High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach

• Sergio López-Ureña ^[1] ; Rosa Donat ^[1]
  1. [1] Universitat de València

     Universitat de València

     Valencia, España

     
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 2, Nº. 2, 2017, págs. 367-384
• Idioma: inglés
• DOI: 10.21042/amns.2017.2.00030
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• Resumen

  • In the present work, we analyze a technique designed by Geraci et al. in cite{TE2014,TE2016} named the Truncate and Encode TE strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations PDEs in Uncertainty Quantification UQ, and as a weakly intrusive method in the unsteady case.

    We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a high performance of the algorithm.