About me

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.

Numerical Analysis and Applied Mathematics Section
Celestijnenlaan 200A - box 2402
B-3001 Heverlee (Leuven)

Room : 02.49


last update 05/2018


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 $$f(x)=10e^x-17-10\cos(x-2.3)$$



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 \([-1,1]\).



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.


Publications, talks and posters