@TechReport{ it:2001-024,
author = {Larisa Beilina and Klas Samuelsson and Krister
{\AA}hlander},
title = {A hybrid method for the wave equation},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2001},
number = {2001-024},
month = oct,
note = {Also available as Preprint 2001-14 in Chalmers Finite
Element Center Preprint series},
abstract = {Hybrid finite element/finite difference simulation of the
wave equation is studied. The simulation method is hybrid
in the sense that different numerical methods, finite
elements and finite differences, are used in different
subdomains. The purpose is to combine the flexibility of
finite elements with the efficiency of finite differences.
The construction of proper geometry discretisations is
important for the hybrid approach. A decomposition of the
computational domain is described, which yields simple
communication between structured and unstructured
subdomains.
An explicit hybrid method for the wave equation is
constructed where the explicit finite difference schemes
and finite element schemes coincide for structured
subdomains. These schemes are used in the hybrid approach,
keeping finite differences on the structured subdomains and
applying finite elements on the unstructured domains. As a
consequence of the discretisation strategy, the resulting
hybrid scheme can be regarded as a pure finite element
scheme. Any numerical difficulties such as instabilities at
the interfaces are thus avoided.
The feasibility of the hybrid approach is illustrated by
numerous wave equation simulations in two and three space
dimensions. In particular, the approach can easily be used
for implementing absorbing boundary conditions.
The efficiency of different approaches is a key issue of
the current study. For our test cases, the hybrid approach
is about 5 times faster than a corresponding highly
optimised finite element method. It is concluded that the
hybrid approach may be an important tool to reduce the
execution time and memory requirement for this kind of
large scale computations. }
}