Maximum-entropy methods for time-harmonic acoustics

This paper explores the application of maximum-entropy methods (max-ent) to time harmonic acoustic problems. Max-ent basis functions are mesh-free approximants that are constructed observing an equivalence between basis functions and discrete probability distributions and applying Jaynes's maximum entropy principle. They are C∞-continuous and therefore they are particularly suited for the resolution of Helmholtz problems, where classical finite element methods show a poor accuracy in the high frequency region. In addition, it was recently shown that max-ent approximants can be blended with isogeometric basis functions on the boundary of the domain. This preserves the correct representation of the boundary like in Isogeometric Analysis, with the advantage that the discretization of the interior of the domain is straightforward. In this paper the max-ent mathematical formulation is reviewed and then some numerical applications are studied, including a 2D car cavity geometry defined by B-spline curves. In all cases, if the same nodal discretization is used, finite elements results are significantly improved.