Research Report: Manuscript CMCU-95-03, July 1995
A Space-Time Finite Element
Method for Structural Acoustics
in Infinite Domains, Part II:
Exact Time-Dependent
Non-Reflecting Boundary Conditions
Lonny L. Thompson
Computational Mechanics at Clemson University
Department of Mechanical Engineering
Clemson, South Carolina 29634-0921
Abstract
In Part I, a new space-time finite
element method for transient structural acoustics in
exterior domains was given.
The formulation employs a finite computational fluid domain
surrounding the structure and incorporates local time-dependent
non-reflecting boundary conditions on the fluid truncation
boundary.
In this paper, new exact time-dependent
non-reflecting boundary conditions
are developed for solutions of the scalar wave equation in three
space dimensions.
These high-order accurate absorbing boundary
conditions are
based on the exact impedance relation for the acoustic fluid through
the Dirichlet-to-Neumann (DtN) map in the frequency domain and are
exact for solutions consisting of the first $N$ spherical
wave harmonics.
Time-dependent boundary conditions are obtained through
an inverse Fourier transform procedure.
Two alternative sequences of boundary conditions are derived;
the first involves both temporal and spatial derivatives (local in
time and local in space version), and the second involves
temporal derivatives and a spatial integral (local in time and
nonlocal in space version).
These non-reflecting boundary conditions are incorporated
as `natural'
boundary conditions in the space-time variational equation, i.e.
they are enforced weakly in both space and time.
Several numerical examples involving transient radiation
are presented to illustrate the high-order accuracy and efficiency
achieved by the new space-time finite element formulation for transient
structural acoustics with non-reflecting boundaries.
Postscript file of Manuscript CMCU-95-03