Exact boundary conditions for time-harmonic wave propagation in locally perturbed periodic media

2009 ◽  
Vol 59 (9) ◽  
pp. 2155-2178 ◽  
Author(s):  
Sonia Fliss ◽  
Patrick Joly
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Harmonic Wave ◽  
Periodic Media ◽  
Time Harmonic ◽  
Exact Boundary ◽  
Perturbed Periodic

scholarly journals Sweeping preconditioners for stratified media in the presence of reflections

2020 ◽  
Vol 1 (4) ◽  
Author(s):  
Janosch Preuß ◽  
Thorsten Hohage ◽  
Christoph Lehrenfeld
Keyword(s):  
Boundary Conditions ◽  
Harmonic Wave ◽  
Absorbing Boundary Conditions ◽  
Stratified Medium ◽  
Stratified Media ◽  
Absorbing Boundary ◽  
Small Perturbations ◽  
Numerical Tests ◽  
Time Harmonic ◽  
Dirichlet To Neumann Operator

Abstract In this paper we consider sweeping preconditioners for time harmonic wave propagation in stratified media, especially in the presence of reflections. In the most famous class of sweeping preconditioners Dirichlet-to-Neumann operators for half-space problems are approximated through absorbing boundary conditions. In the presence of reflections absorbing boundary conditions are not accurate resulting in an unsatisfactory performance of these sweeping preconditioners. We explore the potential of using more accurate Dirichlet-to-Neumann operators within the sweep. To this end, we make use of the separability of the equation for the background model. While this improves the accuracy of the Dirichlet-to-Neumann operator, we find both from numerical tests and analytical arguments that it is very sensitive to perturbations in the presence of reflections. This implies that even if accurate approximations to Dirichlet-to-Neumann operators can be devised for a stratified medium, sweeping preconditioners are limited to very small perturbations.

scholarly journals A class of discontinuous Petrov–Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D

2011 ◽  
Vol 230 (7) ◽  
pp. 2406-2432 ◽  
Author(s):  
J. Zitelli ◽  
I. Muga ◽  
L. Demkowicz ◽  
J. Gopalakrishnan ◽  
D. Pardo ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Harmonic Wave ◽  
Galerkin Methods ◽  
Optimal Test ◽  
Time Harmonic
Sign in / Sign up

Export Citation Format

Share Document