The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics

Details The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics

Jun 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005geoji.161..789f&link_type=abstract

Geophysical Journal International, Volume 161, Issue 2, pp. 789-812.

Statistics

Computation

27

Scientific paper

Perfectly matched layers (PMLs) provide an exponential decay, independent of the frequency, of any propagating field along an assigned direction without producing spurious reflections at the interface with the elastic volume. For this reason PMLs have been applied as absorbing boundary conditions (ABCs) and their efficiency in attenuating outgoing wave fields on the outskirts of numerical grids is more and more recognized. However, PMLs are designed for first-order differential equations and a natural extension to second-order Partial Differential Equations (PDEs) involves either additional variables in the time evolution scheme or convolutional operations. Both techniques are computationally expensive when implemented in a spectral element (SE) code and other ABCs (e.g. paraxial or standard sponge methods) still remain more attractive than PMLs.
Here, an efficient second-order implementation of PMLs for SE is developed from interpreting the Newmark scheme as a time-staggered velocity-stress algorithm. The discrete equivalence with the standard scheme is based on an L2 approximation of the stress field, with the same polynomial order as the velocity. In this case, PMLs can be introduced as for first-order equations preserving the natural second-order time stepping. Subsequently, a non-classical frequency-dependent perfectly matched layer is introduced by moving the pole of the stretching along the imaginary axis. In this case, the absorption depends on the frequency and the layer switches from a transparent behaviour at low frequencies to a uniform absorption as the frequency goes to infinity. It turns out to be more efficient than classical PMLs in the absorption of the incident waves, as the grazing incidence approaches, at the cost of a memory variable for any split component. Finally, an extension of PMLs to general curvilinear coordinates is proposed.

Affiliated with

Also associated with

No associations

Rating

The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Newmark scheme as velocity-stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-873954