20 September 2007 A refining estimation for adaptive solution of wave equation based on curvelets
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Abstract
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.
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Jianwei Ma, Gang Tang, M. Y. Hussaini, "A refining estimation for adaptive solution of wave equation based on curvelets", Proc. SPIE 6701, Wavelets XII, 67012J (20 September 2007); doi: 10.1117/12.730336; https://doi.org/10.1117/12.730336
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