, Volume 9, Issue 3, pp 259-281

A fast Legendre transform algorithm and applications to the adhesion model

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Abstract

A new algorithm for the computation of discrete Legendre transforms is discussed. Classical solutions have a running time proportional toN 2d , whereN is the size of the spatial grid andd is the space dimension. The new algorithm has a running timeO((N log2 N) d ). A general application of this algorithm is to the weak solutions of hyperbolic systems of conservation laws as considered by Lax (1973,Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, S.I.A.M.). The potential of the method is illustrated on the “adhesion model,” a multi-dimensional version of the Burgers equation, used to study the formation of large-scale structures in cosmology.