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Huybrechs, D., Iserles, A., Nørsett, S. (2011). From high oscillation to rapid approximation V: The equilateral triangle. IMA Journal of Numerical Analysis, 31 (2), 442-468.
Huybrechs, D., Iserles, A., Nørsett, S. (2011). From high oscillation to rapid approximation IV: Accelerating convergence. IMA Journal of Numerical Analysis, 31 (2), 442-468.
Huybrechs, D., Olver, S. (2011). Superinterpolation in highly oscillatory quadrature. Foundations of Computational Mathematics.
Deano, A., Huybrechs, D., Kuijlaars, A. (2010). Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature. Journal of Approximation Theory, 162 (12), 2202-2224.
Asheim, A., Huybrechs, D. (2010). Asymptotic analysis of numerical steepest descent with path approximations. Foundations of Computational Mathematics, 10 (6), 647-671.
Asheim, A., Huybrechs, D. (2010). Local solutions to high frequency 2D scattering problems. Journal of Computational Physics, 229 (14), 5357-5372.
Honnor, M., Trevelyan, J., Huybrechs, D. (2010). Numerical evaluation of 2D partition of unity boundary integrals for Helmholtz problems. Journal of Computational and Applied Mathematics, 234 (6), 1656-1662.
Huybrechs, D. (2010). On the Fourier extension of non-periodic functions. SIAM Journal on Numerical Analysis, 47 (6), 4326-4355.
Huybrechs, D. (2009). Stable high-order quadrature rules with equidistant points. Journal of computational and applied mathematics, 231 (2), 933-947.
Cools, R., Huybrechs, D., Nuyens, D. (2009). Recent topics in numerical integration. International Journal of Quantum Chemistry, 109 (8), 1748-1755.
Deaño, A., Huybrechs, D. (2009). Complex Gaussian quadrature of oscillatory integrals. Numerische Mathematik, 112 (2), 197-219.
Huybrechs, D., Cools, R. (2009). On generalized Gaussian quadrature rules for singular and nearly singular integrals. SIAM Journal on Numerical Analysis, 47 (1), 719-739.
Huybrechs, D., Vandewalle, S. (2008). An efficient implementation of boundary element methods for computationally expensive Green's functions. Engineering Analysis with Boundary Elements, 32 (8), 621-632.
Huybrechs, D., Vandewalle, S. (2007). The construction of cubature rules for multivariate highly oscillatory integrals. Mathematics of Computation, 76 (260), 1955-1980.
Huybrechs, D., Vandewalle, S. (2007). A sparse discretization for integral equation formulations of high frequency scattering problems. SIAM Journal on Scientific Computing, 29 (6), 2305-2328.
Huybrechs, D., Vandewalle, S. (2006). A two-dimensional wavelet-packet transform for matrix compression of integral equations with highly oscillatory kernel. Journal of Computational and Applied Mathematics, 197 (1), 218-232.
Huybrechs, D., Vandewalle, S. (2006). On the evaluation of highly oscillatory integrals by analytic continuation. SIAM Journal on Numerical Analysis, 44 (3), 1026-1048.
Huybrechs, D., Vandewalle, S. (2005). Composite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions. Journal of Computational and Applied Mathematics, 180 (1), 119-135.
Huybrechs, D., Simoens, J., Vandewalle, S. (2004). A note on wavenumber dependence of wavelet matrix compression for integral equations with oscillatory kernel. Journal of computational and applied mathematics, 172 (2), 233-246.
Boettcher, A., Grudsky, S., Huybrechs, D., Iserles, A. (2012). First-order trace formulae for the iterates of the Fox–Li operator. In: Ball J., Dym H., Kaashoek M., Langer H., Tretter C. (Eds.), A panorama of modern operator theory and related topics. The Israel Gohberg Memorial Volume (pp. 207-224). New York: Springer.
Huybrechs, D., Olver, S. (2009). Rapid function approximation by modified Fourier series. In: Engquist B., Fokas T., Hairer E., Iserles A. (Eds.), Highly Oscillatory Problems, Chapt. 3 (pp. 51-71). Cambridge: Cambridge University Press.
Huybrechs, D., Olver, S. (2009). Highly oscillatory quadrature. In: Engquist B., Fokas T., Hairer E., Iserles A. (Eds.), Highly Oscillatory Problems, Chapt. 2 (pp. 25-50). Cambridge: Cambridge University Press.
Atak, O., Bergen, B., Huybrechs, D., Pluymers, B., Desmet, W. (2011). Application of a Hybrid Boundary Element Wave Based Method on a 2D Multiple Scatterer Problem. . International Congress on Sound & Vibration. Rio De Janeiro, Brazil, 10-14 July 2011.
