![]() |
Computational & Technology Resources
an online resource for computational,
engineering & technology publications |
Civil-Comp Proceedings
ISSN 1759-3433 CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 71
Wave Problems in Infinite Domains M. Premrov and I. Spacapan
Faculty of Civil Engineering, University of Maribor, Maribor, Slovenia Full Bibliographic Reference for this paper
M. Premrov, I. Spacapan, "Wave Problems in Infinite Domains", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 71, 2001. doi:10.4203/ccp.73.71
Keywords: applied mechanics, wave motion, infinite domains, artificial boundary, halfspace condition, finite element.
Summary
This paper presents an iterative method for solving two dimensional wave
problems in infinite domains. The method is based on an iterative variation of fictive
boundary conditions on an artificial finite boundary. The finite computational
domain is in each iteration subjected to actual boundary conditions and to different
(Dirichlet or Neumann) fictive boundary conditions on the artificial boundary. The
halfspace Dirichlet to Neumann (DtN) operator is used only to determinate new
fictive boundary conditions and is not included into a finite element formulation.
Thus any finite elements can be used and the method is especially applicable for
computing higher harmonics.
In solving wave problems in infinite domains the main problem is to satisfy the radiation condition - the boundary condition at infinity. Radiation condition is satisfied automatically as a part of the fundamental solution in the boundary element method. Unfortunately, the fundamental solution is not always available. Although the boundary-element method is regarded as the most powerful procedure for modeling the unbounded medium, it requires a strong analytical and numerical background.
More flexible is the finite element method. The infinite domain is first truncated
by introducing an artificial finite boundary (
In the presented method an iterative solution for solving wave problems in
infinite domains is obtained. The infinite domain outside of the artificial boundary is
represented with halfspace operator. The exact non-local operator ( The method in this paper was tested on two dimensional out of plane problems. Future work will include the extension of these ideas to two dimensional in plane problems. Finally we expect that the method will be applicable for solving three dimensional problems. References
purchase the full-text of this paper (price £20)
go to the previous paper |
|