Publications: Daan Huybrechs

Publications (cv in pdf)

Technical reports

B. Adcock and D. Huybrechs
On the resolution power of Fourier extensions for oscillatory functions
Preprint as Technical Report TW-597 [abstract][pdf].

Journal papers

(Note that preprints and technical reports may differ from published versions)

A. Asheim, A. Deano, D. Huybrechs and H. Wang
A Gaussian quadrature rule for oscillatory integrals on a bounded interval
Discrete and Continuous Dynamical Systems A. To appear.
Preprint as Technical Report TW-621 [abstract][pdf] or on arXiv.
B. Adcock, D. Huybrechs and J. Martin-Vaquero
On the numerical stability of Fourier extensions
Foundations of Computational Mathematics. To appear.
Preprint as Technical Report TW-615 [abstract][pdf] or on arXiv.
H. Wang, D. Huybrechs and S. Vandewalle
Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials
Mathematics of Computation. To appear.
Preprint as Technical Report TW-604 [abstract].
A. Asheim and D. Huybrechs
Complex Gaussian quadrature for oscillatory integral transforms
IMA Journal of Numerical Analysis. 2013.
DOI. Preprint as Technical Report TW-594 [abstract][pdf].
H. Wang, L. Zhang and D. Huybrechs
Asymptotic expansions and fast computation of oscillatory Hilbert transforms
Numerische Mathematik. To appear.
Preprint as Technical Report TW-605 [abstract][pdf].
D. Huybrechs and S. Olver
Superinterpolation in highly oscillatory quadrature
Foundations of Computational Mathematics 12(2):203-228, 2012.
DOI. Preprint as Technical Report TW-569 [abstract][pdf].
D. Huybrechs, A. Iserles and S. P. Nørsett
From high oscillation to rapid approximation V: The equilateral triangle
IMA J. Numer. Anal. 31(3):755-785, 2011.
DOI. Preprint as Technical Report in Numerical Analysis NA2009_04 (University of Cambridge) [pdf].
A. Deaño, D. Huybrechs and A. Kuijlaars
Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature
Journal of Approximation Theory 162(12):2202-2224, 2010.
DOI. Preprint as Technical Report TW-557 [abstract][pdf].
A. Asheim and D. Huybrechs
Local solutions to high frequency 2D scattering problems
J. Comp. Phys., 229(14):5357-5372, 2010.
DOI. Preprint as Technical Report TW-524 [abstract][pdf].
A. Asheim and D. Huybrechs
Asymptotic analysis of numerical steepest descent with path approximations
Foundations of Computational Mathematics, 10(6):647-671, 2010.
DOI. Preprint as Technical Report TW-536 [abstract][pdf].
D. Huybrechs, A. Iserles and S. P. Nørsett
From high oscillation to rapid approximation IV: Accelerating convergence

IMA J. Numer. Anal., 31(2):442-468, 2011.
DOI. Preprint as Technical Report in Numerical Analysis NA2007_07 (University of Cambridge) [pdf].
D. Huybrechs
On the Fourier extension of non-periodic functions
SIAM J. Numer. Anal., 47(6):4326-4355, 2010.
Article as published. DOI.
D. Huybrechs
Stable high-order quadrature rules with equidistant points
J. Comput. Appl. Math., 231(2):933-947, 2009.
DOI. Preprint as Technical Report TW-528 [abstract][pdf].
M. Honnor, J. Trevelyan and D. Huybrechs
Numerical evaluation of 2D partition of unity boundary integrals for Helmholtz problems
J. Comput. Appl. Math., 234:1656-1662, 2010.
DOI.
R. Cools, D. Huybrechs and D. Nuyens
Recent topics in numerical integration
Int. J. Quant. Chem., 109:1748-1755, 2009.
DOI.
A. Deaño and D. Huybrechs
Complex Gaussian quadrature of oscillatory integrals
Numer. Math., 112(2):197-219, 2009.
DOI. Preprint as Technical Report TW-519 [abstract][pdf].
D. Huybrechs and R. Cools
On generalized Gaussian quadrature for singular and nearly singular integrals
SIAM J. Numer. Anal., 47(1):719-739, 2009.
DOI. Preprint as Technical Report TW-523 [abstract][pdf].
D. Huybrechs and S. Vandewalle
An efficient implementation of boundary element methods for computationally expensive Green's functions
Eng. Anal. Boundary Elem., 32(8):621-632, 2008.
DOI. Preprint as Technical Report TW-510 [abstract][pdf].
D. Huybrechs and S. Vandewalle
A sparse discretisation for integral equation formulations of high frequency scattering problems
SIAM J. Sci. Comput., 29(6):2305-2328, 2007.
DOI. Preprint as Technical Report TW-447 [abstract][pdf].
D. Huybrechs and S. Vandewalle
The construction of cubature rules for multivariate highly oscillatory integrals
Math. Comp., 76(260):1955-1980, 2007.
DOI. Preprint as Technical Report TW-442 [abstract][pdf].
D. Huybrechs and S. Vandewalle
On the evaluation of highly oscillatory integrals by analytic continuation
SIAM J. Numer. Anal., 44(3):1026-1048, 2006.
Article as published. DOI. Preprint as Technical Report TW-431 [abstract][pdf].
D. Huybrechs and S. Vandewalle
A two-dimensional wavelet packet transform for matrix compression of integral equations with highly oscillatory kernel
J. Comput. Appl. Math., 197(1):218-232, 2006.
DOI. Preprint as Technical Report TW-417 [abstract][pdf].
D. Huybrechs and S. Vandewalle
Composite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions
J. Comput. Appl. Math. 180(1):119-135, 2005.
DOI. Preprint as Technical Report TW-388 [abstract][pdf].
D. Huybrechs, J. Simoens and S. Vandewalle
A note on wave number dependence of wavelet matrix compression for integral equations with oscillatory kernel
J. Comput. Appl. Math. 172(2):233-246, 2004.
DOI. Preprint as Technical Report TW-356 [abstract][pdf].

