NJIT Applied Mathematics Colloquium
Friday, March 2, 2012, 11:30am
Cullimore Lecture Hall II
New Jersey Institute of Technology
Multiscale Modeling and Analysis of the Wave Equation
Susan Minkoff
University of Maryland at Baltimore County
Imaging the Earth's subsurface requires determination of the "important
information" inherent in data that ranges over multiple scales. While
numerical upscaling is a common approach for speeding up solution of
the fluid flow equations, simulation of waves through the same Earth is
generally accomplished using single scale finite differences. We
describe a two-scale finite-element based wave simulator and the
associated adjoint problem used for inversion.
Operator-based upscaling decomposes the solution into coarse and subgrid components.
Fine-scale solution information is incorporated in the coarse solution.
I will describe adapting operator-based upscaling to the acoustic and
elastic wave equations in 2 and 3D, and will
give a matrix analysis of this two-stage process that produces an
explanation of the underlying physical equations being solved by this
technique. We see that the coarse grid solution involves solving a
matrix problem with entries that are averages of the original parameter
field on coarse grid boundaries. Calculation of the adjoint for the
upscaled wave equation simulator is
straight-forward if differentiation of the continuous pde model is accomplished before
discretization. The result is that the adjoint problem can be solved by
the same upscaling method as the standard acoustic wave equation.
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