5 papers
Applications of QR-based Vector-Valued Rational Approximation
Simon Dirckx
Several applications of the QR-AAA algorithm, a greedy scheme for vector-valued rational approximation, are presented. The focus is on demonstrating the flexibility and practical e…
An overlapping domain decomposition method based on solution-transfer operators
Simon Dirckx, Anna Yesypenko, Per-Gunnar Martinsson
An overlapping domain decomposition method is described for variable-coefficient elliptic boundary value problems on domains that can be decomposed into slabs or shells. The method…
QR-based Parallel Set-Valued Approximation with Rational Functions
Simon Dirckx, Karl Meerbergen, Daan Huybrechs
In this article a fast and parallelizable algorithm for rational approximation is presented. The method, called (P)QR-AAA, is a (parallel) set-valued variant of the AAA algorithm f…
On the computation of the SVD of Fourier submatrices
Simon Dirckx, Daan Huybrechs, Robbe Ongenae
Contiguous submatrices of the Fourier matrix are known to be ill-conditioned. In a recent paper in SIAM Review A. Barnett has provided new bounds on the rate of ill-conditioning of…
Frequency extraction for BEM-matrices arising from the 3D scalar Helmholtz equation
Simon Dirckx, Daan Huybrechs, Karl Meerbergen
The discretisation of boundary integral equations for the scalar Helmholtz equation leads to large dense linear systems. Efficient boundary element methods (BEM), such as the fast…