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Mathematical Problems in Engineering
Volume 2011, Article ID 503791, 12 pages
Research Article

Fictitious Domain Technique for the Calculation of Time-Periodic Solutions of Scattering Problem

1Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China
2College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received 8 July 2010; Accepted 27 December 2010

Academic Editor: Maria do Rosário de Pinho

Copyright © 2011 Ling Rao and Hongquan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The fictitious domain technique is coupled to the improved time-explicit asymptotic method for calculating time-periodic solution of wave equation. Conventionally, the practical implementation of fictitious domain method relies on finite difference time discretizations schemes and finite element approximation. Our new method applies finite difference approximations in space instead of conventional finite element approximation. We use the Dirac delta function to transport the variational forms of the wave equations to the differential form and then solve it by finite difference schemes. Our method is relatively easier to code and requires fewer computational operations than conventional finite element method. The numerical experiments show that the new method performs as well as the method using conventional finite element approximation.