Atak, O., Bergen, B., Huybrechs, D., Pluymers, B., Desmet, W. (2011). A hybrid Boundary Element - Wave Based Method in a Multi-Level concept for steady-state 2D acoustic analysis. . International Conference on Structural Dynamics. Leuven, Belgium, 4-6 July 2011.
Asheim, A., Huybrechs, D. (2011). High-frequency scattering with extraction of uniformly accurate phase. Proceedings of the 10th International Conference on the Mathematical and Numerical Aspects of Waves. International Conference on the Mathematical and Numerical Aspects of Waves. Vancouver, 25-29 July 2011 (pp. 615-618). Vancouver: Pacific Institute for the Mathematical Sciences.
Adcock, B., Huybrechs, D. (2011). Accuracy of the Fourier extension method for oscillatory phenomena. Proceedings of the 10th International Conference on the Mathematical and Numerical Aspects of Waves. International Conference on the Mathematical and Numerical Aspects of Waves. Vancouver, 25-29 July 2011 (pp. 289-292). Vancouver: Pacific Institute for the Mathematical Sciences.
Huybrechs, D. (2011). Superinterpolation in highly oscillatory quadrature. In Hairer, E. (Ed.), Hochbruck, M. (Ed.), Iserles, A. (Ed.), Lubich, C. (Ed.), Oberwolfach Reports: Vol. 8 (1). Geometric Numerical Integration. Oberwolfach, 20-26 March 2011 (pp. 826-829) European Mathematical Society.
Adcock, B., Huybrechs, D. (2011). Multivariate modified Fourier expansions. In Hesthaven, J. (Ed.), Ronquist, E. (Ed.), Proceedings of the International Conference on Spectral and High Order Methods 2009. International Conference on Spectral and High Order Methods. Trondheim, Norway, 22-26 June 2009 (pp. 85-92). New York: Springer.
Asheim, A., Huybrechs, D. (2009). The computation of local solutions to high frequency scattering problems. In Barucq, H. (Ed.), Proceedings of the 8th International Conference on Mathematical and Numerical Aspects of Waves. International Conference on the Mathematical and Numerical Aspects of Waves Propagation. Pau, France, 15-19 June 2009 (pp. 216-217).
Huybrechs, D. (2007). On the localization principle in high-frequency scattering problems. In Trevelyan, J. (Ed.), Proceedings of the 6th UK Conference on Boundary Integral Methods. 6th UK Conference on Boundary Integral Methods. Durham, UK, September 16-17, 2007 (pp. 23-31).
Huybrechs, D. (2007). Efficient computations in high frequency scattering problems. In Biggs, N. (Ed.), Proceedings of the 8th International Conference on Mathematical and Numerical Aspects of Waves. The 8th International Conference on Mathematical and Numerical Aspects of Waves. Reading, UK, July 23-27, 2007 (pp. 77-79).
Langdon, S., Huybrechs, D., Chandler-Wilde, S. (2007). A fully discrete collocation method for high frequency scattering by convex polygons. In Biggs, N. (Ed.), Proceedings of the 8th International Conference on Mathematical and Numerical Aspects of Waves. The 8th International Conference on Mathematical and Numerical Aspects of Waves. Reading, U.K., July 23-27, 2007 (pp. 84-86).
Trevelyan, J., Honnor, M., Huybrechs, D. (2007). Numerical steepest descent evaluation of 2D partition of unity boundary integrals for Helmholtz problems. In Hiptmair, R. (Ed.), Hoppe, R. (Ed.), Joly, P. (Ed.), Langer, U. (Ed.), Oberwolfach Reports: Vol. 4. Computational Electromagnetism and Acoustics. Oberwolfach, 4-10 February 2007 (pp. 354-357). Zürich: European Mathematical Society.
Huybrechs, D., Vandewalle, S. (2006). An efficient solution method for oscillatory integral equations. In Simos, T. (Ed.), Psihoyios, G. (Ed.), Tsitouras, C. (Ed.), ICNAAM 2006 proceedings. International conference on numerical analysis and applied mathematics 2006. Greece, September 15-19, 2006 (pp. 155-158).
Huybrechs, D., Vandewalle, S. (2005). The efficient evaluation of highly oscillatory integrals in BEM by analytic continuation. In Chen, K. (Ed.), Advances in Boundary Integral Methods. 5th UK Conference on Boundary Integral Methods. Liverpool, UK, September 12-13, 2005 (pp. 20-30).
