### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 1pNS9. Wave scattering using a hybrid MMP--FE technique.

**Matthias G. Imhof
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*MIT Earth Resources Lab., Cambridge, MA 02142-1324
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Among the methods amendable to solve acoustic or elastic scattering
problems are the finite elements method (FEM) and multiple multipole (MMP)
expansions [M. G. Imhof, J. Acoust. Soc. Am. 97, 754--763 (1995)]. Among the
difficulties the FEM encounters are long calculation times, large memory
requirements, and the need for absorbing boundary conditions. On the other hand,
the FEM is perfectly suited for heterogeneous media because it automatically
accounts for changes in material properties. In contrast, the computational cost
of MMP expansions is independent of the source--receiver geometry. An unbounded
domain poses no difficulty since the expansion functions account automatically
for the radiation condition. MMP expansions often converge with very few terms
and therefore reduce the computational effort. Unfortunately, expansion
functions for heterogeneous media are difficult to find. Scattering problems
with heterogeneous scatterers embedded in a homogeneous background are difficult
(FEM) or impossible (MMP) to solve with either of these techniques alone.
Therefore, the MMP expansions are coupled with the FE method. For a cylindrical
scattering problem, the resulting solution is compared to the analytical one.
Results for multiple inhomogeneous scatterers embedded in a homogeneous media
are presented.