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1 Computational Seismology
Laboratory
Department of Civil and Environmental Engineering
Carnegie
Mellon University
Pittsburgh, Pennsylvania 15213
(J.B.)
| The first 300 words of the full text of this article appear below. |
We thank Faccioli, Vanini, Paolucci, and Stupazzini for their interest in our
articles (Bielak et
al., 2003;
Yoshimura et al.,
2003; hereafter I and II). We will refer to their comments (Faccioli
et al., 2004) as FVPS. The primary aim of FVPS is
(1) to illustrate the implementation by FVPS of the domain reduction
method (DRM) described in I and II for the hybrid
finite-element–spectral-element (FE–SE) method, and (2)
to show that the use of SEs can lead to dramatic reduction in
computer processing unit (CPU) time and storage requirements, without
loss of accuracy, with respect to the traditional FEs used in II. We
will show (1) that since the FE–SE method is a particular case
of the FE method (FEM), the DRM described in I
and II, and in our earlier work
(Loukakis,
1988; Loukakis
and Bielak, 1994), provides the complete theoretical framework
needed for the application of the DRM to FE–SEs,
and, thus, the section titled "Method" in FVPS is
essentially redundant; and (2) that while SEs are ideally suited for
problems in which the exact solution is smooth within every SE, the
advantages of the SE method (SEM) over other methods for
problems that exhibit discontinuities and singularities is far from having been
demonstrated. To our knowledge, there is no evidence thus far that the
SEM is superior to the FEM for every possible wave
propagation problem in elastodynamics, since each method has its advantages and
disadvantages. We will argue that, in fact, the more traditional FEM
has important advantages over the particular SEM implementation by
FVPS, and that, most likely, it is more efficient
Related articles in Bulletin of the Seismological Society of America:
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