I am a researcher at the KU Leuven Computer Science department after obtaining a PhD at KU Leuven under supervision of Daan Huybrechs. My research is on algorithms for frame approximations and their applications.
My PhD research is on function approximation using frames with certain eigenvalue distributions. These arise when, for example, restricting a Fourier Basis on a rectangular domain to some smaller enclosed domain. This results in an accurate approximation of the function on the smaller domain, that is defined on the larger (and easier to work with) domain.
Function Values
We start from function values that are given on an equispaced grid defined on an arbitrary domain.
Example: data samples from the function $$f(x)=10e^x-17-10\cos(x-2.3)$$
Extension
Our algorithm finds a function approximation that is periodic on some bounding box.
Example: An extension of \(f(x)\) from \([-0.5,0.5]\) to \([-1,1]\).
Applications
The resulting extension is used to easily solve problems such as this Helmholtz differential equation.
Example: the 1D Helmholtz equation
$$\Delta p(x) + 40^2 p(x) = 1000f(x)$$
with homogeneous Neumann boundary conditions.
Helmholtz equation simulated in a star-shaped domain with a hole, for a point source moving from left to bottom. Our algorithms computes an approximate decomposition to the embedded Fourier problem matrix, that can be calculated and applied more efficiently than full singular value decompositions.
Wave equation simulated on a star-shaped domain, with Gaussian initial value. The efficiency of applying the decomposition comes to play when solving the boundary-value problem in each iteration.
My personal github page contains miscellaneous software projects, that may or may not be up to date.
Publications, talks and posters
PhD Defense
March 19, 2018, 17h00
Aula van de Tweede Hoofdwet, Thermotechnisch Instituut
thesisslides
SIAM Journal on Numerical Analysis paper
May, 2017
Function approximation on arbitrary domains using Fourier extension frames
Technical report
FoCM 2017
July 11, 2017
Poster at the 2017 Foundations of Computational Mathematics conference in Barcelona. pdf
AT15 Proceedings paper
December, 2016
Computing with functions on domains with arbitrary shapes Technical report
Approximation Theory 15
May 23, 2016
Presentation at the Approximation Theory 15 conference in San Antonio, Texas. slides
NATW Seminar series talk
April 14, 2016
Presentation in the NATW Seminar series at the KU Leuven Computer Science department. slides
SIAM Journal of Scientific Computing Paper
March 17, 2016
Fast algorithms for the computation of Fourier Extensions of arbitrary length SIAM J. Sci. Comput. Vol. 38, No.2, pp. A899-A922 linkpdf
New Directions in Numerical Computation
August 25, 2015
Contributed talk at the New Directions in Numerical Computations conference, held in celebration of Nick Trefethen's 60th birthday at the Mathematical Institute of Oxford University. slides
SIAM CSE 2015
March 16, 2015
Poster at the 2015 SIAM conference on Computational Science and Engineering in Salt Lake City. pdf
Research cluster at ICERM
November 6, 2014
Research talk as invited participant at the research cluster Computational Challenges in Sparse and Redundant Representations. Held at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University. slides
Woudschoten 2014
October 9, 2014
Poster at the 2014 Woudschoten conference of the Werkgemeenschap Scientific Computing held in Zeist, The Netherlands. pdf
ICOSAHOM 2014
June 23, 2014
Contributed talk at the 2014 International Conference on Spectral And High Order Methods. slides
MCQMC 2014
April 7, 2014
Contributed talk at the 2014 International Conference on Monte Carlo and Quasi Monte Carlo methods, on research done during my Master's thesis. slides