Research Report: Manuscript CMCU-95-02, July 1995
A Space-Time Finite Element
Method for Structural Acoustics
in Infinite Domains, Part I:
Formulation, Stability,
and Convergence
Lonny L. Thompson
Computational Mechanics at Clemson University
Department of Mechanical Engineering
Clemson, South Carolina 29634-0921
Abstract
A space-time finite element method
for solution of
the exterior structural acoustics problem involving the
interaction of vibrating
elastic structures submerged in an infinite acoustic fluid is formulated.
In particular,
new time-discontinuous Galerkin and Galerkin Least-Squares (GLS)
variational
formulations for coupled structural acoustics in unbounded
domains
are developed
and analyzed for stability and convergence.
The formulation employs a finite computational fluid domain
surrounding the structure and incorporates
time-dependent non-reflecting
boundary conditions on the
fluid truncation boundary.
Energy estimates are obtained which allow us to prove the unconditional
stability of the method for the coupled fluid-structure problem
with absorbing boundaries.
The methods developed are especially useful for the application
of adaptive solution strategies for transient acoustics
in which unstructured space-time meshes
are used to track waves propagating along space-time
characteristics.
An important feature
of the space-time formulation
is the incorporation of temporal jump operators
which allow for finite
element interpolations
that are discontinuous in time.
For additional stability,
%and to aid in the proof of convergence,
least-squares operators based on local
residuals of the structural acoustics equations
including the non-reflecting boundary conditions are incorporated.
The energy decay estimates and
high-order accuracy predicted by our {\em a priori} error estimates are
demonstrated numerically in a simple canonical example.
Postscript file of Manuscript CMCU-95-02