Huybrechs, D., Vandewalle, S. (2005). A wavelet-packet transformation for the fast solution of oscillatory integral equations. In Abboud, T. (Ed.), Proceedings of the 7th International Conference on Mathematical and Numerical Aspects of Wave Propagation. 7th International Conference on Mathematical and Numerical Aspects of Wave Propagation. Providence, RI, USA, June 20-24, 2005 (pp. 399-401).
Huybrechs, D. (2009). On the Fourier extension of non-periodic functions. Leslie Fox Prize Meeting. Warwick, UK, 29 June 2009.
Huybrechs, D. (2009). Multivariate modified Fourier expansions. International Conference on Spectral and High Order Methods 2009. Trondheim, Norway, 22-26 June 2009.
Huybrechs, D. (2009). Local solutions to highly oscillatory integral equations. The Mathematics of Finite Elements and Applications. Brunel, UK, 9-12 June 2009.
Huybrechs, D. (2009). On the Fourier extension of non-periodic functions. 2009 International Conference on Scientific Computation and Differential Equations. Beijing, China, 25-29 May 2009.
Huybrechs, D. (2009). Singular and highly oscillatory integrals. 2009 International Conference on Scientific Computation and Differential Equations. Beijing, China, 25-29 May 2009.
Huybrechs, D. (2008). Numerical and asymptotic methods for multivariate oscillatory integrals. Foundations of Computational Mathematics. City University Hong Kong, 16-26 June 2008.
Huybrechs, D. (2008). Hybrid numerical-asymptotic schemes for high-frequency scattering problems. Advanced Computational Methods in Engineering (Acomen08). Liège, Belgium, 26-28 May 2008.
Huybrechs, D., Asheim, A. (2008). High frequency wave scattering, part I. Manifolds and Geometric Integration (MaGIC'08). Renon, Italy, 18-21 February 2008.
Asheim, A., Huybrechs, D. (2008). High frequency wave scattering problems, part II. Manifolds and Geometric Integration (MaGIC'08). Renon, Italy, 18-21 February 2008.
Huybrechs, D. (2007). On the efficient evaluation of multivariate highly oscillatory integrals. International Conference on Scientific Computation and Differential Equations. St. Malo, France, July 9-13, 2007.
Huybrechs, D. (2007). Computing highly oscillatory integrals in modified Fourier expansions. International Conference on Spectral and High Order Methods. Beijing, China, June 18-22, 2007.
Huybrechs, D. (2007). On the localization principle of high freqency scattering problems in integral equation discretizations. The Theory of Highly Oscillatory Problems. Cambridge, UK, March 26-30, 2007.
Huybrechs, D., Vandewalle, S. (2007). Numerical approaches to steepest descent based oscillatory quadrature. Isaac Newton Institute Workshop on Oscillatory Problems. Cambridge, UK, February 12-16, 2007.
Huybrechs, D., Vandewalle, S. (2007). A numerical approach to the method of steepest descent. Highly Oscillatory Problems: Computation, Theory and Application. Cambridge, UK, February 15, 2007.
Huybrechs, D. (2007). On a sparse discretisation for highly oscillatory integral equations. Integral Equation Methods for High-Frequency Scattering Problems, 23rd GAMM-Seminar Leipzig. Leipzig, Germany, January 25-27, 2007.
Huybrechs, D. (2006). The numerical steepest descent method for oscillatory integrals. Summer school on numerical methods for high frequency wave propagation. ETH Zuerich, August 28 - September 1, 2006.
Huybrechs, D., Vandewalle, S. (2005). Wavelet approaches for integral equations at moderate and high frequencies. 8th European Multigrid Conference. Scheveningen (The Hague), The Netherlands, September 27-30, 2005.
Huybrechs, D., Vandewalle, S. (2004). Wavenumber dependence of the wavelet method for high frequency integral equations. Third International Conference on Boundary Integral Methods: Theory and Applications. University of Reading, Reading, UK, September 14-18, 2004.
Huybrechs, D., Vandewalle, S. (2004). Composite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions. Eleventh International Congress on Computational and Applied Mathematics. Leuven, Belgium, July 26-30, 2004.
Huybrechs, D. (2009). On the Fourier extension of non-periodic functions. Applied and Computational Analysis Graduate Seminar. Cambridge, UK, 5 June 2009.
Huybrechs, D. (2009). Local solutions to highly oscillatory integral equations. Numerical Analysis Seminars. University of Reading, Department of Mathematics, 18 May 2009.
