UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: November 1, 1999

TREFFTZ INFINITE ELEMENTS FOR THE HELMHOLTZ EQUATION

Isaac Harari*
Department of Solid Mechanics, Materials and Structures
Tel Aviv University, Tel Aviv, Israel

ABSTRACT

A Trefftz functional for partitioned problems provides a general
framework for domain-based computation in unbounded regions with
particular reference to time-harmonic acoustics.  Continuity of outer
fields in the unbounded domain with finite element interpolation of
inner fields is enforced weakly in the variational setting, precluding
compatibility requirements.  For smooth representations of the outer
field there is no integration over the unbounded domain.  The
formulation conserves energy flux when the outer fields are complete,
guaranteeing uniqueness of solutions.  The specific formulation depends
on the representation of the outer field.  Examples of formulations
employing DtN boundary conditions are reproduced.

Infinite elements are usually based on piecewise smooth functions.  In
this case we account for possible discontinuities across infinite
element boundaries by incorporating a jump term in the formulation.  Two
prominent features simplify the task of discretization:  the infinite
elements mesh the interface only and need not match the finite elements
on the interface.

Various infinite element approximations for two-dimensional
configurations with circular interfaces are reviewed.  Numerical results
demonstrate the good performance of these schemes.  A simple study
points to the proper interpretation of spectral results for the
formulation.  The spectral properties of these infinite elements are
examined with a view to the correct representation of physics and
efficient numerical solution.

For three-dimensional configurations with spherical interfaces the
infinite element interpolation is based on separation of variables in a
spherical system.  The lowest-order element approximations combine
piecewise-linear azimuthal interpolation, latitude variation described
by associated Legendre functions, and oscillatory outgoing radial
behavior.  Singularities at the poles require careful consideration.

This is joint work with Paul Barbone of Boston University, with
contributions by Parama Barai, Rami Shalom, and Michael Slavutin.

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* Currently visiting the University of Colorado.