On the Fourier extension of nonperiodic functions

D Huybrechs - SIAM Journal on Numerical Analysis, 2010 - SIAM
We obtain exponentially accurate Fourier series for nonperiodic functions on the interval -1,1
by extending these functions to periodic functions on a larger domain. The series may be …

A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds

JP Boyd - Journal of Computational Physics, 2002 - Elsevier
The range of Fourier methods can be significantly increased by extending a nonperiodic
function f (x) to a periodic function f̃ on a larger interval. When f (x) is analytically known on …

High-order unconditionally stable FC-AD solvers for general smooth domains I. Basic elements

OP Bruno, M Lyon - Journal of Computational Physics, 2010 - Elsevier
We introduce a new methodology for the numerical solution of Partial Differential Equations
in general spatial domains: our algorithms are based on the use of the well-known …

Frames and numerical approximation

B Adcock, D Huybrechs - Siam Review, 2019 - SIAM
Functions of one or more variables are usually approximated with a basis: a complete,
linearly independent system of functions that spans a suitable function space. The topic of …

Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

OP Bruno, Y Han, MM Pohlman - Journal of computational Physics, 2007 - Elsevier
We present a new method for construction of high-order parametrizations of surfaces:
starting from point clouds, the method we propose can be used to produce full surface …

[HTML][HTML] Tumor location and parameter estimation by thermography

JP Agnelli, AA Barrea, CV Turner - Mathematical and Computer Modelling, 2011 - Elsevier
In non-invasive thermal diagnostics, accurate correlations between the thermal image on
skin surface and interior human physiology are often desired, which require general …

On the numerical stability of Fourier extensions

B Adcock, D Huybrechs, J Martín-Vaquero - Foundations of Computational …, 2014 - Springer
An effective means to approximate an analytic, nonperiodic function on a bounded interval is
by using a Fourier series on a larger domain. When constructed appropriately, this so-called …

A coordinate transformation based barycentric interpolation collocation method and its application in bending, free vibration and buckling analysis of irregular …

ZM Huang, LX Peng - International Journal for Numerical …, 2023 - Wiley Online Library
In this article, a meshless barycentric interpolation collocation method (BICM) with
coordinate transformation is proposed to solve the governing partial differential equations …

Approximating smooth, multivariate functions on irregular domains

B Adcock, D Huybrechs - Forum of Mathematics, Sigma, 2020 - cambridge.org
In this paper, we introduce a method known as polynomial frame approximation for
approximating smooth, multivariate functions defined on irregular domains in, for a large …

[HTML][HTML] On the resolution power of Fourier extensions for oscillatory functions

B Adcock, D Huybrechs - Journal of computational and applied …, 2014 - Elsevier
Functions that are smooth but non-periodic on a certain interval possess Fourier series that
lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be …