Huybrechs, D. (2008). Efficient computations in high-frequency scattering simulations. Seminar über Partielle Differentialgleichungen und Numerik. University of Zurich, Department of Mathematics, 15 May 2008.
Huybrechs, D. (2007). The numerical evaluation of highly oscillatory integrals. Numerical Analysis Seminars. Bogazici University, Istanbul, Turkey, 28 December 2007.
Huybrechs, D. (2007). On the benefits of Gaussian quadrature for oscillatory integrals. Computational Mathematics and Applications Seminars. University of Oxford, Computing Laboratory, 8 November 2007.
Huybrechs, D. (2005). The efficient evaluation of oscillatory integrals. Applied Mathematics and Numerical Analysis Seminars. University of Reading, Department of Mathematics, November 11, 2005.
Huybrechs, D. (2005). The efficient evaluation of oscillatory integrals by analytic continuation. Numerical Analysis Seminars. University of Cambridge, Department of Applied Mathematics and Theoretical Physics, November 3, 2005.
Huybrechs, D. (2003). Wavelets and Wavelet Packets for Integral Operators. FNRS Contact group. Esneux, Belgium, September 9-10, 2003.
Huybrechs, D., Vandewalle, S. (sup.) (2006). Multiscale and Hybrid Methods for the Solution of Oscillatory Integral Equations (Meerschalige en hybride oplossingsmethodes voor oscillatorische integraalvergelijkingen), 246 + xxxiv pp.
Wang, H., Huybrechs, D., Vandewalle, S. (2011). Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials. TW Reports, TW604, 21 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Wang, H., Zhang, L., Huybrechs, D. (2011). Asymptotic expansions and fast computation of oscillatory Hilbert transforms. TW Reports, TW605, 31 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Asheim, A., Huybrechs, D. (2011). Complex Gaussian quadrature for oscillatory integral transforms. TW Reports, TW594, 20 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Adcock, B., Huybrechs, D. (2011). On the resolution power of Fourier extensions for oscillatory functions. TW Reports, TW597, 30 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Olver, S. (2010). Superinterpolation in highly oscillatory quadrature. TW Reports, TW569, 23 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Deaño, A., Huybrechs, D., Kuijlaars, A. (2010). Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature. TW Reports, TW557, 32 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Boettcher, A., Grudsky, S., Huybrechs, D., Iserles, A. (2010). First-order trace formulas for the iterates of the Fox-Li operator. Cambridke, UK.
Huybrechs, D., Iserles, A., Nørsett, S. (2009). From high oscillation to rapid approximation V: The equilateral triangle. Cambridge NA Reports, nr. NA2009/04.
Asheim, A., Huybrechs, D. (2009). Asymptotic analysis of numerical steepest descent with path approximations. TW Reports, TW536, 21 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D. (2009). On the Fourier extension of non-periodic functions. TW Reports, TW534, 33 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D. (2008). Stable high-order quadrature rules with equidistant points. TW Reports, TW528, 18 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Asheim, A., Huybrechs, D. (2008). Local solutions to high frequency 2D scattering problems. TW Reports, TW524, 24 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Cools, R. (2008). On generalized Gaussian quadrature rules for singular and nearly singular integrals. TW Reports, TW523, 21 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Deaño, A. (2008). Complex Gaussian quadrature of oscillatory integrals. TW Reports, TW519, 22 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Vandewalle, S. (2007). An efficient implementation of boundary element methods for computationally expensive Green's functions. TW reports, TW510. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Iserles, A., Nørsett, S. (2007). From high oscillation to rapid approximation IV: Accelerating convergence. Cambridge NA Reports, nr. NA2007/07. Cambridge, UK: Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
Huybrechs, D., Vandewalle, S. (2006). A sparse discretisation for integral equation formulations of high frequency scattering problems. TW Reports, TW447. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Vandewalle, S. (2005). The construction of cubature rules for multivariate highly oscillatory integrals. TW Reports, TW442, 26 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Vandewalle, S. (2005). On the evaluation of highly oscillatory integrals by analytic continuation. TW Reports, TW431, 26 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Vandewalle, S. (2005). A two-dimensional wavelet packet transform for matrix compression of integral equations with highly oscillatory kernel. TW Reports, TW417, 17 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Vandewalle, S. (2004). Composite quadrature formulae for the approximation of wavelet coefficients of piecewise smooth and singular functions. TW Reports, TW388, 17 pp. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Huybrechs, D., Simoens, J., Vandewalle, S. (2003). A note on wavenumber dependence of wavelet matrix compression for integral equations with oscillatory kernel. TW Reports, TW356. Leuven, Belgium: Department of Computer Science, K.U.Leuven.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
