A refining estimation for adaptive solution of wave equation based on curvelets

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.