6533b830fe1ef96bd12966fc

RESEARCH PRODUCT

Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing

Chi-wang ShuJuan Ruiz-álvarezSergio AmatDionisio F. Yáñez

subject

Signal processing0209 industrial biotechnologyDiscretizationComputer science02 engineering and technologyClassification of discontinuitiesCell-averageMathematics::Numerical Analysis020901 industrial engineering & automationImproved adaption to discontinuitiesNew optimal weightsPosition (vector)Multiresolution schemesFOS: Mathematics0202 electrical engineering electronic engineering information engineeringMathematics - Numerical AnalysisSignal processingWENO65D05 65D17 65M06 65N0612 MatemáticasApplied MathematicsOrder of accuracyMatemática Aplicada020206 networking & telecommunicationsNumerical Analysis (math.NA)Expression (mathematics)Computational MathematicsNonlinear systemGravitational singularityAlgorithm

description

In this paper we translate to the cell-average setting the algorithm for the point-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F. Y\'a\~nez, A new WENO-2r algorithm with progressive order of accuracy close to discontinuities, submitted to SIAM J. Numer. Anal.. This new strategy tries to improve the results of WENO-($2r-1$) algorithm close to the singularities, resulting in an optimal order of accuracy at these zones. The main idea is to modify the optimal weights so that they have a nonlinear expression that depends on the position of the discontinuities. In this paper we study the application of the new algorithm to signal processing using Harten's multiresolution. Several numerical experiments are performed in order to confirm the theoretical results obtained.

yearjournalcountryeditionlanguage
2020-09-20Applied Mathematics and Computation
https://doi.org/10.1016/j.amc.2021.126131