This paper presents a refining estimation to control the process of adaptive mesh refinement (AMR) based on the curvelet transform. The curvelet is a recently developed geometric multiscale system that could provide optimal approximation to curve-singularity functions and sparse representation of wavefront phenomena. Utilizing these advantages, we attempt to introduce the curvelet transform into AMR as a criterion estimate of refinement for adaptive solving of the wave equation. Numerical simulations show that the proposed method could optimally capture interesting areas where refinement is needed, so that a high accuracy result is obtained.

Date Published: 20 September 2007
PDF: 10 pages
Proc. SPIE 6701, Wavelets XII, 67012J (20 September 2007); doi: 10.1117/12.730336

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)