abstract.txt

High-order accurate solutions to acoustic-elastic interface problems
on adapted parallel meshes using a discontinuous Galerkin method

Lucas C. Wilcox [1]
Carsten Burstedde [1]
Georg Stadler [1]
Omar Ghattas [1,2,3,4]

[1] Institute for Computational Engineering and Sciences, The
University of Texas at Austin, Austin, TX 78712, USA

[2] Jackson School of Geosciences, The University of Texas at Austin,
Austin, TX 78712, USA

[3] Department of Mechanical Engineering, The University of Texas at
Austin, Austin, TX 78712, USA

[4] Institute for Geophysics, The University of Texas at
Austin, J.J. Pickle Research Campus, Austin, TX 78758, USA

The overall goal of the this research project is to create systematic,
rigorous, and scalable algorithms for global seismic waveform
inversion.  The first step we took along this path was to create an
accurate solver for numerically simulating wave propagation
in materials with acoustic-elastic interfaces.  We have chosen
a high-order method to effectively eliminate numerical dispersion
enabling simulations over many periods of the wave.  The numerical
method uses a strain-velocity formulation allowing for acoustic and
elastic wave equations to be solve in the same framework.  Careful
attention has been taken to develop a numerical flux to ensure that
the method remains high-order in the presence of material
discontinuities.  A sketch of its derivation is given.  To study the
numerical accuracy of the proposed method we compare with
reference solutions of classical interface problems, including Raleigh
waves, Lamb waves, Stoneley waves, Scholte waves, and Love waves.

In designing our numerical method we kept the goal of numerical
inversion in mind.  The problem of inferring a medium from
observations of scattered waveforms is fundamentally a ill-posed
problem.  Using a least-squares misfit of the waveform at discrete
locations is know to produce local minimum in the objective function.
One way to overcome this is to use grid continuation which requires
adaptive mesh refinement (AMR).  Applying this to the global inverse
problem demands parallel scalability from the ground up.  We show
numerical results with adaptive meshes of Earth models that display
the method's accuracy on curvilinear nonconforming meshes.  Since
these simulation require large-scale computing we report
strong and weak parallel scaling results for mesh generation and
solution of the equations.