Boletín SEMA, No 31 (2005)

Tamaño de la letra:  Pequeña  Mediana  Grande

Harten framework for multiresolution with applications: From conservation laws to image compression

F. Aràndiga, G. Chiavassa, R. Donat

Resumen


We briefly review Harten s framework for multiresolution decompositions and describe two situations in which two dfferent instances of the general framework have been used with success. In the numerical simulation of Hyperbolic Conservation Laws, the simple point-value setting with a linear centered interpolatory reconstruction is used to design a multilevel algorithm that effectively helps to reduce the computational expense associated to state of the art high resolution shock capturing schemes. The possibility of using nonlinear, data dependent, reconstruction techniques is explored in image compression. For piecewise smooth images, ENO reconstruction techniques outperform classical algorithms based on biorthogonal wavelets.

Palabras clave:  Conservation laws, multiresolution, shock capturing schemes, image compression.

Clasificación por materias AMS:
65M06, 65D05, 35L65, 94A08.

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