17 citations · 95 across the 41 of their papers we have counts for
5 papers · 1 filter
Pointwise and uniform convergence of Fourier extensions
Marcus Webb, Vincent Coppé, Daan Huybrechs
Fourier series approximations of continuous but nonperiodic functions on an interval suffer the Gibbs phenomenon, which means there is a permanent oscillatory overshoot in the neig…
A numerical method for oscillatory integrals with coalescing saddle points
Daan Huybrechs, Arno B. J. Kuijlaars, Nele Lejon
The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoi…
An oversampled collocation approach of the Wave Based Method for Helmholtz problems
Daan Huybrechs, Anda-Elena Olteanu
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis co…
Frames and numerical approximation II: generalized sampling
Ben Adcock, Daan Huybrechs
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offe…
Approximating smooth, multivariate functions on irregular domains
Ben Adcock, Daan Huybrechs
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in dimensions, where…