Abstract
An adaptive finite element method is developed for acoustic wave propagation in unbounded media. The efficiency and high accuracy of the method are achieved by combining an exact nonreflecting boundary condition [SIAM J. Appl. Math. 55 (1995) 280; J. Comput. Phys. 127 (1996) 52] with space–time adaptivity [East–West J. Numer. Math. 7(4) (1999) 263]. Hence the computational effort is concentrated where needed, while the artificial boundary can be brought as close as desired to the scatterer. Both features combined yield high accuracy and keep the number of unknowns to a minimum. An energy inequality is derived for the initial-boundary value problem at the continuous level. Together with an implicit second order time discretization it guarantees unconditional stability of the semi-discrete system. The resulting fully discrete linear system that needs to be solved every time step is unsymmetric but can be transformed into an equivalent sequence of small nonsymmetric and large symmetric positive definite systems, which are efficiently solved by conjugate gradient methods. Numerical examples illustrate the high accuracy of the method, in particular in the presence of complex geometry.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Computer Methods in Applied Mechanics and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
