Adaptive bivariate Chebyshev approximation

Abstract

We propose an adaptive algorithm which extends Chebyshev series approximation to bivariate functions, on domains which are smooth transformations of a square. The method is tested on functions with different degrees of regularity and on domains with various geometries. We show also an application to the fast evaluation of linear and nonlinear bivariate integral transforms.2000 AMS subject classification: 41A10, 65D10, 65R10.

Hermite Methods for Aeroacoustics: Recent Progress

“…Our work adapts the univariate Chebyshev approximation algorithm of the Chebfun Team 11 to model bivariate functions, following the method of Sommariva, Vianello, and Zanovello. 12 The Chebfun algorithm was translated into Fortran and applied with minor adaptations to the bivariate problem. The univariate Chebyshev series expansion of a function takes the form…”