ABC implementation
Spectral element modeling of three dimensional wave propagation in a self-gravitating Earth with an arbitrarily stratified outer core
This paper deals with the spectral element modeling of seismic wave
propagation at the global scale. Two aspects relevant to low-frequency studies
are particularly emphasized. First, the method is generalized beyond the
Cowling approximation in order to fully account for the effects of
self-gravitation. In particular, the perturbation of the gravity field outside
the Earth is handled by a projection of the spectral element solution onto the
basis of spherical harmonics. Second, we propose a new formulation inside the
fluid which allows to account for an arbitrary density stratification. It is
based upon a decomposition of the displacement into two scalar potentials, and
results in a fully explicit fluid-solid coupling strategy. The implementation
of the method is carefully detailed and its accuracy is demonstrated through a
series of benchmark tests.Comment: Sent to Geophysical Journal International on July 29, 200
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