Chapters in books

A. Boettcher, S. Grudsky, D. Huybrechs and A. Iserles
First-order trace formulas for the iterates of the Fox-Li operator
In: A Panorama of Modern Operator Theory and Related Topics, Springer, pp. 207-224, 2012.
Preprint as Technical Report in Numerical Analysis NA2010_08 (University of Cambridge) [pdf].

Proceedings of the HOP programme

D. Huybrechs and S. Olver.
Highly oscillatory quadrature
Chapter 2 in: Highly Oscillatory Problems, Cambridge University Press, pp. 25-50, 2009.
Preprint available [pdf].
D. Huybrechs and S. Olver.
Rapid function approximation by modified Fourier series
Chapter 3 in: Highly Oscillatory Problems, Cambridge University Press, pp. 51-71, 2009.
Preprint available [pdf].

Papers in proceedings

Reviewed papers in proceedings

B. Adcock and D. Huybrechs
Multivariate modified Fourier expansions
Proceedings of the International Conference on Spectral and High Order Methods (Rønquist, E. et al, ed.), to appear.
[pdf]
D. Huybrechs
The computation of local solutions to high frequency scattering problems
Proceedings of the 9th International Conference on Mathematical and Numerical Aspects of Wave Propagation (Barucq, H. et al, ed.), pp. 216-217. INRIA, 2009.
D. Huybrechs
On the localization principle in high-frequency scattering problems
Proceedings of the 6th UK Conference on Boundary Integral Methods (Trevelyan, J., ed.), pp. 23-31, Durham University, 2007.
S. Langdon, D. Huybrechs and S. N. Chandler-Wilde
A fully discrete collocation method for high frequency scattering by convex polygons
Proceedings of the 8th International Conference on Mathematical and Numerical Aspects of Wave Propagation (Biggs, N. et al, ed.), pp. 84-86. University of Reading, 2007.
D. Huybrechs
Efficient computations in high frequency scattering problems
Proceedings of the 8th International Conference on Mathematical and Numerical Aspects of Wave Propagation (Biggs, N. et al, ed.), pp. 77-79. University of Reading, 2007.
[pdf]
J. Trevelyan, M. Honnor, and D. Huybrechs
Numerical steepest descent evaluation of 2D partition of unity boundary integrals for Helmholtz problems
Computational Electromagnetics and Acoustics (R. Hiptmair et al, ed.),
Oberwolfach Reports, vol. 4, issue 1, pp. 354-357, European Mathematical Society Publishing House, 2007.
D. Huybrechs and S. Vandewalle
An efficient solution method for oscillatory integral equations
Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2006, pp. 155-158, Wiley-VCH, 2006.
D. Huybrechs and S. Vandewalle
The efficient evaluation of highly oscillatory integrals in BEM by analytic continuation
Proceedings of the 5th UK Conference on Boundary Integral Methods (Chen, K., ed.), pp. 20-31, Liverpool University Press, 2005.
[pdf]
D. Huybrechs and S. Vandewalle
A wavelet-packet transformation for the fast solution of oscillatory integral equations
Proceedings of the 7th International Conference on Mathematical and Numerical Aspects of Wave Propagation, pp. 399-401, Brown University, 2005.
[pdf]

Other publications

PhD thesis

D. Huybrechs
Multiscale and hybrid methods for the solution of oscillatory integral equations
Ph.D. Thesis, Dept. of Computer Science, K.U. Leuven, 2006.
[abstract][pdf][ps]

Master thesis

D. Huybrechs
Wavelets en wavelet packets voor integraalvergelijkingen
M.Sc. Thesis, Dept. of Computer Science, K.U. Leuven, 2002.